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Heat Transfer and Entropy Generation Study of Non-Darcy Double-Diffusive Natural Convection in Inclined Porous Enclosures with Different Source Configurations
Abstract
In the present study, steady double-diffusive natural convection of two-phase flow through a square enclosure filled with a fluid-saturated porous medium, in presence of the internal thermal and solutal source is investigated numerically. Darcy-Brinkman-Forchheimer model is used to describe the fluid flow in porous media. This research aims to obtain a deep understanding about details of physical processes involved in such flows, using both the first and the second law analysis for different internal source(s) configurations. To this end, an in-house finite volume numerical solver is developed and validated against available data in literatures. Results are presented in terms of streamlines, isotherms and concentration contours for different values of Darcy, Rayleigh and Lewis numbers. First the effect of inclination angle of the cavity on heat and mass transfer characteristics of flows is investigated in presence of an internal source with the square and rectangular shape. Next, twelve different internal source configurations with distinctive shapes, locations and arrangements are studied and their effects on Nusselt and Sherwood numbers are investigated. Finally an entropy generation analysis is conducted to identify the best internal source configuration from the viewpoint of the second law of thermodynamics.
... Conservation equations are expressed as follows based on the presumptions mentioned above [44,45]: ...
... For the PL of the plate (P-I or PP-I) [44,45]: ...
... The followings can be used to express the governing equations in their non-dimensional form [44]: , respectively. For the conductive panels: ...
In this study, a single cooling channel system is suggested for conductive double panel systems. The cooling channel for the vertical component uses perforated porous insert (PP-I) and porous insert (P-I), while cylinders are used in the PP-I case. The permeability of the porous channel (Da between 1{0}^{-5} and 1{0}^{-1} ), size of the cylinders (Rc between 0 and 0.25), and location of the PP plate (Yp between 1 and 4.5) are all taken into account when calculating the effectiveness of the cooling system using finite element method. It is found that PP-I can effectively control the vortex size and enhance cooling performance, particularly for vertical plate. Nusselt number is enhanced in the absence of cylinders in the vertical channel by 92% as contrasted to 51% in the presence of cylinders. When cylinders are used for the vertical channel, the temperature drop of 1{3}^{^\circ }{\rm{C}} is computed. The flow field noticeably changes when the permeability of the P-I and PP-I is altered. The equivalent temperature increases for P-I and PP-I with setups at {\rm{Da}}=1{0}^{-5} and {\rm{Da}}=1{0}^{-2} are {\text{7.7}}^{^\circ }{\rm{C}} and {\text{4.4}}^{^\circ }{\rm{C}} , respectively. The performance of cooling for the vertical plate is influenced favorably by the higher values of the porous plate’s vertical placement. By moving the porous object, it is possible to reduce the temperature by {8}^{^\circ }{\rm{C}} . For panel surface temperature, a proper orthogonal decomposition (POD)-based reconstruction model with 12 POD modes is used. The POD-based model accurately captures the effects of utilizing P-I and PP-I on the panel temperature.
... Furthermore, the study unveiled that implementing a magnetic field enhanced HT and reduced E gen compared to scenarios where a magnetic field was not employed. Siavashi et al. [6] explored the realm of non-Darcy doublediffusive natural convection within inclined porous cavities, considering diverse source configurations. Their investigation unveiled that using inclined porous cavities with varying source arrangements enhanced HT and mitigated E gen , in contrast to the absence of a source. ...
... for HFBC (6) where, ∆T = T h − T c and T re f is a reference temperature can be considered the cylindrical surface temperature. Furthermore, β f , α f , and g represent the coefficient of volumetric expansion, thermal diffusivity, and gravitational acceleration, respectively. ...
... Furthermore, in the case of air subjected to a cylinder under the same isothermal boundary condition, the Nu avg value rises from 3.43 to 20.22, the E avg value increases from 3.73 to 1373.95, while the Be value drops from 0.94 to 0.015 with increasing Ra values from 10 3 to 10 6 . For water subjected to a cylinder under the same isothermal boundary condition, the Nu avg value rises from 3.44 to 21.39, the E avg value increases from 3.74 to 1570.48, while the Be value drops from 0.94 to 0.01 with increasing Ra values from 10 3 to 10 6 . ...
Understanding fluid dynamics and heat transfer is crucial for designing and improving various engineering systems. This study examines the heat transfer characteristics of a buoyancy-driven natural convection flow that is laminar and incompressible. The investigation also considers entropy generation (Egen) within an octagonal cavity subject to a cold cylinder inside the cavity. The dimensionless version of the governing equations and their corresponding boundary conditions have been solved numerically using the finite element method, employing triangular mesh elements for discretization. The findings indicated that incorporating a cold cylinder inside the octagonal cavity resulted in a higher heat transfer (HT) rate than in the absence of a cold cylinder. Furthermore, using the heat flux condition led to a higher average Nusselt number (Nuavg) and a lower Bejan number (Be) than the isothermal boundary condition. The results also showed that HT and Egen were more significant in the Al2O3-H2O nanofluid than the basic fluids such as air and water, and HT increased as χ increased. The current research demonstrates that employing the heat flux condition and incorporating nanoparticles can enhance the rate of HT and Egen. Furthermore, the thermo-fluid system should be operated at low Ra to achieve greater HT effectiveness for nanofluid concerns.
... It should be noted that systems with energy sources of different type have great importance in industry. Research in this area can be found in [13][14][15][16][17][18]. Many researchers are considering a source of constant temperature [13][14][15]17,18], while the most relevant are problems with the heat-generating elements [16]. ...
... Research in this area can be found in [13][14][15][16][17][18]. Many researchers are considering a source of constant temperature [13][14][15]17,18], while the most relevant are problems with the heat-generating elements [16]. Oueslati et al. [13] analyzed the double-diffusive convective energy transport in a vertical chamber having thermal and diffusive sources. ...
... Authors have ascertained that the low thermal transmission rate can be obtained when the heat source places at the mid of vertical border. Steady thermosolutal transport within a rectangular porous chamber having local heat and mass sources has been calculated by Siavashi et al. [15]. Results have revealed that the chambers with two local sources have better mass and energy transport parameters compared to the case of the single element. ...
Development of electronic devices demands to create an effective cooling system using optimal working liquid and porous insertions near the heat-generating elements. Such features allow intensifying the heat disposal from the heated element area. In this study, the unsteady convection of a variable viscosity liquid within a chamber having a heat-generating element under the impact of porous insertion is investigated. A porous layer surrounds the energy source located on the lower surface. The horizontal and vertical walls are thermally insulated, kept at constant cooling temperatures, respectively. Partial differential equations written in non-dimensional non-primitive variables with appropriate additional conditions are worked out by the finite difference method. The governing characteristics are the non-dimensional medium permeability, volumetric heat flux, variable viscosity and thickness of the porous insertion. The influence of these properties on local and mean fields’ characteristics for the energy transport and flow structures are studied in details. The calculations demonstrate that the inclusion of a porous insertion and the variation of its properties lead to more essential cooling of the heater.
... A 2D, laminar flow model is considered, while impacts of thermal radiation, free convection and viscous dissipation are not taken into account. Above the porous zone, conservation equations of mass, momentum and energy are stated as [59,60]: ...
... In the porous region where hot cylinders are embedded, the generalized Darcy-Brinkmann-Forchheimer extended model is used [59,60]: ...
A cooling system with impinging jets is used extensively in diverse engineering applications , such as solar panels, electronic equipments, battery thermal management, textiles and drying applications. Over the years many methods have been offered to increase the effectiveness of the cooling system design by different techniques. In one of the available methods, nano-jets are used to achieve a higher local and average heat transfer coefficient. In this study, convective cooling of double rotating cylinders embedded in a porous medium is analyzed by using hybrid nano-jets. A finite element formulation of the thermo-fluid system is considered, while impacts of Reynolds number, rotational speed of the double cylinders, permeability of the porous medium and distance between the cylinders on the cooling performance are numerically assessed. Hybrid and pure fluid performances in the jet cooling system are compared. It is observed that the cooling performance improves when the rotating speed of the cylinder, permeability of the medium and jet Reynolds number are increased. The heat transfer behavior when varying the distance between the cylinders is different for the first and second cylinder. Higher thermal performances are achieved when hybrid nanofluid with higher nanoparticle loading is used. An optimization algorithm is used for finding the optimum distance and rotational speeds of the cylinders for obtaining an improved cooling performance , while results show higher effectiveness as compared to a parametric study. The outcomes of the present work are useful for the thermal design and optimization of the cooling system design for configurations encountered in electronic cooling, energy extraction and waste heat recovery.
... A 2D, laminar flow model is considered, while impacts of thermal radiation, free convection and viscous dissipation are not taken into account. Above the porous zone, conservation equations of mass, momentum and energy are stated as [59,60]: ...
... In the porous region where hot cylinders are embedded, the generalized Darcy-Brinkmann-Forchheimer extended model is used [59,60]: ...
A cooling system with impinging jets is used extensively in diverse engineering applications, such as solar panels, electronic equipments, battery thermal management, textiles and drying applications. Over the years many methods have been offered to increase the effectiveness of the cooling system design by different techniques. In one of the available methods, nano-jets are used to achieve a higher local and average heat transfer coefficient. In this study, convective cooling of double rotating cylinders embedded in a porous medium is analyzed by using hybrid nano-jets. A finite element formulation of the thermo-fluid system is considered, while impacts of Reynolds number, rotational speed of the double cylinders, permeability of the porous medium and distance between the cylinders on the cooling performance are numerically assessed. Hybrid and pure fluid performances in the jet cooling system are compared. It is observed that the cooling performance improves when the rotating speed of the cylinder, permeability of the medium and jet Reynolds number are increased. The heat transfer behavior when varying the distance between the cylinders is different for the first and second cylinder. Higher thermal performances are achieved when hybrid nanofluid with higher nanoparticle loading is used. An optimization algorithm is used for finding the optimum distance and rotational speeds of the cylinders for obtaining an improved cooling performance, while results show higher effectiveness as compared to a parametric study. The outcomes of the present work are useful for the thermal design and optimization of the cooling system design for configurations encountered in electronic cooling, energy extraction and waste heat recovery.
... At the same time, the mentioned complex analysis for combined convective energy and mass transport within porous cabinets is very important in the case of entropy generation investigation. Nowadays, there are several published papers on convective energy and mass transference in a chambers combined with entropy generation analysis [40][41][42][43][44][45][46]. Mchirgui et al. [40,41] have numerically studied double-diffusive thermal convection in a tilted porous enclosure using Darcy-Brinkman formulation with local thermal equilibrium approach. ...
... Using the lattice Boltzmann technique, author has shown that the power-law index has a non-monotonic influence on the entropy generation intensity. Siavashi et al. [44] have performed the computational analysis of double-diffusive thermal convection and entropy production in a tilted porous chamber with internal isothermal heaters. Employing the finite volume method, authors have investigated the entropy generation strength behavior with several governing parameters. ...
Entropy generation minimization approach is a very good method allowing to analyze the engineering systems to exclude technical failure. The present study deals with computational analysis of triple diffusive flow, energy transference and entropy production in different porous cavities from square to triangular through trapezoidal shape. The formulated boundary-value problem has been worked out using the finite element technique and non-primitive variables. The developed computational code has
been verified using numerical results of other researchers. Analysis of entropy production due to energy and mass transport, motion friction, and porous material has been performed for different chamber’s shapes. Entropy generation analysis in chambers of various geometries under the triple-diffusive flow is a novelty of the present research, where different entropy production mechanisms have been scrutinized for one complex problem. It has been ascertained that average total entropy generation strength raises with buoyancy ratios, Lewis and Rayleigh numbers, but it has the minimum value for the square chamber in comparison with triangular and trapezoidal shapes. Moreover, obtained results characterize a neglecting influence of motion friction on the total entropy generation.
... In the case of diffusive flows, an entropy generation analysis can be found in (Parveen and Mahapatra, 2019;Oueslati and Ben-Beya, 2013;Kefayati, 2018;Chen, 2011;Arun and Satheesh, 2019;Hussain et al., 2018;Chen et al., 2015;Siavashi et al., 2017;Hussain, 2016;Ahmed et al., 2017). Parveen and Mahapatra (2019) numerically studied MHD double-diffusive free convection combined with entropy generation in a wavy chamber filled with alumina-water nanofluid. ...
... The authors showed that the total entropy production decreases with an increase in the concentration of nanoparticles. Some impressive results for the thermodynamics second-law analysis of double-diffusive convective transport in various chambers can be found in Siavashi et al. (2017), Hussain (2016). ...
The combined natural heat and mass transfer, the so-called thermosolutal convective problem, has become an attractive field of research in many diversified areas. In this paper, for the first time, entropy analysis has been carried out for triple diffusive flow. A comprehensive model is developed for the entropy generation due to fluid friction, porous medium, heat, and mass transfer across a finite temperature and concentration difference in the chemical potential of two salts. In this model, a new term showing the entropy generation due to the coupling of concentration gradients of both salts is included. Furthermore, we have introduced a new mass Bejan number for the salts concentrations. The selected salts include sodium chloride and sucrose, which are added in water with different concentrations. The concentrations of both salts are assumed to be higher at the surface. The previously established dimensionless governing equations with Boussinesq approximation and Darcy law were solved numerically. The resulting velocity, temperature, and concentration gradients are employed in the entropy generation model. The impacts of the pertinent parameters and related dimensionless numbers on the dimensionless entropy generation rate, irreversibility ratio and Bejan numbers are examined for both assisting and opposing flows. It has been found that entropy generation rates are
higher for assisting flows than opposing flows. At the same time, it is possible to reduce the entropy generation rate with a rise of the Darcy and Lewis numbers while the mass Bejan number increases with Lewis number.
... With the aid of porous media such as porous metal foams, the heat transfer performance can be improved especially for the cooling of internal heat source like electronic components [28]. However, most studies on the existence of both internal heat source and porous media in the square cavity focused on natural convection [29][30][31]. Lam et al. [29] performed a numerical study on natural convection and entropy generation in a porous enclosure with heat sources. Siavashi et al. [30] studied steady double-diffusive natural convection of two-phase flow through a porous square enclosure with the internal thermal and solutal source. ...
... Lam et al. [29] performed a numerical study on natural convection and entropy generation in a porous enclosure with heat sources. Siavashi et al. [30] studied steady double-diffusive natural convection of two-phase flow through a porous square enclosure with the internal thermal and solutal source. They found that different internal source configurations with distinctive shapes, locations and arrangements have great effects on Nusselt and Sherwood numbers. ...
... Siavashi et al. [5] quantitatively analyzed natural convection throughout a square container, incorporating a porous medium supplied with fluid. They determined that situation (a), which was more successful, represented the best design, as it generated the least amount of entropy. ...
In this study, minimizing entropy generation in a horizontal pipe is numerically investigated through two passive techniques: in the first mode, the helical wire inserts in the pipe were placed at three various ratios of pitch ratio. The second mode is adding cupric oxide nanoparticles at various volume concentrations. Experiments were conducted for Reynolds numbers ranging from 4,000 to 14,000 under a uniform heat flux scenario of 25,000 W/m². The study utilized the ANSYS 14.5 software, employing the K-omega standard model, which involves three primary governing equations: continuity, momentum, and energy. According to the data, it was determined that the helical wire placed inside the pipe with a small pitch ratio decreased the entropy generation number. Cupric oxide nanoparticles also have a substantial impact on the entropy generation number. The higher volume concentration models had lower entropy generation numbers and Bejan numbers than the other models. Comparative analyses further emphasize the substantial advantages of using cupric oxide nanofluids and helical-wire inserts, with efficiency gains ranging from 5.08 to 11.7%.
... It was observed that the stream function maximum absolute value increases as the porous material width decreases. Siavashi et al. 28 conducted a two-phase fluid for a closed square chamber with a fluid inside non-Darcy porous material under the heat source and a solvent influence. The problem was solved with the finite volume method by employing the Darcy-Brinkman-Forkheimer model. ...
This article investigates natural convection with double-diffusive properties numerically in a vertical bi-layered square enclosure. The cavity has two parts: one part is an isotropic and homogeneous porous along the wall, and an adjacent part is an aqueous fluid. Adiabatic, impermeable horizontal walls and constant and uniform temperatures and concentrations on other walls are maintained. To solve the governing equations, the finite element method (FEM) employed and predicted results shows the impact of typical elements of convection on double diffusion, namely the porosity thickness, cavity rotation angle, and thermal conductivity ratio. Different Darcy and Rayleigh numbers effects on heat transfer conditions were investigated, and the Nusselt number in the border of two layers was obtained. The expected results, presented as temperature field (isothermal lines) and velocity behavior in X and Y directions, show the different effects of the aforementioned parameters on double diffusion convective heat transfer. Also results show that with the increase in the thickness of the porous layer, the Nusselt number decreases, but at a thickness higher than 0.8, we will see an increase in the Nusselt number. Increasing the thermal conductivity ratio in values less than one leads to a decrease in the average Nusselt number, and by increasing that parameter from 1 to 10, the Nusselt values increase. A higher rotational angle of the cavity reduces the thermosolutal convective heat transfer, and increasing the Rayleigh and Darcy numbers, increases Nusselt. These results confirm that the findings obtained from the Finite Element Method (FEM), which is the main idea of this research, are in good agreement with previous studies that have been done with other numerical methods.
... Convective flows in porous media feature prominently in several technological areas, including high-performance insulation for buildings, combustion in porous substrates, chemical catalysis reactors, poro-elastic transport in cartilage, packed-bed energy storage system, geo-hydrology, hybrid fuel cells, percolating hydrocarbons, geothermal reservoirs, and transdermal drug delivery. [23][24][25] Javed et al. 26 numerically scrutinized the energy transmission and natural convective flow within copper-water nanofluid-filled porous trapezoidal cavities. They noticed that as the Darcy number is increased, the strength of streamlines circulations is intensified and the isotherms are significantly modified. ...
... Convective flows in porous media feature prominently in several technological areas, including high-performance insulation for buildings, combustion in porous substrates, chemical catalysis reactors, poro-elastic transport in cartilage, packed-bed energy storage system, geo-hydrology, hybrid fuel cells, percolating hydrocarbons, geothermal reservoirs, and transdermal drug delivery. [23][24][25] Javed et al. 26 numerically scrutinized the energy transmission and natural convective flow within copper-water nanofluid-filled porous trapezoidal cavities. They noticed that as the Darcy number is increased, the strength of streamlines circulations is intensified and the isotherms are significantly modified. ...
Inspired by the applications in electromagnetic nanomaterials processing in enclosures and hybrid fuel cell technologies, a mathematical model is presented to analyze the mixed convective flow of electrically conducting nanofluids ([Formula: see text]-[Formula: see text] and [Formula: see text]-[Formula: see text]) inside a square enclosure saturated with porous medium under an inclined magnetic field. The Tiwari–Das model, along with the viscosity, thermal conductivity, and effective Prandtl number correlations, is considered in this study. The impacts of Joule heating, viscous dissipation, and internal heat absorption/generation are taken into consideration. Strongly nonlinear conservation equations, which govern the heat transfer and momentum inside the cavity with associated initial and boundary conditions, are rendered dimensionless with appropriate transformations. The marker-and-cell technique is deployed to solve the non-dimensional initial-boundary value problem. Validations with a previous study are included. A detailed parametric study is carried out to evaluate the influences of the emerging parameters on the transport phenomena. When [Formula: see text]-[Formula: see text] nanoparticles are suspended into [Formula: see text] base-fluid, the average heat transfer rate of [Formula: see text]-[Formula: see text] nanoliquid is increased by [Formula: see text] compared with the case where nanoparticles are absent. When [Formula: see text]-[Formula: see text] nanoparticles are suspended into [Formula: see text] base-fluid, the average heat transfer rate of [Formula: see text]-[Formula: see text] nanofluid is increased by [Formula: see text] compared with the case where nanoparticles are absent. Furthermore, when the heat source is present, the average heat transfer rate of [Formula: see text]-[Formula: see text] nanofluid is [Formula: see text] higher than that in the case of [Formula: see text]-[Formula: see text] nanofluid.
... The authors concluded the additional surface area provided by the baffles, as well as the vortex shedding caused by the addition of the baffles located at the upper wall of the channel, certainly increased the heat transfer rate. Siavashi et al. [13] implemented a numerical code using a double-diffusive technique and researched about the thermal energy exchange and the doublediffusive flow in enclosures using porous surfaces. Abu-Nada et al. [14] evaluated the impact of curly surfaces on the heat transfer rate as well as its performance when using an enclosure filled with fluids containing nanoparticles. ...
In this study, the effect of gradient and multi-layered porous media is assessed for the optimized properties and arrangement in the tested novel baffle design arrangement, which results in further enhancement in its thermo-hydraulic performance. The computational study is carried out using ANSYS FLUENT; wherein the permeability and porosity for each layer is varied. It's executed in two steps: case 1-porous layers with variations implemented (constant, linear/stepwise, increasing/decreasing) and case 2-porosity varied over the length. The findings show that the linear/stepwise increments in both cases give almost similar performance evaluation criteria (PEC) values. The increase in heat transfer rate and pressure drop can be compared using PEC, for better evaluation of the performance of different arrangements. With the simulation data genetic algorithm optimization model is used to find the optimal arrangement of the porous layers for both cases to maximize PEC further. The optimal arrangement for case 1 and case 2 taken individually, gives PEC of 2.425 and 2.401 respectively. And their simultaneous optimization gives highest PEC of 2.508. Additionally, to improve the heat transfer rate further, Al 2 O 3 (5 w/v %) nanoparticles in water is tested with optimized conditions, which improves the PEC by almost double magnitude.
... Gravity is the principal factor causing natural convection, and it could be more affected in tilted cavities or channels. Therefore, the effect of inclination angle in convective heat transfer cavities was the center of interest by many researchers [25][26][27]. Souayeh et al. [28] investigated numerically the 3D convective heat transfer of a cubical enclosure induced by a centrally located isothermal cylinder at different inclination angles varying from 0 • to 90 • by using two ranges of Rayleigh numbers to avoid the unsteadiness. ...
A numerical study is conducted to evaluate the steady natural convective heat transfer problem and entropy generation of both single wall (SWCNT) and multi wall (MWCNT) nanoparticles with water as a base liquid over two spaced spheres. The isothermally heated spheres are located between two plates of short length. The cooled plates are maintained at different inclination angles. A numerical approach based on the finite volume method and multigrid acceleration was used to solve the governing equations. The effects of nanoparticle type, volume fraction, the inclination angle of the plates and the Rayleigh numbers are well-considered. Results reveal that there is a remarkable enhancement of the average Nusselt number over the plates for MWCNT nanoparticles with 63.15% from the inclination angle 0° to 30°. Furthermore, optimal heat transfer rates over the plates for MWCNT nanoparticles equates to 1.9, which is obtained for the inclination 30° and a Rayleigh number of 106. However, for SWCNT nanoparticles, the same equates 0.9, which is obtained for the inclination 90° and a Rayleigh number of 106. The comprehensive analysis is presented under some well-defined assumptions which show the reliability of the present investigation.
... Considering the previously-mentioned assumptions, the governing equations are [27][28][29][30][31]:. ...
... However, attention has been confined to rigid boundaries. Future studies may examine wavy sinusoidal boundaries 50 and efforts in this regard will be communicated imminently. ...
A theoretical and computational study of MHD natural convection in an isotropic non-Darcian porous medium saturated with electrically conducting helium gas in an enclosure in the presence of heat generation is presented. A Brinkman extended Darcy-Forchheimer model is employed and the working fluid is assumed to be incompressible. The model is non-dimensionalised and converted into pressure-velocity form. The Harlow-Welch marker and cell (MAC) finite difference technique is employed to solve the nonlinear boundary value problem via pressure-vorticity coupling. A parametric investigation of the influence of Grashof number ( Gr), Hartmann magnetic number ( Ha), Darcy number ( Da), and the internal heat generation parameter ( Γ) on streamline and isotherm distributions with Prandtl number ( Pr) is 0.71 (Helium) is conducted. The variation in local Nusselt number along the left and right walls of the computational 2 D enclosure is also studied. Validation house-computational numerical MATLAB code is tests are included. Local Nusselt number is elevated at both left and right walls with greater Darcy number (higher medium permeability) and Grashof number. However, with greater internal heat generation, local Nusselt number magnitudes are enhanced at the left (cold) wall only but suppressed at the right (hot) wall. Increasing magnetic field reduces local Nusselt number at both left and right walls. With increasing magnetic field, the single vortex is strongly distorted and skewed towards the top left and lower right corners of the enclosure. Temperature contours at the left and right wall are however less intense with greater magnetic field effect. The simulations are of relevance to hybrid electromagnetic gaseous fuel cells, magnetic field control of filtration processes and porous media materials processing systems.
... The entropy generation (S gen ) is then investigated for double diffusive NC by some researchers. Siavashi et al. [37] studied S gen of a non-Darcy double diffusive NC of a two-phase flow in a square container. Darcy-Brinkman-Forchheimer model is used for fluid flow in porous media. ...
Double diffusive natural convection (DDNC) is caused by temperature and concentration gradients in buoyancy-driven flows which is applicable in printing, HVAC, and solar collectors. A numerical study is accomplished to investigate DDNC of a hybrid Cu–Al2O3-water nanoliquid inside an H-shaped cavity with a baffle at the top wall. The Finite Element technique and Boussinesq approximation with no slip wall condition are applied to solve the governing equations. The left and right walls are at the cold temperature, while the inner up and down ribs and baffle are at constant heat flux, and other walls are insulated. The effect of Rayleigh number (10⁴-10⁶), Lewis number (2–8), and Buoyancy ratio (1–3) on Nusselt, Sherwood numbers, and entropy generation is investigated. Besides, the effects of baffle inclination angle (−60°to 60°) and also the aspect ratio of the corrugated bottom rib (0.375, 0.75, 1.5) on the mean Sherwood and Nusselt numbers are investigated to find the optimum geometry with the highest heat transfer performance. The results depict that the geometry with baffle angle −60°and with no corrugation has the best Nuavg; however, the geometry with baffle angle +60° and with no corrugation has the best Shavg.
... Kefayati [26][27][28] reported numerical studies of thermosolutal convection and entropy generation inside cavities filled with non-Newtonian fluids, which indicated the impact of magnetic field, power-law index, Carreau and Eckert numbers on thermal and solutal transfer processes and entropy generation. Siavashi et al. [29] conducted impact of various heat source configuration, which obtained the optimal configuration according to second law of thermodynamics. Gibanov et al. [30] considered the entropy generation inside an enclosure attached with porous layer saturated with ferrofluid, which found that an inclusion of ferric nanoparticles would lead to decrease the entropy generation. ...
An analysis of thermosolutal convection and entropy generation considering Soret and Dufour effects inside an inclined rectangular enclosure attached with porous wall has been investigated. The physical parameters are in the ranges such as buoyancy ratio (-10 ≤ N ≤ 10), permeability (10⁻⁹ ≤ Da ≤ 10⁻¹) and thickness (0 ≤ d ≤ 1.0) of porous wall, enclosure inclination angle (0° ≤ Φ ≤ 90°), Soret number (0 ≤ Sr ≤ 1.5) and Dufour number (0 ≤ Du ≤ 1.5). Heatlines and masslines taking Soret and Dufour effects into account are obtained as effective tools that visualizes the heat and species transported paths. Results demonstrate that Soret number has mild impact on heat transfer rate and promotes moisture transportation, while increasing Dufour number could boot heat transfer rate and reduce moisture transfer rate. Furthermore, increasing Soret numbers enhances entropy generation induced by heat transfer and fluid friction, while entropy generation induced by fluid friction, heat and moisture transfer is dropped with stronger Dufour effect. Present work can benefit the heat and moisture transfer performance and entropy generation minimization of thermal storage wall system.
... T 2 and T 1 are the lower and upper temperature boundaries, respectively (Börsing et al. 2017;Siavashi et al. 2017), similar to Eq. (3). These temperatures need to be defined for assessing an average initial temperature T 0 . ...
Abstract Hydrothermal convection in porous geothermal reservoir systems can be seen as a double-edged sword. On the one hand, regions of upflow in convective systems can increase the geothermal energy potential of the reservoir; on the other hand, convection introduces uncertainty, because it can be difficult to locate these regions of upflow. Several predictive criteria, such as the Rayleigh number, exist to estimate whether convection might occur under certain conditions. As such, it is of interest which factors influence locations of upwelling regions and how these factors can be determined. We use the thermodynamic measure entropy production to describe the influence of spatially heterogeneous permeability on a hydrothermal convection pattern in a 2D model of a hot sedimentary aquifer system in the Perth Basin, Western Australia. To this end, we set up a Monte Carlo study with multiple ensembles. Each ensemble contains several hundred realizations of spatially heterogeneous permeability. The ensembles only differ in the horizontal spatial continuity (i.e., correlation length) of permeability. The entropy production of the simulated ensembles shows that the convection patterns in our models drastically change with the introduction and increase of a finite, lateral correlation length in permeability. An initial decrease of the average entropy production number with increasing lateral correlation length shows that fewer ensemble members show convection. When neglecting the purely conductive ensembles in our analysis, no significant change in the number of convection cells is seen for lateral correlation lengths larger than 2000 m. The result suggests that the strength of convective heat transfer is not sensitive to changes in lateral correlation length beyond a specific factor. It does, however, change strongly compared to simulations with a homogeneous permeability field. As such, while the uncertainty in spatial continuity of permeability may not strongly influence the convective heat transfer, our findings show that it is important to consider spatial heterogeneity and continuity of permeability when simulating convective heat transfer in an aquifer.
... In several useful applications, natural convection is not induced by a hot boundary condition. Instead, it can be generated by an internal discrete heat source (Fontana et al. 2011;Fontana et al. 2013;Fontana et al. 2015;Baudoin et al. 2017;Siavashi et al. 2017;Duluc & Fraigneau 2017). Depending on the geometrical configuration and distribution of the heat sources, the flow pattern can be very complex, as reported in Fontana et al. (2015), where the natural convection of air in a partially open cavity with internal heat source was investigated. ...
A transient numerical analysis of natural convection of near-freezing water in a cavity with lateral openings and internal heat sources is carried out to investigate the influence of the heat dissipation rate in the flow configuration. The heat sources were positioned to create buoyancy-opposing and buoyancy-assisted conditions simultaneously and the top and bottom walls are kept at 0•C. The non-linear dependence of the physical properties with temperature is considered in the governing equations. Based on the heat dissipation rate, six different regimes were observed and classified through a qualitative analysis of the temporal evolution of the velocity and temperature fields. The characteristics of heat transfer for each regime are analyzed to define the most important mechanisms of heat removal. In the upper layer (heated from below), the buoyancy forces eventually overcome the viscous forces and unsteady thermal plumes are formed, increasing the heat removal through the openings, while the heat transfer with the top wall is not significant. In the lower layer, the development of wave-like instabilities leads to oscillatory regimes for intermediate heat dissipation rates, while for high dissipation rates a steady convective regime is observed. This behavior increases the heat transfer with the bottom wall, making it much more significant when compared with the upper layer.
... Thermosolutal buoyancy, generated by coexisted temperature gradient and concentration gradient, is an important driving force for fluid flow and heat transfer in nature and engineering. One of the most familiar and extensively investigated scenarios is a porous cavity with horizontal/vertical temperature and concentration gradients [1,2], encountered widely in the fields of thermal engineering, chemical engineering, environmental processes, geophysics and geology. In this scenario, fluid flow and heat transfer driven by thermosolutal buoyancy are acknowledged as thermosolutal convection or double-diffusive convection. ...
Natural ventilation for underground coal fires (UCF) is characterized by thermosolutal buoyancy driven air flow through thermally decomposed porous coalbed in an analogous U-shaped channel. Conventional models in terms of natural ventilation fail to include effects of solutal buoyancy and decomposed porous media. This paper aims to improve models for better prediction of thermosolutal buoyancy driven air flow, and further to facilitate the understanding of persistent burning of UCF. An experimental research framework was proposed to quantify buoyancy-driven natural ventilation for UCF. High-volatile bituminous coal was sampled for UCF experiments. Three fire depths of −1.6, −2.6, and −3.6 m were considered. Four models were developed and testified by experimental data. Results showed that proposed two models had good performances in prediction of natural ventilation for UCF. Validated models indicated that air velocity induced by solutal buoyancy is linearly proportional to molar mass difference between air and smoke, and effect of decomposed porous media can be characterized by temperature-dependent discharge coefficients and power exponent of natural ventilation model.
... Loganathan and Arasu [22] analyzed the influence of thermophoresis on MHD mixed convective heat and mass transfer of viscous fluid past a wedge embedded in non-Darcy porous media. Majid et al. [23] studied the heat transfer and entropy generation of non-Darcy double-diffusive natural convection of two-phase flow in a porous cavity. Further details are available in refs. ...
Non-Newtonian viscoelastic fluid flow past an isothermal sphere embedded in non-Darcy porous medium is examined numerically in this work. To be specific, the non-Newtonian Powell–Eyring fluid in the presence of both the heat and mass characteristics is mathematically modelled in terms of differential system. A non-Darcy drag force model is employed to simulate the effects of linear porous media drag and second-order Forchheimer drag. The surface of the sphere is maintained at a constant temperature and concentration. The numerical solution of the resultant system is reported via the Keller box method. Both tabular and graphical forms are adopted to identify the variations in Powell–Eyring fluid velocity, Powell–Eyring fluid temperature, and Powell–Eyring fluid concentration. In addition, the surface physical quantities, namely, skin friction and heat and mass transfer rates, are explored. The obtained observations are validated with earlier Newtonian studies. We found an excellent match in this regard. It is found that the velocity is reduced with increasing fluid parameter (ε), Forchheimer parameter (Λ), and tangential coordinate (ξ). In contrast, the temperature and concentration are increasing with increasing value of ε. A very slight increase in velocity is seen with an increase in the local non-Newtonian parameter, δ. But the temperature and concentration decrease slightly with an increase in δ. An increase in Darcy parameter enhances velocity but reduces both temperature and concentration. The present study finds an extensive array of applications in modern nuclear engineering, mineral and chemical process engineering, nuclear waste in geomaterial repositories, petroleum product filtration, and insulation systems.
... Out of all heat transfer enhancement methods that can be applied for fluids, the combination of strategies to improve the convective heat transfer and those to increase the conduction heat transfer, have been the objective of many researchers. Convective Greek letters thermal diffusivity (m 2 s − 1 ) thermal expansion coefficient (K − 1 ) angular velocity nanoparticle volume fraction dynamic viscosity (kg m − 1 s − 1 ) density (kg m − 3 ) shear stress (Pa) stream function thermal conductivity (W m − 1 K − 1 ) dimensionless temperature two-phase methods namely Eulerian-Lagrangian model [17] , volume of fluid (VOF) [18] , Eulerian mixture or two-phase mixture model [19] , Eulerian-Eulerian model [20] and double-diffusive model [21] . In comparison with the single-phase model, two-phase models provide the opportunity to model nanofluids more accurately, but they require comparatively more computational costs. ...
In this study, mixed convection inside a square cavity filled with Cu-water nanofluid is simulated using the Eulerian two-phase mixture model. The base fluid is considered to be non-Newtonian and obeys from the power law. Two rotating cylinders are placed inside the heat exchanger and heat is transferred through the nanofluid from the hot cylinder to the cold one. In addition to the natural convection heat transfer inside the heat exchanger, rotation of the internal cylinders can provide forced convection heat transfer. The direction of rotation of cylinders can strengthen or weaken the natural convection effects in different regions, hence, four cases with various rotation directions for the cylinders are considered. The effects of changes in the value of imposed angular velocity (in terms of Richardson number), non-Newtonian power-law index, Rayleigh number and nanofluid volume fraction on both the heat transfer and entropy generation are discussed. The results have been illustrated that the shear-thinning or shear-thickening behavior of the non-Newtonian nanofluid can noticeably change the effect of forced convection on the heat transfer efficiency. Besides, regarding the values of Rayleigh number, Richardson number and non-Newtonian power-law index, the addition of nanoparticles into the non-Newtonian base fluid might adversely affect the heat transfer efficiency. In addition, to investigate irreversibilities, total entropy generation is discussed. It is indicated that shear-thinning nanofluids result in higher values of total entropy generation.
... While the natural convection around a tilted heated square cylinder in an enclosure in the range of (10 3 Ra 10 6 ) was studied by De and Dalal [3], Chamkha et al. [4] performed the study of two-dimensional (2D) mixed convection from a heated square solid cylinder located at the center of a vented cavity filled with air (Pr ¼ 0.71). It is also possible to note that the results did not change much when using the rectangular cylinder compared with the square cylinder, and this is what was observed in the researchers [5,6]. As for the researchers who studied a triangular cylinder, El Abdallaoui et al. [7] studied numerically of natural convection around a decentered triangular cylinder placed in a square cylinder using the Lattice-Boltzmann method. ...
Numerical simulations are carried out for fluid flow and natural convection heat transfer induced by a temperature difference between a hot inner cylinder with different geome-tries (i.e., circular; triangular; elliptic; rectangular; and rhombic) and a cold outer square enclosure filled with nanofluid superposed porous-nanofluid layers. The Darcy-Brinkman model is applied for the saturated porous layer with nanofluid. Moreover , the transport equations (mass, momentum, and energy) are solved numerically using the Galerkin weighted residual method by dividing the domain into two sets of equations for every layer with incorporating a nonuniform mesh size. The considered domains in this investigation are closely examined over a wide range of Rayleigh number (10 3 Ra 10 6), Darcy number (10 À5 Da 10 À1), the thickness of porous layer (0% X p 100%), thermal conductivity ratio (1 R k 20), and nanoparticle volume fraction (0 u 0.1), respectively. The nanofluid is considered to be composed of Ag-nanoparticle and water as a base fluid. The results showed that the obtained total surfaces-averaged Nusselt numbers of the enclosure, in all cases, at the same operating conditions, the rate of heat transfer from the outer enclosure which the triangular cylinder is located inside is better. Also, as the thickness of the porous layer is increased from 20% to 80%, the free convection performance will decrease significantly (to about 50%) due to the hydrodynamic properties of the porous material.
... Particularly, metal foams [41]-which have strong structure with high porosity and permeability, low density and large surface area in a limited volume-have attracted much attention [42,43]. Metal foams are commonly utilized to design more efficient systems such as thermoelectric generators [44], photovoltaic modules [45], lithium-ion batteries [46], PCM-based energy storage systems and heat sinks [47], double-diffusive flow [48], fuel cells [49,50], as well as heat exchangers [51,52]. ...
Simultaneous application of nanofluid and porous media in a counter-flow double-pipe heat exchanger is studied in order to enhance its heat transfer with minimum power increase. Both channels of the heat exchanger are partially/completely filled with porous media, and different configurations of porous layers with various Darcy values are analyzed in different Reynolds numbers. Nanofluid flow is simulated using two-phase mixture model and flow through porous media obeys from Darcy–Brinkman–Forchheimer rule. Results are presented in terms of the performance evaluation criterion. First, the inner and outer pipes were filled with porous media having the same Darcy number. Depending on Darcy value, two optimal regions exist: 1—partial filling of only the inner pipe and 2—complete filling of the both pipes. Next, different combinations of Darcy number of the inner and outer pipes have been investigated for various filling portions and Reynolds numbers. Depending on Re and Da numbers, three different optimum situations exist: 1—partial filling of the inner pipe; 2—partial filling of the outer pipe; and 3—complete filling of the both pipes. For instance at Rei = 500 and Dao = 10⁻⁴, when a very low (Dai = 10⁻⁴), moderate (Dai = 10⁻²) or high (Dai = 10⁻¹) permeable porous medium is used in the inner pipe, the optimal situations are, respectively, the first, third and second situations. Based on the working conditions of the heat exchanger, proper porous layer thickness and Darcy configuration have to be selected to meet the maximum performance.
... There has been a lot of works done in the field of heat transfer in the porous media. Extensive applications of porous media have attracted the attention of many researchers in fields such as geology, water engineering, oil and gas reservoirs (Whitaker 1986;Siavashi et al. 2014), double-diffusive mass transfer (Siavashi et al. 2017b;Mchirgui et al. 2012), cooling of electronic components and heat exchangers (Siavashi et al. 2018d;Kefayati 2016;Kasaeian et al. 2017;Varol et al. 2008;Jamarani et al. 2017). analyzed magneto-hydrodynamic CuO-water nanofluid inside a porous enclosure with consideration of the shape factor. ...
Mixed convection of Cu-water nanofluid inside a two-sided lid-driven enclosure with an internal heater, filled with multi-layered porous foams is studied numerically and its heat transfer and entropy generation number are evaluated. Use of multi-layered porous media instead of homogeneous ones is capable of heat transfer enhancement, by weakening flow where does not impose a pivotal role on heat transfer and amplifying the flow in regions where have more effects on the heat transfer. Eight different arrangements of porous layers are considered and the two-phase mixture model is implemented to simulate nanofluid mixed convection inside the cavity. Results are presented in terms of stream functions, isotherms, Nusselt and entropy generation number for the eight cases considering various Richardson numbers (Ri = 10⁻⁴ to 10³) and nanofluid concentrations (φ = 0 to 0.04). Results indicate that using the multi-layered porous material can confine flow vortices in the vicinity of the moving walls and could enhance the heat transfer up to 17 percent (with respect to the case using homogeneous porous material with the highest permeability), such that this enhancement is more in lower Ri values (stronger convective effects). Entropy generation number also increases by nanofluid volume fraction increment and Ri decrement. Cases with a higher heat transfer rate also have the higher entropy generation number. In addition, an increase of volume fraction decreases the relative entropy generation number (S*) for low Ri number, while contrary fact observed for high Ri values.
... This model is suitable for the reservoirs that have not been fractured. With regard to the fluid-flow simulation in porous media, most researchers [24][25][26] adopted the Darcy-Brinkman-Forchheimer model, in which the viscous loss and the inertial loss are added in the momentum equation as source terms [27]. ...
... They found that vortex shedding produced by the baffle on the upper wall can additionally improve heat transfer together with baffle surfaces. Siavashi et al. [16] developed a double-diffusive numerical code and investigated double-diffusive flow and heat transfer in inclined enclosures with different source configurations in presence of porous media. Abu-Nada et al. [17] studied effects of surface waviness on fluid flow and heat transfer performance of closed cavity filled with nanofluid. ...
Nanofluids and porous inserts are two traditional methods of enhancing heat transfer. Porous media improve heat transfer along with increasing the pressure drop. This study aims to use gradient and multi-layered porous media (GPM and MLPM) with optimized properties and arrangement to maximize the heat transfer and minimize the pressure drop. Fluid flow in a pipe filled with GPM or MLPM is numerically simulated using ANSYS-FLUENT; where the properties of each layer consisting the porosity and the particle size (or permeability) of the porous medium can be adopted independently. First, simple arrangements of porous layers including constant, linear or stepwise increasing or decreasing of particle size (Case I) or porosity (Case II) of layers with respect to the radius are investigated. Results show that the stepwise and linear profiles both in Case I and Case II have nearly the same performance evaluation criteria (PEC) values. Particle swarm optimization (PSO) algorithm is used to find the optimal arrangements of porous layers in the both cases to maximize PEC value. Results show that the optimal arrangement of Case I and Case II gives PEC of 0.845 and 0.789, respectively. In addition, simultaneous optimization of Case I and Case II gives a higher PEC (0.856). Finally, using alumina/water nanofluid (5%) in the simultaneous optimized conditions improves PEC about 3 times.
... It was observed that increasing Reynolds number and nanoparticle concentration results in a decrease in heat transfer entropy generation while it increases the friction entropy generation. Steady double-diffusive natural convection of two-phase flow through a square enclosure filled with a fluid-saturated porous medium, in presence of the internal thermal and solutal source was carried out numerically by Siavashi et al. [21]. They investigated the effect of the enclosure inclination angle on heat and mass transfer rates and the flow strength. ...
A numerical study has been carried out to investigate the natural convection and entropy generation for different nanofluids within an inclined half-annulus heated from above. The conservation equations in cylindrical coordinates are solved using an in-house FORTRAN code based on the finite volume method coupled with multigrid acceleration. Water-based nanofluid containing various types of nanoparticles (Au, Ag, Cu and CuO) are used to examine the fluid flow and potential heat transfer enhancement in the annulus. The effective thermal conductivity and viscosity of nanofluids are calculated using the Maxwell-Garnetts (MG) and Brinkman models, respectively. The results demonstrate clearly that the average entropy generation due to heat transfer ( ) is strengthened by increasing U and Ra. Furthermore, for small inclination angles c = 0° and 45° ( ) and ( ) values are reduced as RR is augmented, whereas, their values were observed to strengthen when RR increases for large tilt angles c = 90°, 135° and 180°. So, several important issues are highlighted that deserve greater attention.
The analysis of heat transmission and fluid flow characteristics within the cavity is useful to improve the features of several applications including energy storage devices and hybrid fuel cells. With this motivation, the present model investigates the characteristics of magneto-convective heat transmission and fluid flow within a square porous enclosure with hot and cold slits. The heat transfer features of electrically conducting hybrid nanofluids [Formula: see text] water and [Formula: see text] kerosene are analyzed inside the enclosure. The non-Fourier thermal flux model is deployed, and the internal heat absorption/generation effect is considered. The marker-and-cell numerical scheme is adopted to solve the transformed dimensionless mathematical model with associated initial–boundary conditions. An exhaustive parametric investigation is implemented to estimate the influence of key parameters on transport phenomena. The computations show that augmenting the Hartmann number values modifies the fluid flow and temperature features substantially for both hybrid nanofluids. Enhancing the values of nanoparticles volume fraction promotes the heat transfer. When 5% [Formula: see text] nanoparticles are suspended into water and kerosene base fluids, [Formula: see text] kerosene hybrid nanofluid achieves 6.85% higher mean heat transfer rate compared to [Formula: see text] water hybrid nanoliquid. In the existence of heat absorption, the mean rate of heat transfer of [Formula: see text] water hybrid nanofluid is 78.92% lower than [Formula: see text] kerosene hybrid nanoliquid. Greater energy transmission is noticed in the case of [Formula: see text] kerosene hybrid nanofluid, and the enhanced fluid flow is noticed in the case of [Formula: see text] water hybrid nanofluid. Fourier's model [Formula: see text] estimates higher heat transfer rate than that of the Cattaneo–Christov (non-Fourier) heat flux model [Formula: see text].
This study investigates the double-diffusive natural convection of the non-Newtonian Casson fluid in a square cavity based on the original viscoplastic stress model without simplification. Therefore, yield stress plays an essential role in understanding fluid behavior. The finite element approach provided a numerical solution to continuity, momentum, energy, and species governing equations. The governing parameters for this problem are Rayleigh number, Ra, yield number, Y, buoyancy ratio number, Nr, and Lewis number, Le. The influence of these parameters on heat and mass transfer, the morphology of yielded/unyielded regions, and fluid flow are thoroughly examined.
The results show that unyielded regions increase at high Rayleigh numbers, despite the increase in buoyancy force and consequently increased heat and mass transfer. On the other hand, as the buoyancy ratio drops, the flow's strength and heat and mass transmission diminish, leading to an increase in plug regions. Accordingly, the mechanisms influencing the growth of unyielded regions are complex and follow different patterns. However, the plug regions always grow with increasing Y. The results indicate that increasing the Lewis number (mass transfer) reduces the effect of the buoyancy ratio on flow, heat transfer, and the unyielded regions in every case. Quantitative analysis of the results indicates that, while buoyancy ratio affects heat and mass transfer almost equally, the Lewis number increases mass transfer up to three times the heat transfer. Meanwhile, changing the buoyancy ratio can increase the maximum yield stress to 400%, while changing the Lewis number has a maximum effect of 20%.
An intention of the current study is to analyze the effect of double-diffusive convection in a hybrid nanofluid filled in an inclined open cavity with the heat gener- ation/ absorption. The cavity walls are insulated whereas the centrally placed baffle is maintained at the high temperature. The CuO + MWCNT nanoparticles suspended in the water is used as a working hybrid nanofluid. The angle of inclination γ = 0◦ - 90◦ is applied for the open cavity. The non-dimensional governing equation in the form of vorticity stream function transport is solved numerically by using the finite difference method. The behavior of fluid flow, heat transfer, and mass transfer are presented as a contour. At various parametric conditions (q = -4 to 4, Br = -4 to 4, Le = 1 to 6), the average Sherwood and Nusselt numbers are calculated and explained graphically. The results report that an inclination angle suppresses the heat and mass transfer rate in an open enclosure.
In this study, the bifurcation phenomenon and the existence of dual asymmetry solutions of double-diffusive convection driven by an internal thermal and solutal source in a horizontal cavity have been investigated systematically. The problem is solved by the SIMPLE algorithm with the QUICK scheme in a non-uniform staggered grid system. The Rayleigh numbers, 200 ≤ Ra ≤ 10⁶, buoyancy ratios, −20 ≤ Nc ≤ 20, Soret numbers, 0 ≤ Sr ≤ 0.8, and Dufour numbers, 0 ≤ Df ≤ 0.8, are considered in this study. Different streamlines for the onset and evolution of static bifurcation are tracked. The paper aims to determine the critical Rayleigh numbers and buoyancy ratios for the onset of symmetry-breaking through bifurcation diagrams based on the vortex length. The results indicate that increasing buoyancy can destabilize the symmetric system. The strong couple diffusion effect delays the onset of bifurcation flow. A pair of asymmetric modes can be obtained under different initial conditions.
Multifunctional membranes with outstanding heat dissipation, wave‐transparent, and self‐cleaning performance, as well as strength and ventilation, are urgently needed to meet the rapid development of portable electronics. Herein, we reported an improved phase separation process to prepare thermoplastic polyurethane (TPU)/multi‐wall carbon nanotube (MWCNT) composite membranes with open‐cell porous structure. Their morphology can be manipulated by regulating the content of MWCNT and varying processing parameters. These TPU/MWCNT composite membranes exhibit outstanding mechanical properties. For example, they can possess elastic deformation behavior in a wide temperature range from −50 to 100°C, and bear a load of more than 40,000 times their own weight. Moreover, there is not any obvious crease on the surface of membranes after a forced folding process, indicating their outstanding shape‐recovery ability and elasticity. Furthermore, these membranes have low dielectric constant and loss factor, and they are almost transparent to X‐band electromagnetic waves. What's more, these membranes also show outstanding water‐vapor breathable performance. In addition, MWCNT and open‐cell porous structure endow TPU/MWCNT membranes efficient heat dissipation capacity and good self‐cleaning performance.
In this study, the significance of porous circular cylinder and magnetic field on the double-diffusive natural convection and entropy generation in an enclosure is analysed using lattice Boltzmann method. Prime objective of this study is to assess the impression of permeability, buoyancy force variation, magnetic field and its direction on the thermo-solutal convection around a porous zone. The parametric study concentrates on the effects of Buoyancy ratio (BR=−5 to 5), Darcy number (Da=10−5, 10−4, & 10−3), Hartmann number (Ha=0, 25, & 50), and magnetic field angle (γM=0∘, 45∘, & 90∘) on the flow, heat and concentration transfer, and the variation in irreversibilities in and around the porous circular cylinder with high temperature and concentration. The Darcy-Brinkman-Forchheimer model is coupled with LB flow evolution equation to acquire flow features in the porous cylinder. Results indicate that Da, BR, and γM increment improves the heat and concentration transfers. Permeability increment significantly enhances the flow-field intensity around the cylinder. Effect of Ha on the reduction in mean Nusselt number and Sherwood number can be significantly controlled by the direction of magnetic field. However, magnetic field influences trivially on the flow field in the porous cylinder. Besides, the amalgamation of Da and γM induces unsteady characteristics in the enclosure. Also, γM increment widens the range of BR for the production of unsteady traits. The entropy generation augments with Ha, when the magnetic field direction is aligned with the fluid flow. Further, the irreversibilities due to concentration transfer is observed to be higher than that of other associated irreversibilities in the enclosure. The increment in BR (positive values) tends to suppress the fluid-friction and magnetic irreversibilities.
Researchers in heat transfer field always attempt to find new solutions to optimize the performance of energy devices through heat transfer enhancement. Among various methods which are implemented to reinforce the thermal performance of energy systems, one is utilizing porous media in heat exchangers. In this study, characteristics of laminar mixed convection in a porous two-sided lid-driven square cavity induced by an internal heat generation at the bottom wall have been carried out by using a numerical methodology based on the finite volume method and the full multigrid acceleration. The two-sided and top walls of the enclosure are assumed to have cold temperature while the remaining walls of the bottom wall are insulated. The working fluid is air so that the Prandtl number equates 0.71. The behavior of different physical parameters is shown graphically so that computations have been conducted over a wide range of pertinent parameters; (10-2≤ Ri ≤10), Darcy number (10-4≤ Da ≤10-1), internal Rayleigh number (0≤ RaI≤104), the porosity (0.2≤ϵ≤0.8) and the Grashof number (103≤ Gr ≤106). Results revealed that heat transfer mechanism and the flow characteristics inside the enclosure are strongly dependent on the Grashof number. For instance, the best heat transfer rates at the considered values of internal Rayleigh numbers are obtained for a high Grashof number. Furthermore, an increase of internal heat generation (RaI) leads to a higher flow and temperature intensities for Grashof numbers ranging from 104 to 106 and a specific Richardson number value. Besides, an increase in porosity values (ϵ) leads to an obvious decrease in the average Nusselt number. Maximum temperature θmax is optimal for high (ϵ) value. A correlation expression for the average Nusselt number relative to the internal heat source was established in function of two control parameters such as Darcy and Richardson numbers.
Current work involves entropy generation studies within nine porous containers involving identical area for Prm = 155 (engine oil), Dam=10−5−10−2 at Ram=106. The entropy generation maps for lesser values of Dam depict that Sθ is dominant at the boundaries whereas Sψ is dominant at the central zone. On the other hand, for larger values of Dam, Sψ is found to be dominant throughout the porous containers. Zones corresponding to Sθ,max are found at the bottom corners of all porous containers due to the hot cold junction whereas zones corresponding to Sψ,max vary with the shapes of porous containers. An energy efficient process corresponds to larger Nub¯, larger θ̂ and lesser Stotal. Containers with curved walls are found to be thermally efficient for thermal processing of engine oil saturated porous medium.
The study discusses the issue of entropy generated in a mixed convection Cu–water nanofluid flow in an inclined channel filled with a non-Darcy porous medium with variable permeability taking into account the Navier slip and convection at the boundary. The equations of momentum and temperature are highly nonlinear and coupled, and these are solved using the homotopy analysis method after converting to the dimensionless form. The flow velocity and temperature expressions as required during the entropy generation analysis are obtained. Bejan number is also obtained which indicates the role of heat transfer and viscous dissipation in the entropy generation process. The consequences of the relevant flow parameters are discussed, and the results are shown graphically. It was observed that entropy is minimum just above the center of the channel width.
Metal foams as porous media have very high porosity and good strength. These materials could easily be applied to exterior surfaces of metals used in different industries. Porous media have been used less in the external flows to control the wake region or reduce the generated sound in high-speed flows. In this study, a numerical investigation is done to explore the effect of different characteristics of a porous medium—such as PPI and porosity or porous coating thickness—on the sound generated by a porous-coated cylinder. The governing transport equations in the clear and porous regions are solved using 3D Navier–Stokes and non-Darcy equations, respectively, and employing the large eddy simulation turbulence model. The generated noise is estimated using the Ffowcs-Williams and Hawkings model at the observer location. The results show that use of porous media could considerably reduce the aerodynamic noise provided that its characteristics are selected precisely. For example, results show that a porous-coated cylinder with PPI = 40 has about 30 dB higher overall sound pressure level (OASPL) than one with PPI = 10 with the same porosity and thickness. Same conditions are also observed about the thickness of the coating. The results indicate that an optimal thickness exists for which the OASPL is minimal. For example, porous-coated cylinders with coating thickness of 5 and 15 mm have about 25 dB higher OASPL compared to a cylinder with the coating thickness of 10 mm.
Present numerical study examines the heat and mass transfer characteristics of magneto-hydrodynamic Casson fluid flow between two parallel plates under the influence of thermal radiation, internal heat generation or absorption and Joule dissipation effects with homogeneous first order chemical reaction. The non-Newtonian behaviour of Casson fluid is distinguished from those of Newtonian fluids by considering the well-established rheological Casson fluid flow model. The governing partial differential equations for the unsteady two-dimensional squeezing flow with heat and mass transfer of a Casson fluid are highly nonlinear and coupled in nature. The nonlinear ordinary differential equations governing the squeezing flow are obtained by imposing the similarity transformations on the conservation laws. The resulting equations have been solved by using two numerical techniques, namely Runge-Kutta fourth order integration scheme with shooting technique and bvp4c Matlab solver. The comparison between both the techniques is provided. Further, for the different set physical parameters, the numerical results are obtained and presented in the form of graphs and tables. However, in view of industrial use, the power required to generate the movement of the parallel plates is considerably reduced for the negative values of squeezing number. From the present investigation it is noticed that, due to the presence of stronger Lorentz forces, the temperature and velocity fields eventually suppressed for the enhancing values of Hartmann number. Also, higher values of squeezing number diminish the squeezing force on the fluid flow which in turn reduces the thermal field. Further, the destructive nature of the chemical reaction magnifies the concentration field; whereas constructive chemical reaction decreases the concentration field. The present numerical solutions are compared with previously published results and show the good agreement.
The non-Darcy double-diffusive mixed convection in a double lid-driven porous cavity with two thermosolutal sources is numerically investigated in this article, depicting the effects of different physical parameters on heat and mass transfer in the drying chamber. The flow is generated due to the motion of the horizontal moving lids and the buoyancy produced by the temperature and concentration gradients. The governing equations are discretized by the Legendre spectral element method (SEM) with high accuracy, and an improved time-splitting method is developed to deal with the coupled pressure and velocity in the Brinkman-Forchheimer extended Darcy model. The effects of Darcy number (Da = 10⁻⁵∼10⁻¹), Richardson number (Ri = 10⁻²∼10¹), and buoyancy ratio (Br = −5 ∼ 5) are investigated, and numerical results are analyzed by contours of streamline, isotherm, heatline, isoconcentration, and massline in detail. Results reveal the pattern of heat and mass transfer with the variation on significant parameters by the average Nusselt and Sherwood numbers on the moving lids of the cavity.
This article focuses on a numerical study for the effect of porosity and internal heat generation/absorption parameters on the mixed convective flow of nanofluid over a backward facing step along with the entropy generation. The channel downstream bottom wall is isothermally heated while the remaining walls of the channel are thermally insulated. The dimensionless governing equations are discretized utilizing the Galerkin-based finite element method. The discrete systems of nonlinear algebraic equations are computed using the Newton method and the corresponding linearized systems are treated using the monolithic geometric multigrid solver. Effect of different physical parameters in the specified ranges such as , , , , , and on the fluid flow is analyzed with the help of the streamlines, isotherm patterns, and various graphs. It is noticed that the average heat transfer increases with the porosity parameter and reduces with the internal heat generation parameter. Furthermore, the entropy generation produced by the heat transfer and fluid friction is found to amplify with the porosity parameter, whereas a decline is recorded in it due to the magnetic field.
This paper investigates the energetic and entropic characteristics of a microchannel with thick walls. A first-order, catalytic chemical reaction is imposed on the inner surfaces of the microchannel walls, and local thermal non-equilibrium approach is employed to analyse heat transfer within the porous section of the microchannel. Further, endo-/exothermic physicochemical processes are incorporated into the fluid phase and solid structure of the microchannel. Two models describing the fluid–porous interface conditions known as Models A and B are incorporated. It is shown that for both interface models, and with the considered parametric values, the optimum thickness of the porous insert to achieve the maximum Nu is around 0.6. However, when PEC is considered, this optimum thickness may vary between 0 and 0.5. It is further shown that depending on the specification of the microreactor, either Model A or B may result in the prediction of the minimum total entropy generation rate. It is also demonstrated that by altering the endothermicity of the microreactor it is possible to find an optimal value, which minimizes the total rate of entropy generation.
Purpose
The purpose of this paper is to investigate the three-dimensional natural convection and entropy generation in a cuboid enclosure filled with two immiscible fluids of nanofluid and air.
Design/methodology/approach
One surface of the enclosure is jagged and another one is smooth. The finite volume approach is applied for computation. There are two partially side heaters. Furthermore, the Navier–Stokes equations and entropy generation formulation are solved in the 3D form.
Findings
The effects of different governing parameters, such as the jagged surface (JR=0, 0.02, 0.04, 0.08, 0.12 and 0.16), Rayleigh number (10³⩽Ra⩽10⁶) and solid volume fraction of nanofluid (φ=1, 1.5, 2 vol%), on the fluid flow, temperature field, Nusselt number, volumetric entropy generation and Bejan number are presented, comprehensively. The results indicate that the average Nusselt number increases with the increase in the Rayleigh number and solid volume fraction of nanofluid. Moreover, the flow structure is significantly affected by the jagged surface.
Originality/value
The originality of this work is to analyze the natural-convection fluid flow and heat transfer under the influence of jagged surfaces of electrodes in high-current lead–acid batteries.
In this work, we have presented the numerical results for 2D, steady, laminar and incompressible flow in a square, two-sided, lid-driven cavity with a decentered heated triangular block (maintained at the isothermal thermal condition, TH) for non- Newtonian power-law fluids. The range of flow governing parameters considered for the numerical experimentations are Reynolds number (100≤Re≤1000), Richardson Number (Ri=0.01, 1, 10) power law index; (0.2≤n≤1.8), blockage (10% and 30% of the height of cavity) and Prandtl number of Pr=1. The upper and lower walls of the square cavity are kept moving in the opposite directions along –x axis (ux,-ux) and are thermally insulated. The left and right stationary walls are exposed to ambient condition (Tc). The governing flow equations are solved by using the finite volume approach and SIMPLE algorithm. Heat transfer characteristics and flow kinematics are revealed by systematic variation of streamlines and temperature contours. The effect of mixed convection parameter, i.e., Ri, found to have a negligible impact on fluid and thermal structure inside the cavity for fluids with n=0.2.Heat transfer rate found to be lower for Ri=0.01 for both blockages
The natural convection and entropy generation during double-diffusive MHD natural convection in a tilted sinusoidal corrugated porous enclosure is investigated numerically in this work by using heatline visualization technique. The top and bottom horizontal walls are assumed as adiabatic and non-diffusive, while the left and right vertical corrugated sidewalls are maintained at a constant hot and cold temperatures and concentrations respectively. The flow in the enclosure is subjected to an inclined magnetic field. The enclosure is filled with an electrically conducting fluid [Pr = 0.024] saturated with a porous media. The numerical computations are presented for various values of Rayleigh number (Ra), Hartmann number (Ha), Lewis number (Le), Darcy number (Da), buoyancy ratio (N), magnetic field orientation angle (φ) and enclosure inclination angle (Φ). In addition, the entropy generation due to fluid friction, thermal gradients, diffusion, and magnetic field beside the total entropy generation are studied and discussed. It is found that the flow circulation decreases strongly when the magnetic field applied horizontally and the enclosure is considered vertical. Heatline visualization concept is successfully applied to the considered problem. The average Nusselt number decreases when the Lewis number increases, while the average Sherwood number increases when the Lewis number increases. Also, both average Nusselt and Sherwood numbers increase when the Darcy number and buoyancy ratio increase. Moreover, the results show that the entropy generations due to magnetic field when the enclosure is subjected to the horizontal magnetic field are higher than the corresponding values when it subjected to the vertical magnetic field.
We investigate the flow in a porous medium subjected to an oscillatory (sinusoidal) pressure gradient. Direct numerical simulation (DNS) has been performed to benchmark the analytical solutions of the unsteady Darcy equation with two different expressions of the time scale: one given by a consistent volume averaging of the Navier–Stokes equation with a steady-state closure for the flow-resistance term, another given by volume averaging of the kinetic energy equation with a closure for the dissipation rate. For small and medium frequencies, the analytical solutions with the time scale obtained by the energy approach compare well with the DNS results in terms of amplitude and phase lag. For large dimensionless frequencies ((Formula presented.)), we observe a slightly smaller damping of the amplitude than predicted by the unsteady Darcy equation with the low-frequency time scale. This can be explained by a change in the velocity fields towards a potential flow solution. Note that at those high frequencies, the flow amplitudes remain below 1 % of those of the steady-state flows. Our DNSs, however, indicate that the time scale predicted by the steady-state closure for the flow-resistance term is too small. In general, this study supports the use of the unsteady form of Darcy’s equation with constant coefficients to solve time-periodic Darcy flow, provided the proper time scale has been found.
Simultaneous application of nanoparticles and porous media to enhance heat transfer inside an annulus is investigated numerically. Two-phase mixture model along with Darcy–Brinkman–Forchheimer relation has been implemented for nanofluid flow simulation in porous media. Different configurations consisting of various porous layer thicknesses, porous layer positions (at inner/outer wall of the annulus), and its permeabilities are analyzed as a function of nanoparticle concentrations and Reynolds from the view point of the first and the second laws of thermodynamics. A new PN (performance number) – defined as the ratio of enhanced heat transfer to pressure loss – is introduced to better judge the first law's performance of configurations. Results showed that the configuration's parameters, nanoparticles concentration and Reynolds number have considerable effects on both the performance and entropy generation numbers. For configurations with high permeabilities (Da = 0.1, 0.01), PN has an increasing trend with porous layer thickness; while for configurations with low permeabilities (Da = 0.0001), PN has a decreasing trend with porous layer thickness; and for configurations with a moderate permeability (Da = 0.001), an optimum thickness corresponds to PN. The study of the second law also reveals that an optimum porous media thickness exists for each nanofluid flowing in a porous medium at a specific Reynolds.
Karst aquifers have a high degree of heterogeneity and anisotropy in their geologic and hydrogeologic properties which makes predicting their behavior difficult. This paper evaluates the application of the Equivalent Porous Media (EPM) approach to simulate groundwater hydraulics and contaminant transport in karst aquifers using an example from the North Coast limestone aquifer system in Puerto Rico. The goal is to evaluate if the EPM approach, which approximates the karst features with a conceptualized, equivalent continuous medium, is feasible for an actual project, based on available data and the study scale and purpose. Existing National Oceanic Atmospheric Administration (NOAA) data and previous hydrogeological U. S. Geological Survey (USGS) studies were used to define the model input parameters. Hydraulic conductivity and specific yield were estimated using measured groundwater heads over the study area and further calibrated against continuous water level data of three USGS observation wells. The water-table fluctuation results indicate that the model can practically reflect the steady-state groundwater hydraulics (normalized RMSE of 12.4%) and long-term variability (normalized RMSE of 3.0%) at regional and intermediate scales and can be applied to predict future water table behavior under different hydrogeological conditions. The application of the EPM approach to simulate transport is limited because it does not directly consider possible irregular conduit flow pathways. However, the results from the present study suggest that the EPM approach is capable to reproduce the spreading of a TCE plume at intermediate scales with sufficient accuracy (normalized RMSE of 8.45%) for groundwater resources management and the planning of contamination mitigation strategies.
Household water treatment and safe storage (HWTS) provides a solution, when employed correctly and consistently, for managing water safety at home. However, despite years of promotion by non-governmental organizations (NGOs), governments and others, boiling is the only method to achieve scale. Many HWTS programs have reported strong initial uptake and use that then decreases over time. This study maps out enablers and barriers to sustaining and scaling up HWTS practices. Interviews were carried out with 79 practitioners who had experience with HWTS programs in over 25 countries. A total of 47 enablers and barriers important to sustaining and scaling up HWTS practices were identified. These were grouped into six domains: user guidance on HWTS products; resource availability; standards, certification and regulations; integration and collaboration; user preferences; and market strategies. Collectively, the six domains cover the major aspects of moving products from development to the consumers. It is important that each domain is considered in all programs that aim to sustain and scale-up HWTS practices. Our findings can assist governments, NGOs, and other organizations involved in HWTS to approach programs more effectively and efficiently.
Copyright © 2015 The Authors. Published by Elsevier GmbH.. All rights reserved.
This study examined the evolution of columnar-basalt structures using simple laboratory experiments and numerical simulation in double-diffusive finger system. Effect of various parameters like Prandtl and Rayleigh numbers has been considered in the study. Columnar-basalts are geological formations observed in some of the ponded basalt-lava found at many parts of the world. They are prismatic rock joints having polygonal cross-section with straight edges and parallel faces. The typical cross-sectional dimensions vary from few centimeters to meter size and typical height from 30-50 meters. Hence the aspect ratio of the columnar-basalt in most cases is greater than 100. The limitations for the evolution of columnar basalts provided in the literature have been discussed. An order of magnitude analysis has been presented for the thickness of the unstable layer at the interface. In this paper, we demonstrate that the double diffusive finger convection system can produce features similar to those observed in columnar basalt and can serve as an alternative, plausible explanation for the evolution of columnar basalt structure.
In the present study, the combination of differential transform method (DTM) and Padé approximant, called DTM-Padé, is employed to investigate the entropy generation in the magnetohydrodynamic (MHD) stagnation-point flow with heat transfer in a porous medium. Entropy generation equation is derived as functions of velocity and temperature gradients. A very good agreement is observed between some of the obtained results of the current study and those of the shooting method results. The results are given to survey the effect of various parameters like magnetic interaction number, Brinkman number, Reynolds number and Hartmann number on the entropy generation rate and Bejan number. In addition, the rates of two irreversibility mechanism are investigated for each of involved parameters.
Entropy generation analysis is one of the most powerful tools to investigate the performance of thermal systems. Many researchers have studied entropy generation of thermal systems to find the optimum operating conditions. This paper numerically investigates the effects of Al2O3 nanoparticle concentration on the entropy generation of water-Al2O3 nanofluid flow through a circular pipe under constant wall heat flux boundary condition in laminar and turbulent regimes. The nanofluid flow is simulated using a CFD (Computational Fluid Dynamics) finite volume code and the k − e model is applied to simulate the turbulent flow. The code which is employed for the simulation of the
nanofluid flow is validated with the available empirical correlations. Approved formulations are used to model the density, specific heat, viscosity and conductivity of the nanofluid. It is observed that adding nanoparticles to the slurry results in a decrease in the heat transfer entropy generation and an increase in the friction entropy generation. In the turbulent flow both of the friction and thermal entropy generation terms are of the same order of magnitude, while in the laminar regime the effect of the heat transfer entropy generation strongly outweighs that of the friction entropy generation. In this article, the total entropy generation is plotted versus Reynolds number for laminar and turbulent regimes and the optimum Reynolds number minimizing the entropy generation is obtained. Moreover, the contours of the friction, thermal and total entropy generations are displayed in laminar and turbulent regimes. It is found that application of Al2O3 nanofluid slurry instead of
pure water in low Reynolds numbers decreases the entropy generation and is beneficial.
In the present manuscript effect of different Rayleigh number of non-darcy fully developed mixed convection in a vertical pipe filled with porous media is numerical investigation. The motion in the pipe caused by external pressure gradient and byoucey force. Non-Darcy Brinkmen-Forchheimer extended model has been introduces in momentum equation. The basic state of the flow model using fundamental assumption is formed in the form of coupled differential equation which is solved using Chebyshev Spectral collocation technique. The study is best based on double diffusive mixed convection which is governed in mathematical formulation of the problem, in which the velocity profile posses point of inflection beyond the threshold value of RaT (Positive Rayilegh thermal number). In case of Negative Rayliegh thermal number, the velocity profile may contain point of inflection in the centre zone and point of separation at the vicinity of the wall. Point of separation is create a back flow near the wall.
Double-diffusive convection caused by variations in solute concentration
and temperature within a fluid body has previously been studied in
connection with oceanic mixing processes, astrophysics, metallurgy,
geology, and vadose zone hydrology but has not previously been studied
in connection with thermohaline transport in a groundwater well. This
paper considers whether double-diffusive convection induced by salinity
and/or temperature variations is a plausible mechanism for heat and
solute transport in a groundwater well. This is examined theoretically
using Rayleigh number stability "onset" criteria for fluid in a cylinder
that considers the cylindrical well geometry and geothermal/solute
boundary conditions. Theoretical results suggest that both monotonic and
oscillatory double-diffusive convection are plausible transport
phenomena in groundwater wells. These analyses have important
implications for hydrogeology because they provide another theoretically
plausible mechanism by which heat and solute may mix in a well. This
previously unaccounted for thermohaline mixing phenomenon may therefore
be critical in the interpretation of well hydrogeologic and
hydrochemical data.
Soret effect on fluid flow and heat and mass transfer induced by double-diffusive natural convection in a square porous enclosure, submitted to cross gradients of temperature and concentration, is studied numerically. The cavity is heated from below and cooled from the top, while its vertical walls are adiabatic and maintained at constant but different concentrations. Numerical results are presented for governing parameters varying in the following ranges: 40 ≤ RT ≤ 1,000, Le = 10, − 0.2 ≤ N ≤ 0.2 and − 30 ≤ M ≤ 30, where RT, Le, N, and M are the thermal Rayleigh number, the Lewis number, the buoyancy ratio, and the Soret parameter, respectively. The effect of the buoyancy ratio and the Soret parameter on the maintenance and disappearance of the multiple steady-state solutions obtained in the case of purely thermal convection is analyzed. It is found that only one monocellular flow mode persists at large values of N (or − N), both in the presence and in the absence of the Soret effect. Some flow modes are destroyed by the solutal buoyancy forces in the absence of the Soret effect (M = 0) but reappear in some range of the parameter M. The Soret effect may affect considerably the heat and mass transfer in the medium; it leads to an enhancement or to a reduction of the mass transfer, depending on the flow structure and the sign of M. There are situations where a solution transfers the solute toward the wall with the highest concentration. Such behavior is observed when the temperature gradient and the magnitude of the Soret parameter M are such that the thermodiffusion flux opposes and overcomes the convection flux, resulting in a net mass flux directed from the least concentrated wall toward the most concentrated one.
This updated edition of a widely admired text provides a user-friendly introduction to the field that requires only routine mathematics. The book starts with the elements of fluid mechanics and heat transfer, and covers a wide range of applications from fibrous insulation and catalytic reactors to geological strata, nuclear waste disposal, geothermal reservoirs, and the storage of heat-generating materials. As the standard reference in the field, this book will be essential to researchers and practicing engineers, while remaining an accessible introduction for graduate students and others entering the field. The new edition features 2700 new references covering a number of rapidly expanding fields, including the heat transfer properties of nanofluids and applications involving local thermal non-equilibrium and microfluidic effects.
• Recognized as the standard reference in the field
• Includes a comprehensive, 350-page reference list
• Cited over 5900 times to date in its various editions
• Serves as an introduction for those entering the field and as a comprehensive reference for experienced researchers
• Covers the latest developments in research on nanofluids and CO2 sequestration
In this article, numerical investigation of entropy generation due to heat transfer and fluid fiction is performed on a confined slot impinging jet. The non-Newtonian nanofluid is an aqueous solution of 0.5 wt% carboxymethyl cellulose (CMC) with 10 nm diameter TiO2 nanoparticles. Two-dimensional laminar flow is considered and a constant temperature is applied on the impingement surface. The nanofluid, as well as the base fluid, exhibits pseudoplastic behavior. The thermal and rheological properties of the base fluid and nanofluid are temperature-dependent. In this paper, correlations for the power law and consistency indices, as well as thermal conductivity, as a function of temperature of the fluid based on some existing experimental data in the literature are developed. In order to consider the effect of converging angle and groove amplitude on entropy generation in the channel, the numerical simulation is performed for different converging angles between 0° and 5° and groove amplitudes in the range of 0–0.007 m. The results showed that a large portion of entropy generation is concentrated in the impingement surface. The total entropy generation increases with increasing volume fraction and converging angle. The minimum value of exergy loss tends to occur at higher converging angles by increasing the Reynolds number and jet-impingement surface to distance ratio. Also, the exergy loss decreases with the concave groove amplitudes.
This article presents an alternative approach for the design of a heat sink as a solution of the thermal management problem in microelectronic components. The design was carried out based on the entropy generation minimisation criterion and it was optimised through three different non-conventional methods, such as: Unified Particle Swarm Optimisation, Spiral Optimisation and Cuckoo Search. A rectangular microchannel heat sink manufactured from a High Thermal Conductive Graphite was considered and a colloid of H2O-TiO2 was used as working fluid. The performance of this nanofluid was compared against traditional fluids like air and ammonia gas. Also, nanoparticles were considered and studied at different volume fractions. Moreover, the performance solving the thermal problem was compared for the implemented global optimisation techniques. It was noticed that nanofluids represent a good alternative for designs with lower volume flow rates, requiring a lower nanoparticle volume fraction. Furthermore, the Cuckoo Search algorithm was more accurate and faster than the other two methods.
Turbulent fully developed flow of TiO2-water nanofluid through annuli with different radius ratios (RR) are numerically simulated using k-ε turbulence model and two-phase mixture model. Heat transfer and entropy generation studies are conducted to scrutinize the performance of systems in order to find the optimal working condition to reach the minimum irreversibility. Two cases for thermal boundaries are considered in which a constant and uniform heat flux is exerted on one of annulus walls, while the other wall is insulted. To confirm the validity of numerical solver, results are compared against those of other numerical and experimental data. The effects of Reynolds number (Re), nanoparticles concentration and the radius ratio of annuli - with the same cross sectional area - on heat transfer and entropy generation rates are studied. It is revealed that Re and RR have optimal values to maximize Nusselt and also the heat transfer enhancement due to addition of nanoparticles. In addition, it has been shown that RR has a high impact on entropy generation rate and for each nanofluid flowing inside an annulus, there is an optimal Re value to minimize entropy generation. Finally, by definition of the evaluation parameter of PE, which is a trade-off between the first and the second laws of thermodynamics, the optimum Re is found to reach the best PE of the nanofluid flowing inside annuli with different RRs.
Air jet impingement is an effective enhanced heat transfer technique which has been widely applied in cooling of electronic components and drying of continuous sheets of materials, etc. Although steady and unsteady impingement systems have led to many studies on jet impingement flow and heat transfer, the vast majority of them focus on smooth surfaces. As the flow and thermal physics of jets impingement on a rough surface are significantly different from that on a smooth surface, a numerical study was performed on two-dimensional air jet impingement with a model rough surface by computational fluid dynamics method. A sinusoidal wave was employed to model the rough impinging target surface subjected to a slot jet nozzle. A dimensionless heat transfer enhancement factor was introduced to quantify the effect of jet flow Reynolds number, jet impingement dimension, and surface roughness as well as temperature difference between jet flow and impinging target on the heat transfer of jet impingement. It is observed that the roughness effect is minimal in the impingement zone while it is prominent in the wall jet region, and the surface roughness plays a dominant role on the enhancement factor of heat transfer rate compared with jet geometrical dimension, Reynolds number of jet flow as well as temperature difference. Furthermore, entropy generation analysis was also performed on the heat and mass transfer in air jet impingement, and optimal designs were found with entropy generation minimization principle accordingly.
This work presents the comparison between CFD and experimental results obtained on a sensible thermal energy storage system based on alumina beads freely poured into a carbon steel tank. Experimental investigations of charging and discharging phases were carried out at a constant mass flow rate using air as heat transfer fluid. The experimental set-up was instrumented with several thermocouples to detect axial and radial temperature distribution as well as reservoir wall temperature. The experimental results were compared with those obtained from CFD simulations carried out with the FLUENT software. The computational domain consists of an axisymmetric tank of cylindrical shape filled with a porous bed coupled with the wall. The governing equations are solved for incompressible turbulent flow and fully developed forced convection, based on the two-phase transient model equation (LTNE-local thermal non-equilibrium) to calculate the temperature of fluid and solid phases. The porosity of the bed is considered variable in the radial direction, while the thermodynamic properties of both phases are temperature-dependent. The influence of the thermal dispersion within the porous bed, as well as the effective conductivity between the beads was considered. The heat transfer coefficient was calculated according to correlation for forced convection within porous media. Numerical results show a good agreement with experimental ones if thermal properties are considered temperature-dependent and the experimental temperature profile at the inlet of the bed is applied as a boundary condition in the simulations.
This paper reports a numerical study with two and three-dimensional flows, in an enclosure domain partially filled with a vertical porous media layer saturated by a mixture of air with another gaseous component, the Prandtl number Pr is kept at 0.7. The domain right and left vertical walls are considered at uniform different temperature and concentration, the other walls are adiabatic and impermeable. The results of two-and three-dimensional models were compared. The influence of the main parameters of double diffusive convection is investigated, namely the buoyancy ratio, (-0.1 ≤ N ≤ -4) and Lewis number (0.1 ≤ Le ≤ 10) on the flow structure and heat and mass transfer rate are depicted. The temperature and concentration effect (on density) could be opposing (N < 0). By The resulting flow is consequence of buoyancy forces (density) field affected by the relative conductivity and the porous media permeability. The complex obtained flow structure and corresponding heat and mass transfer (velocity, temperature profiles) are discussed at steady state. The numerical results are reported and analyzed in terms of stream trace, streamlines, isotherms, isoconcentrations lines and averaged Nusselt and Sherwood numbers.
In this paper, entropy generation of associated with double diffusive natural convection of non-Newtonian power-law fluids in an inclined porous cavity has been analyzed by Finite Difference Lattice Boltzmann Method (FDLBM). The entropy generations due to fluid friction, heat and mass transfer have been simulated and analyzed for the certain pertinent parameters of thermal Rayleigh number (RaT =104 and 105), Darcy number (Da =10-4, 10-3, and 10-2), power-law index (n =0.6-1.4), Lewis number (Le =2.5 and 5), inclined angles (θ =0°, 40°, 80°, and 120°), Dufour parameter (Df =0, 1, and 5), Soret parameter (Sr =0, 1, and 5) and the buoyancy ratio (N =-1 and 1). Results indicate that the augmentation of the thermal Rayleigh number enhances different entropy generations and declines the average Bejan number. The increase in the Darcy number provokes various irreversibilities to enhance and the average Bejan number decreases significantly. The augmentation of the inclined angle from θ =0° to 40° enhances various total entropy generations and plummets the average Bejan number. The increase in the inclined angle from θ =40° to 80° results in the drop of different total entropy generations and rises the average Bejan number. The rise of Soret and Dufour parameters enhances the entropy generations due to heat transfer and fluid friction. The change of power-law index alters various entropy generations, but the alteration does not follow a specific manner in different studied parameters.
A numerical model is developed to study the natural convection in a horizontal porous annulus with a heated inner cylinder and a colder outer cylinder. Sequential pairs of radial baffles are attached to the inner cylinder and arranged symmetrically relative to the vertical plane of symmetry. A numerical procedure based on the finite volume method is adopted to solve the system of coupled 2D Darcy-Brinkman-Boussinesq and energy equations. Numerical results show that the insertion of medium-sized baffles modifies the unicellular flow to a co-rotating multicellular flow and induces maximal heat transfer reduction when the baffles are located at appropriate angles measured from the bottom of the inner cylinder. The optimal conditions for maximal heat transfer reduction are determined as a function of the number, size and position of the pairs of baffles for the betterment of thermal insulation of a horizontal pipe. The best improvement for thermal insulation efficiency is obtained with a successive insertion of three pairs of baffles, wherein the maximal reduction of heat transfer can reach 12% as compared to the bare case without baffles. Subsequent insertion of four pairs of baffles generates Rayleigh-Bénard thermal instabilities in the upper part of the porous annulus, which is unfavorable for purposes of thermal insulation.
This work describes a simplified methodology to model (air-side) a heat exchanger within a computational fluid dynamics analysis of an oil cooler device for aerospace applications. Although several CFD solvers provide specific tools to simulate a heat exchanger, sometimes the available data, as for example, cooling plate geometries, dimensions and their arrangement in the heat exchanger, are not exhaustive enough to set up the numerical simulation. Hence, in the present research was used a porous media model to simulate the main effects of the heat exchanger, such as pressure drop and heat rejection, on the flowfield occurs place inside an aircraft oil cooler system. In this way, the need to model the real complex geometry of the heat exchanger is avoided. In this framework, present analyses aim at verifying that the heat exchanger, under investigation, is able to satisfy the system requirements in terms of heat rejection of the engine's oil cooling system, foreseen for the aircraft operating conditions. In particular, the paper analyzes a turboprop oil cooler heat exchanger when the aircraft is flying at cruise conditions, namely 2743 m (9000 ft) altitude, focusing attention on several heat exchanger flow field features such as air pressure drop, temperature change and mass flow rate. Finally, those numerical results are analyzed in detail and compared to experimental data available for the heat exchanger, thus pointing out that this design approach represents a viable option in the framework of oil cooling heat exchanger performance investigation.
The flow field of the diesel particulate filter (DPF) with porous media and the swirl regeneration burner is complex, so which kind of turbulence model to be chosen has a great influence on the accuracy and performance on the computational fluid dynamics (CFD) simulation. Based on Fluent software and with the same conditions, the standard k - ε, RNG k - ε, Realizable k - ε and SST k - ω turbulence models were adopted to get the back-flow characteristics and the distribution of velocity, pressure and turbulent kinetic energy in the swirl burner and the porous media, then the results were compared and analyzed. It shows that, at the sudden expansion zones and near-wall region, the flow characteristics and back-flow features of the Realizable k - ε model are clearer than that of the standard k - ε model and the RNG k - ε model, and the maximum peaks of turbulent kinetic energy and the larger gradient are gotten by the RNG k - ε model, but better back-flow characteristics and more abundant details of flow field by the SST k - ω model, and the center average velocity and pressure at the inlet and outlet all agreed well with experiments.
This paper deals with a numerical investigation of double-diffusive natural convective heat and mass transfer in a cavity filled with Newtonian fluid. The active parts of two vertical walls of the cavity are maintained at fixed but different temperatures and concentrations, while the other two walls, as well as inactive areas of the sidewalls, are considered to be adiabatic and impermeable to mass transfer. The length of the thermally active part equals half of the height. The non-dimensional forms of governing transport equations that describe double-diffusive natural convection for two-dimensional incompressible flow are functions of temperature or energy, concentration, vorticity, and stream-function. The coupled differential equations are discretized via FDM (Finite Difference Method). The Successive-Over-Relaxation (SOR) method is used in the solution of the stream function equation. The analysis has been done for an enclosure with different aspect ratios ranging from 0.5 to 11 for three different combinations of partially active sections. The results are presented graphically in terms of streamlines, isotherms and isoconcentrations. In addition, the heat and mass transfer rate in the cavity is measured in terms of the average Nusselt and Sherwood numbers for various parameters including thermal Grashof number, Lewis number, buoyancy ratio and aspect ratio. It is revealed that the placement order of partially thermally active walls and the buoyancy ratio influence significantly the flow pattern and the corresponding heat and mass transfer performance in the cavity.
In the work presented in this paper, a two-dimensional mathematical model of soot regeneration was developed for a single-channel catalytic diesel particulate filter. The commercial computational fluid dynamics (CFD) code ANSYS Fluent 15.0 was used to simulate the gas flow field, whereas the regeneration kinetics was implemented through user-defined-subroutines. Both mechanisms of catalyzed and non-catalyzed (i.e., thermal) oxidation were used to describe combustion of the soot trapped inside the porous wall of the filter. Conversely, only non-catalyzed oxidation was assumed for the cake layer. The aim of the work was at investigating the effect of the catalyst activity on the regeneration dynamics of the filter in the light of the thermal interaction between combustion of the soot in the (catalytic) porous wall and combustion of the cake. To this end, computations were run by increasing the pre-exponential factor in the Arrhenius equation for the catalytic reaction rate, thus simulating the effect of increasing catalyst activity.
A performance assessment method for compact heat transfer surfaces is proposed, consisting of sizing a cross flow heat exchanger for given fluids, temperature and flow rate values. The resulting configuration is then used in a rating routine where only the heat transfer surface type on one exchanger side is modified while maintaining all design parameters constant. Heat exchanger core dimensions resulting from the sizing routine and the reference type on one side of the heat exchanger are maintained as well in the rating procedure, which was repeated for all heat transfer surfaces in the set. Thus, the change in entropy generation rate observed is caused exclusively by changing the heat transfer surface type as no other parameter is modified. This makes possible a classification of a set of heat transfer surfaces based on entropy generation criteria. The augmentation entropy generation number criterion was adapted to assess and cross check the procedure proposed. Consistency between augmentation entropy generation number criterion and the method proposed was found. The classifications generated by the method proposed were confirmed by augmentation entropy generation number criterion. It was found that the method proposed predicts also the Re value for which an inversion in the classification occurs. The method proposed was implemented for a cross flow heat exchanger type. No other type was studied. A total of 30 heat transfer surfaces of three types, louvered fin, plain fin and strip fin were studied.
Double-diffusive mixed convection of pseudoplastic fluids between two-square concentric duct annuli has been analyzed by FDLBM. Results indicate that the augmentation of Richardson number decreases heat and mass transfer. The fall of the power law index declines heat and mass transfer at Ri = 0.00062 and 0.01. The increase in the size of the adiabatic body enhances the heat and mass transfer in the lid-driven enclosure generally.
The second law aspects of heat transfer by forced convection are illustrated in terms of four fundamental flow configurations: pipe flow, boundary layer over flat plate, single cylinder in cross-flow, flow in the entrance region of a flat rectangular duct. The interplay between irreversibility due to heat transfer along finite temperature gradients and, on the other hand, irreversibility, entropy generation profiles or maps, and those flow features acting as strong sources of irreversibility are presented. It is shown how the flow geometric parameters may be selected in order to minimize the irreversibility associated with a specific convective heat transfer process.
The effects of buoyancy ratio on unsteady double-diffusive natural convection in a cavity filled with porous medium with uniform and non-uniform boundary conditions are analyzed in this paper. It is assumed that the left vertical wall and bottom wall are heated and concentrated (uniformly and non-uniformly), while the right vertical wall is maintained at a constant cold temperature, and the top wall is well insulated. The governing equations are solved numerically using a staggered grid finite-difference method to determine the streamlines, isotherms, isoconcentrations, local Nusselt number, local Sherwood number, average Nusselt number and average Sherwood number for various values of buoyancy ratio and Rayleigh number. The change of flow patterns with respect to time depicted and described here. The results are compared with previously published work and excellent agreement has been obtained.
In this paper, heat transfer and entropy generation due to laminar natural convection in a square cavity filled with non-Newtonian nanofluid have been analyzed by Finite Difference Lattice Boltzmann Method (FDLBM). The cavity is filled with water and nanoparticles of copper (Cu) while the mixture shows shear-thinning behavior. This study has been conducted for the certain pertinent parameters of Rayleigh number (Ra = 104-105), power-law index (n = 0.6-1), and the volume fraction has been studied from φ = 0 to 0.06. Results indicate that the augmentation of the power-law index causes heat transfer to drop while increase in volume fraction of nanoparticles augments it. Entropy generation due to fluid friction and heat transfer rises as the Rayleigh number enhances. Augmentation of volume fraction enhances entropy generations due to heat transfer and fluid friction in different power-law indexes. The total entropy generation declines slightly as power-law index increases.
The present study is focused to analyse buoyancy opposed double diffusive natural convection in a square porous cavity having partially active thermal and solutal walls. Five different partially active zones are considered along the vertical walls, while the remaining portions of the vertical walls along with the top and bottom walls of the cavity are considered to be adiabatic and impermeable. Darcy–Brinkman–Forchheimer model is used to study the flow, heat and solute transfer in porous media. The solution is done by control volume integration. Modified MAC method is used for the numerical solution of governing equations. Gradient dependent consistent hybrid upwind scheme of second order (GDCHUSSO) is used for discretization of the convective terms. Numerical simulations have been done for different combinations of partially active zones to reveal their effect on heat and mass transfer. The pertinent parameters those affect the flow such as; buoyancy ratio, Darcy number and active zone locations have been identified and their effects have been studied. The parametric results are provided in graphical and tabular form. Flow lines, isotherms, isoconcentrations contour maps are provided to bring clarity in the understanding of the momentum, heat and solute transport phenomenon.
A numerical study has been carried out to present flow field, temperature and concentration distribution in a
triangular enclosed space with corrugated base surface using finite element method. The cavity consists of an
absorber plate and two inclined glass covers. At the base corrugated wall high concentrations and temperature
are considered. The study was done for various wave lengths (0.1, ≤, λ, ≤, 1.0), thermal Rayleigh number
(103 ≤ Ra ≤ 105) and Prandtl number (0.071, ≤, Pr, ≤, 7). Isotherms, iso-concentration, streamlines, overall
Nusselt and Sherwood numbers are obtained for the aforesaid parameters. It is found that wave length plays
a dominant role on flow strength for any Rayleigh numbers. Variation of Prandtl number becomes significant
for greater values of Rayleigh numbers and multiple cells are formed at the lowest value of Prandtl number.
This paper aims to numerically investigate the effects of adding nanoparticles on the entropy generation of water-Al2 O3 nanofluid flows through a circular pipe under constant wall temperature also constant heat flux thermal boundary conditions in laminar regime. Approved formulations of mixtures are used for density and specific heat of the nanofluids. Nanofluid model proposed by Koo and Kleinstreuer [1] based on experimental data of Das et al. [2] is employed for conductivity of the nanofluids and an experimental correlation presented by Rea et al. [3] is used to model the viscosity of the nanofluid. The problem has been simulated numerically using a CFD finite-volume code and results are validated with the available experimental data. It is found that for the case of constant heat flux boundary condition, adding nanoparticles decreases the entropy generation and improves the thermal performance of water-Al2 O3 flow. Moreover optimum Reynolds number to minimize the ratio of nanofluid entropy generation number to water is obtained for this case. For the case of wall constant temperature boundary condition, adding nanoparticles to water leads to heat flux increase, therefore the entropy generation number remains approximately constant.
This paper deals with numerical investigation of double-diffusive natural convective flow in an annular space between confocal elliptic cylinders filled with a Newtonian fluid. Uniform temperatures and concentrations are imposed along walls of the enclosure so as to induce aiding thermal and mass buoyancy forces within the fluid. Equations of concentration, energy and momentum are formulated using the dimensionless form of transport equations in elliptic coordinates for laminar two-dimensional incompressible flow which is expressed in terms of stream function, vorticity, temperature and concentration. Laminar regime is considered under steady state condition. The coupled differential equations are discretized by the finite volume method (FVM) and are solved via an in house-built computer code. Beforehand, this last has been validated through reliable results available elsewhere. The present study considered the effects of pertinent parameters on fluid flow, heat and mass transfer: the Rayleigh number up to 5.105. Throughout the study, the Prandtl number has been varied from 0.3 to 1. The relevant results are presented in terms of isotherms, streamlines and iso-concentrations. In addition, the heat and mass transfer rate in the annulus is translated in terms of the average Nusselt and Sherwood numbers along the enclosure's sides. Based on the obtained results, it is concluded that, in the context of double diffusive natural convective flows in elliptic-shape annuli, the potential of the proposed approach is demonstrated.
The behavior of a prism-shaped solar collector with a right triangular cross sectional area is investigated numerically. The water-CuO nanofluid is taken as the functioning liquid through the solar collector. The leading differential equations with boundary conditions are solved by the penalty finite element method using Galerkin's weighted residual scheme. The performance of parameters in terms of temperature, mass, velocity distributions, radiative, convective heat and mass transfer, mean temperature and concentration of nanofluid, mid height horizontal-vertical velocities, and sub-domain average velocity field are investigated systematically. These parameters include the Rayleigh number Ra and the solid volume fraction φ. The outcome explains that the performance of the solar collector can be enhanced with the largest Ra and φ. The code validation shows excellent concurrence with the hypothetical outcome obtainable in the literature. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21039
Streamline-based simulation is extended to simulate non-isothermal two-phase flow of hot water injection in three-dimensional (3D) realistic field-scale reservoirs containing heavy oil. First the pressure equation is solved on the 3D Eulerian grid for a global time-step and the total velocity is calculated at cell faces. Then the streamlines are traced from injector wells to producers, implementing a semi-analytical method and the time-of-flight (TOF) is computed over the streamlines. The mass and energy transport equations are mapped onto streamlines using the TOF as the distance variable. The advective part of the transport equations are solved along the streamlines. The saturation and temperature are calculated in the TOF domain until the end of the global time-step and then mapped back to the 3D grid. The effects of gravity and heat conduction are included by an operator splitting technique, at the end of each global time-step.
A 2D petroleum reservoir model without gravity is tested to show the feasibility of the method. To further test the approach, a 3D heterogeneous model with a fine grid and multiple wells is simulated, and the results are compared with those of a commercial grid-based thermal simulator. The predicted saturation distribution, temperature and oil production at the wells are in good agreement with the commercial code; furthermore the streamline technique is significantly faster while generating results similar to those obtained using a conventional method that has a finer grid. We conclude that the streamline method can simulate non-isothermal two-phase flow of water–oil in heterogeneous porous media accurately with lower cost and better performance than grid-based approaches.
The unsteady laminar natural convection in an inclined square enclosure with heat-generating porous medium whose heat varies by a cosine function is investigated by a thermal equilibrium model and the Brinkman–Darcy–Forchheimer model numerically, with the four cooled walls of closure as isothermal. The numerical code based on the finite-volume method has been validated by reference data before it was adopted. Influence of dimensionless frequency and inclination angle on heat transfer characteristics in a square enclosure, such as flow distribution, isotherm, averaged Nusselt number on each wall, and time-averaged Nusselt number, are discussed, with specified value for Rayleigh number = 108, Darcy number = 10−4, Prandtl number = 7, porosity = 0.4, and specific heat ratio = 1. It is found that when the internal heat source varies by cosine, the Nusselt numbers of the four walls oscillate with the same frequency as the internal heat source; however, phase difference occurs. Moreover, frequency has little impact on time-averaged Nusselt number of the four walls, which is different from the phenomenon discovered in natural convection with suitable periodic varying wall temperature boundary condition. Moreover, inclination angle plays an important role in the heat transfer characteristics of the walls studied.
A numerical study is carried out on double-diffusive natural convection in a vertical annular porous layer whose vertical walls are at constant temperatures and concentrations. The investigation covers the range 10 Document Type: Research Article DOI: http://dx.doi.org/10.1080/104077899274822 Publication date: August 1, 1999 More about this publication? Information for Authors Subscribe to this Title ingentaconnect is not responsible for the content or availability of external websites (document).ready(function() { var shortdescription = (".originaldescription").text().replace(/\\&/g, '&').replace(/\\, '<').replace(/\\>/g, '>').replace(/\\t/g, ' ').replace(/\\n/g, ''); if (shortdescription.length > 350){ shortdescription = "" + shortdescription.substring(0,250) + "... more"; } (".shortdescription a").click(function() { (".originaldescription").slideDown(); return false; }); }); Related content In this: publication By this: publisher In this Subject: Heat By this author: Beji, H. ; Bennacer, R. ; Duval, R. ; Vasseur, P. GA_googleFillSlot("Horizontal_banner_bottom");
Two-dimensional double-diffusive natural convective heat and mass transfer in an inclined rectangular porous medium has been investigated numerically. Two opposing walls of the cavity are maintained at fixed but different temperatures and concentrations; while the other two walls are adiabatic. The generalized model with the Boussinesq approximation is used to solve the governing equations. The flow is driven by a combined buoyancy effect due to both temperature and concentration variations. A finite volume approach has been used to solve the non-dimensional governing equations and the pressure velocity coupling is treated via the SIMPLER algorithm. The results are presented in streamline, isothermal, iso-concentration, Nusselt and Sherwood contours for different values of the non-dimensional governing parameters. A wide range of non-dimensional parameters have been used including, aspect ratio (2 ≤ A ≤ 5), angle of inclination of the cavity (0 ≤ ϕ ≤ 85), Lewis number (0.1 ≤ Le ≤ 10), and the buoyancy ratio (− 5 ≤ N ≤ 5).
This paper presents the results of a numerical study of double-diffusive convection in an inclined rectangular collector filled with two parallel porous layers. Each porous layer is considered homogeneous, isotropic and saturated with the same fluid. The vertical walls of porous cavity are subjected to uniform temperature and concentration whereas the other surfaces are assumed to be adiabatic and impermeable. The set of equations governing the heat and mass coupled problem within the enclosure are solved numerically. The numerical results are presented and analyzed in terms of streamlines, isotherms, isoconcentrations lines and average Nusselt and Sherwood numbers. A scale analysis is used to characterize the effect of the permeability ratio on the heat and mass transfer. It is found that the numerical solutions of the full governing equations are in good agreement with the scaling results for some specific conditions. Optimum operating tilted angle are deduced.
Turbulent double-diffusive natural convection is of fundamental interest and practical importance. In the present work we investigate systematically the effects of thermal Rayleigh number (Ra), ratio of buoyancy forces (N) and aspect ratio (A) on entropy generation of turbulent double-diffusive natural convection in a rectangle cavity. Several conclusions are obtained: (1) The total entropy generation number (Stotal) increases with Ra, and the relative total entropy generation rates are nearly insensitive to Ra when Ra ≤ 109; (2) Since N > 1, Stotal increases quickly and linearly with N and the relative total entropy generation rate due to diffusive irreversibility becomes the dominant irreversibility; and (3) Stotal increases nearly linearly with A. The relative total entropy generation rate due to diffusive and thermal irreversibilities both are monotonic decreasing functions against A while that due to viscous irreversibility is a monotonic increasing function with A. More important, through the present work we observe a new phenomenon named as “spatial self-copy” in such convectional flow. The “spatial self-copy” phenomenon implies that large-scale regular patterns may emerge through small-scale irregular and stochastic distributions. But it is still an open question required further investigation to reveal the physical meanings hidden behind it.
This paper analytically examines the effects of adding nanoparticles on the entropy generation of water–Al2O3 and ethylene glycol–Al2O3 nanofluid flows through a circular pipe under uniform wall heat flux thermal boundary condition in both laminar and turbulent regimes. Approved formulations of mixtures are used for density and specific heat of the nanofluids, and a model developed by Maiga et al. [9] based on experimental studies is used for viscosity and conductivity of the nanofluids. It is found that adding nanoparticles improves the thermal performance of water–Al2O3 flow with Re numbers less than 40,000 and ethylene glycol–Al2O3 flow with Re