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Abstract
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.
... This paper introduces the piecewise information entropy calculation and the multi-microphone entropy weighting method (MMEWM) to analyze acoustic signals measured in a centrifugal compressor experimental setup. In physics, entropy represents the degree of disorder in a system, 25 and in statistics, it carries a similar meaning. [25][26][27][28] Signal changes before and during surge events inevitably lead to changes in entropy. ...
... In physics, entropy represents the degree of disorder in a system, 25 and in statistics, it carries a similar meaning. [25][26][27][28] Signal changes before and during surge events inevitably lead to changes in entropy. Therefore, changes in entropy allow for the assessment of surge occurrence likelihood. ...
Centrifugal compressors play a crucial role in energy and power systems, and compressor surge significantly impact their safe operation. Monitoring typical surge inception characteristics in a compressor can effectively serve as an early warning indicator, thereby enhancing safety. This paper presents the results of an acoustic experiment conducted on a centrifugal compressor setup. Four microphones were positioned in front of the compressor inlet to record the noise emitted as the compressor entered its surge region from a near-surge state. An entropy-based method is proposed to extract surge inception from acoustic signals by evaluating the informational complexity. Four types of entropy, including approximate entropy, sampling entropy, fuzzy entropy, and information entropy, were calculated from the acoustic signals. Their time-domain curves exhibit a clear increasing trend prior to surge inception. Further analysis reveals differing growth rates of the entropy curves among the four microphones, confirming the impact of microphone position on the capture of flow information and, consequently, on surge warning accuracy. Eventually, an entropy-weight method is proposed to eliminate the effects of positions and enhance surge warning capabilities by accounting for multiple acoustic signals.
... The efficiency of air separators, nuclear reactors, chillers, fuel cells, refrigeration, air conditioning, power generation systems, chemical processes, and renewable energy systems can be enhanced by reducing the system's entropy. Pioneer works on irreversibility was done by Bejan [45]. Shah et al. [46] investigated the performance of manganese nickel and zinc ferrite nanoparticles in heat transfer improvement of engine oil flow with entropy analysis. ...
... The entropy generation for the considered flow is mathematically defined as [45][46][47][48]53]: ...
The phenomenon of bioconvection in nanofluid flows represents a significant interdisciplinary research area that combines fluid dynamics, biotechnology, and nanotechnology. Understanding the interplay between biological organisms and nanoparticle-laden fluids is crucial for various applications in engineering, medicine, and environmental science. This study aims to scrutinize the production of entropy in bioconvective Sutterby nanomaterial flow over porous rotating disk. Impacts of surface roughness and Lorentz force are considered in relation to momentum. Mathematical expressions for energy and mass concentration are developed accounting Brownian and thermophoretic features of nanoparticles. Effects of thermal radiation and internal fluid friction are further measured in the thermal transport equation. Boundary layer norms are considered throughout modeling. PDEs demonstrating the flow are altered into ODEs via transformations. The numerical scheme Runge–Kutta-Fehlberg(RKF-45) is implemented via NDSolve code in Mathematica. The impacts of dominant parameters of flow on velocity, motile density, concentration, temperature, Bejan number, and irreversibility are deliberated. Physical quantities are studied numerically through tables. Results reveal that for larger magnetic and surface porosity variables velocity diminishes. The thermal field escalates for greater magnetic variable while it declines for higher Prandtl number. Entropy enhances for up surging values of radiation, diffusion, and Brinkman variables.
... It causes the irreversibility and induces energy losses; therefore, it is quite imperative to investigate the entropy generation of the system. A pioneering work in this regard was done by Bejan [48,49] by defining a Bejan number as a measure of thermal irreversibility versus the total entropy generation owing to fluid friction factors. Almakki et al. [50] studied entropy generation caused by the thermal radiation in a magneto nanofluid over nonlinear expanded sheet. ...
... The study of entropy generation is not complete without analyzing the Bejan number Be ð Þ. The Bejan number Be ð Þ is defined as [48,49] It is obvious from Eqn. (33) that 0 � Be � 1:0, with the significance that when Be ¼ 0, which clearly indicates that the entropy generation owing to thermal irreversibility is dominated by the entropy generation caused by the fluid friction and mass transportation. Meanwhile, in the reverse case, we can perceive for Be ¼ 1:0. ...
... Following the pioneering studies of Bejan [15][16][17], entropy generation analysis for convective flow has gained prominence as a basis for energy optimization methods. He contended that the second law of thermodynamics can be applied to measure thermodynamic irreversibility confronted by thermo-fluidic systems. ...
... Following Bejan [15][16][17], the volumetric rate of entropy generation for the current problem is ...
The paper presents the execution of the Adomian Decomposition Method to treat thermo‐fluidics of Williamson fluid flow in a vertical parallel plates channel filled with Williamson fluid–saturated porous medium. The channel walls experience asymmetric cooling. The fully developed flow setup constitutes a non‐linear boundary value problem tackled by the Adomain Decomposition Method (ADM) with the help of MAPLE. The computational procedure yields velocity, temperature distributions, skin friction, and Nusselt number. The results thus obtained are compared with those obtained by the RK‐Fehlberg numerical method to ascertain the accuracy of ADM. The results for quantities of interest viz. Skin friction. Nusselt number, entropy, and global entropy are shown in tabular/pictorial forms. These quantities exhibit qualitative and quantitative responses to embedded parameters discussed in detail in results and discussions section.
... The optimization of the efficiency of machine processes and minimization of energy losses have led many engineers and scientists to focus on the investigation of entropy generation. Bejan [15] proposed a thorough investigation of entropy generation. Khan et al. [16] analyzed the magnetized flow of Williamson hybrid nanoparticles (titanium oxide and cobalt ferrite) with the impact of surface-catalyzed reactions and entropy generation across the vertical needle. ...
... Equation (13) therefore turns into The analytical solution that depends on boundary conditions for equation (15) can be obtained as follows: ...
The need for efficient nanotechnology has led to unexpected developments. Conserving continuous thermal propagation is essential in many industrial and thermal systems because it improves the efficiency of thermal engineering engines and machinery. Therefore, a promising platform to increase thermal power energy is the hybridization of magnetic nanoparticles in a heat-supporting, non-Newtonian fluid. In light of the above applications, a mathematical model is established to analyze the variable fluid features of the thermally radiative and chemically reactive flow of a micropolar Williamson ternary hybrid nanofluid with electromagnetohydrodynamic and electroosmosis forces on a porous stretching surface. Stratification boundary conditions and variable fluid properties were used to analyze the thermal and solutal behavior of the fluid flow. Furthermore, to measure the disorder of the flow system, entropy generation was considered by the impact of Joule heating and viscous dissipation. To develop the numerical scheme BVP4C in MATLAB, we first converted the mathematical flow model into two ordinary differential equations using a suitable transformation. The graphical and numerical results were determined against several parameters of a ternary hybrid nanofluid ( MWCNT , A l 2 O 3 , SiC ) ({\rm{MWCNT}},\hspace{0.25em}{\rm{A}}{{\rm{l}}}_{2}{{\rm{O}}}_{3},\hspace{0.25em}{\rm{SiC}}) and unary nanofluid ( A l 2 O 3 ) ({\rm{A}}{{\rm{l}}}_{2}{{\rm{O}}}_{3}) . The results indicate that the heat transfer rate is more prominent in the ternary hybrid nanofluid than in the unary nanofluid because the addition of nanofluids to the base fluid is used to improve the heat transport rate. It can be seen from the figures that a greater estimation of the magnetic and electric field parameters improves the fluid velocity because, for low values of M ≤ 1 M\le 1 , the aiding force is dominant compared to the retarding force, which results in an improvement in the velocity profile. Furthermore, the entropy generation rate increases for higher values of the Brinkman number and temperature ratio parameter because more heat is produced due to the greater values of Br {\rm{Br}} .
... Many researchers have contributed their work on entropy generation for a MHD flow. Bejan [6] analysed in detail the generation of entropy owing to heat transfer and viscous effects along finite temperature gradients. Bassam et al. [7] analysed the entropy for free convective flow from a rotating cylinder. ...
... The entropy generation for a free convection is associated with transfer of heat and flow friction of the fluid. The total entropy ( ) t S , according to Bejan [6] is expressed as follows: ...
The purpose of this study is to examine the entropy generation for a Magnetohydrodynamic flow of a Casson fluid subject to a vertical cone. Here the impact of reaction by chemical and diffusion-thermo is scrutinized. Physical aspects of radiative flux transverse to the surface are deliberated. The governing non-linear PDEs and the expression for entropy generation are non-dimensionalized with the help of dimensionless quantities. Finite difference technique is implemented to get numerical and graphical results for the non-linear system. Bejan number for the heat transfer is also examined. The results obtained shows that entropy generation and Bejan number are strongly influence by the embedded flow parameters.
... This analysis supports the enhancement of efficiency and cost-effectiveness in areas such as cooling of electronic devices, designing heat exchangers, and improving energy storage systems. The pioneering work on entropy production and its minimization was presented by Bejan [48,49]. Since then, several researchers have analyzed entropy generation in viscous normal and anomalous fluid flow in various situations including Chauhan and Kumar [50] and Butt et al. [51]. ...
The study of heat and mass transport in non‐Newtonian fluid flow over a stretching surface accompanying relevant characteristics is important in several engineering and industrial processes like annealing and thinning of copper wires, aerodynamic extrusion of plastic and rubber sheet, glass fiber, and so forth. Based on significant practical applications, the objective of this investigation is to assess the time‐dependent flow of Williamson fluid influenced by porous sheet stretching in exponential manner accompanied by thermal and mass transport and entropy generation. Various factors affecting fluid flow, thermal and mass transport (viscous dissipation, non‐linear radiation, porous media, chemical reaction, and heat source) are considered. The regulating PDEs are turned into ODEs in nondimensional form utilizing adequate similarity transformation relations. The problem is solved numerically on MATLAB adopting the Keller‐Box scheme. On fluid flow, temperature, and concentration distribution the effects of relevant parameters are depicted by drawing sketches and discussed. Besides, second law analysis is also evoked in the study in terms of entropy generation accompanying the Bejan number. Moreover, quantities of physical significance such as skin friction coefficient, Sherwood number, and Nusselt number are computed, compared with prior research and found in excellent agreement. It is concluded that temperature profile magnifies due to radiation and heat generation effects. The reaction coefficient and order of the reaction exhibited opposite effects on concentration profile. It is also concluded that entropy production reduces with increasing slips and temperature difference parameter, while opposite effect is observed due to Brinkman number. Furthermore, it is observed that skin‐friction coefficient at the surface decreases with velocity slip and non‐Newtonian parameter however, trend is reversed due to unsteadiness parameter. The results of the study may find applications of practical importance in engineering fields such as designing heat exchangers, cooling processes, improving energy storage systems, and so forth.
... Thus, it is necessary to minimize the entropy production to enhance the performance of the thermal system. Optimisation of the entropy production optimization is useful in various engineering applications like heat exchange, power plants, heat pumps, electronic cooling systems, refrigerators etc. Bejan [18] initiated the study of entropy generation minimization. Since then, many researchers investigated the entropy generation optimization with different physical aspects [8,10,19,20]. ...
Legendre wavelet based numerical method has been developed for the solution of the system of non-linear differential equations arising in the study of a Marangoni convective flow of dusty Ree-Erying fluid over a Riga plate in Darcy-Forchheimer medium with Soret, Dufour, non-linear radiation, activation energy effects and entropy generation analysis. The proposed method is validated by comparing the solutions of the test problem with the Bernoulli wavelet based numerical method and the exact solution and by comparing the results of the considered dusty fluid problem for some fixed parameters with the previously published results. The effects of various factors on the velocity, thermal, concentration attributes are studied by using the proposed method. It is observed that the Ree-Erying fluid parameter and Marangoni ratio parameter escalates the velocity and declines the temperature and concentration. The opposite behaviour is observed for Deborah number. The concentration declines for higher chemical reaction parameter and improves for activation energy. Both entropy generation and Bejan number escalates for radiation parameter and diffusion parameter. The proposed method is reliable, fast computable and powerful tool to solve the differential equations.
... The entropy generation due to heat transfer is given as follows [57]: ...
Prior research suggests that the use of nanotechnology may greatly improve the efficiency of enhanced oil recovery methods, especially hot fluid injection. The thermophysical characteristics of the nanofluid may have an enormous effect on how well the injection process works. However, it takes both time and resources to conduct laboratory analyses of the effects of thermophysical characteristics on the effectiveness of nanofluid-based improved oil recovery methods. Computational models can effectively forecast the thermophysical characteristics of nanofluids and how they affect oil recovery efficiency, which helps overcome this difficulty. The current study investigates the flow of vacuum residue (VR) fluid, which generates entropy when suspended graphene oxide (GO) nanoparticles. When mixed convection and variable thermal conductivity are present, a static/moving wedge allows the nanofluid to propagate. The continuity, energy, entropy, and momentum equations form the foundation of the governing model. We use certain similarity variables to simplify the suggested mathematical formulations into forms for nonlinear differential equations (DEs). We show the results of the reduced equations using the Chebyshev collocation method. We present the graphical and numerical results for all the emerging parameters. For enhanced oil recovery applications, the current results are beneficial.
... Bejan [35][36] worked on "entropy generation analysis (EGA)" for thermal design and convective heat transportation. Numerous investigations about the practical use of entropy production have been analyzed in the works of Cengel and Boles [37]; Mahian et al. [38]; Parvin and Chamkha [39] etc. ...
... In the aforementioned equations, m is the mass flow rate through the channel, Aht is the total heat transfer area, cp,f and kf are specific heat capacity and thermal conductivity of the fluid at the arithmetic mean temperature of the outlet and inlet. Additionally, Q is the total heat transfer rate, Twall is the temperature of the heated walls, To assess thermodynamic performance of the channels with protrusions, the total volumetric entropy generation rate ( g S ), based on the obtained velocity and temperature distribution across the computational domain can be calculated as follow [21,22]. ...
In this study, a flat-plate channel configured with pyramidal protrusions are numerically analysed for the first time. Simulations of laminar single-phase fluid flow and heat transfer characteristics are developed using a finite-volume approach under steady-state condition. Pure water is selected as the coolant and its thermo-physical properties are modelled using a set of temperature-dependent functions. Different configurations of the channel, including a plain channel and a channel with nature-inspired protruded surfaces, are studied here for Reynolds numbers ranging from 135 to 1430. The effects of the protrusion shape, size and arrangement on the hydrothermal performance of a flat-plate channel are studied in details. The temperature of the upper and lower surfaces of the channel is kept constant during the simulations. It is observed that utilizing these configurations can boost the heat transfer up to 277.9% and amplify the pressure loss up to 179.4% with a respect to the plain channel. It is found that the overall efficiency of the channels with pyramidal protrusions is improved by 12.0-169.4% compared to the plain channel for the conditions studied here. Furthermore, the thermodynamic performance of the channel is investigated in terms of entropy generation and it is found that equipping the channels with pyramidal protrusions leads to lower irreversibility in the system.
... Entropy, a key thermodynamic irreversibility parameter, occurs in the second law of thermodynamics. The analysis of entropy production makes a significant contribution to thermal systems design decisions and thus supports optimization of cost and energy in science and engineering areas like the cooling of electronic devices, heat exchangers, energy storage systems (Yessef et al. [51], Chojaa et al. [52], Loulijat et al. [53], and Hamid et al. [54]), etc. Bejan [55,56] presented pioneering work on entropy production and its optimization. Baytas [57] analysed entropy production in free convection via porous medium along with thermal transport and mass transport in a tilted permeable enclosure. ...
This research endeavor investigates the natural convection flow of Williamson fluid in the region between two vertical parallel flat plates via a porous medium. Impacts of viscous dissipation, joule heating, exponential space, and thermal-dependent heat sources (ESHS/THS) are invoked. Mass transfer is also studied in accounting for chemical reaction impact. The governing non-linear PDEs are reduced to ODEs in non-dimensional form under adequate transformation relations. The numerical technique, namely, Runge-Kutta fourth-order, is utilized to tackle the problem with the shooting method. Additionally, second-law analysis is presented in terms of entropy production. The effects of numerous regulating parameters occurred in the problem relevant to flow, heat and mass transport, and entropy production are discussed via graphical mode of representation. Moreover, the quantities of physical significance are computed, displayed in graphical form, and discussed. For verification of acquired results, a comparison is also made using HPM with prior research, which was found to be in excellent agreement. It is concluded that the fluid temperature field enhances with upsurging values of pertinent parameters. The influence of the convective surface parameter and order of reaction are found to make augmentation in mass diffusion. Further, the effect of joule heating is noticed to increase the rate of heat transfer, while the reverse scenario is observed with upsurging values of heat source parameters. The influence of viscous dissipation is seen to increase entropy production.
... It underscores the processes that involves transfer or conversion of energy are irreversible. Bejan [3][4][5] in his innovative works shown that entropy generation minimization can be actualised by selecting parameters' vlues that have bearing on entropy generation. In thermofluidic configurations entropy production is caused by heat transfer, fluid friction, imposed magnetic field, and radiative heat transfer. ...
... It has been realized that a theoretical treatment to thermofluidics can be undertaken for thermodynamic efficiency based on second law. Bejan [4][5] shown that thermo-fluidic systems are essentially irreversible where entropy can be simulated by invoking second law of thermodynamics. Since then the domain has received much attention. ...
The paper offers differential transform method strategy to compute entropy for Couette non-Newtonian MHD fluid flow. The flow takes place in a horizontally placed channel composed of upper impermeable wall and naturally permeable bottom. The motion sets in by the movement of upper wall that bears uniform velocity. The lower wall of the channel is a natural porous bed that enables hydrodynamic slip. Since there is no external pressure gradient, therefore the filter velocity in the porous region is assumed to be zero. This assumption is valid as per Saffman condition. The channel walls bear different uniform temperatures. The phenomenon constitutes a non-linear boundary value problem for which differential transform method is invoked to get velocity and temperature distributions in power series. The DTM solution has been compared with numerical solution derived by Runge Kutta Fehlberg 45 strategy. A rigorously computed data set for the Skin friction and Nusselt number has also been presented. The findings showcased in tables and graphs are discussed.
... In several engineering systems, the entropy generation has different causes. It can be seen in the thermal systems that the initial starting of entropy generation is heat transfer, mass transfer, dissipation of viscous, heat coupling, conduction of electronics and chemicals reacting [4,5]. In the applications mentioned above, the researchers and mathematicians utilized several methods to solve a bunch of differential equations of ordinary as well as arbitrary (fractional) order, especially the fractional partial differential equations (FPDEs). ...
In this present article, by using the Iterative Laplace Transform Method (ILTM), the diffusion equation of fractional order is solved. The ILTM, which works as a combination of two methods, the iterative method and the other is the Laplace transform method, is applied to several diffusion equations to obtain analytical solutions. The proposed method gives the closed-form of series solutions in terms of the Mittag-Leffler function, which is a queen of functions in fractional calculus. The main aim of this work is to present a simple but reliable algorithm for the solution of diffusion equations of the multi-dimensional type, which clearly describes the materials of density dynamics in the diffusion process. The results obtained by using the ILTM approach indicate that this approach is attractive computationally and implemented easily. Due to its straightforward approach and comfortable way of solving problems, the ILTM can be utilized to solve nonlinear fractional problems in various applied and engineering sciences.
... Heat exchangers, turbomachinery, and gadget cooling are among of the practical uses of EG. Bejan [27] first used mathematical modelling to evaluate EG in nanofluid fluid flows. Ellahi et al. [28] reported on EG in radiative water-based fluid-submerged copper nanoparticles, taking the impacts of form factor into consideration. ...
The aim of this study is to examine the entropy generation (EG) associated with the transfer of mass and heat in a concentration-dependent fluid with thermal radiation and activation energy, specifically in the context of an unsteady Riga Plate with gyrotactic microorganism. It is important to solve the ordinary differential equations generated from the controlling partial differential equations using Lie symmetry scaling to verify their quality and reliability. The system’s anticipated physical behavior is compared to Mathematica’s Runge–Kutta–Fehlberg numerical solution. Source parameters are essential for validation since they offer accurate results. Methodically change these values as a percentage to determine how they affect the unsteady fluid’s density, mass, and heat transfer over the Riga plate. Velocity, temperature, nanoparticle concentration and microorganism concentration profiles decrease with varying values of the unsteadiness parameter. EG increases with increasing values of concentration difference, thermal radiation, and Reynold number parameters. The Nusselt number experiences a 26.11% rise as a result of radiation when the unsteadiness parameter is A = − 0.25 A=-0.25 , in comparison with the scenario without radiation. Mass transfer upsurges with increasing values of the Brownian motion parameter and reduces with increasing values of thermophoresis parameter. To verify our conclusions, we compare calculated data, specifically the skin friction factor, to theoretical predictions. Tabular and graphical data can show how physical limits affect flow characteristics.
... The primary processes in thermal systems that generate entropy include chemical reactions, heat transmission, viscous dissipation, and electrical conduction. Bejan [38] explored the several effective components that contribute to EG in industrial thermal engineering, which is the process that destroys a system's potential work. While utilizing the second rule of thermodynamics to study heat transmission and thermal design. ...
... Trends Sci. 2024; 21 (11): 6966 2 of 23 Entropy production concept and its minimization in thermal systems was introduced by Bejan [2,3]. Chauhan and Kumar [4], discussed entropy production in third grade fluid flow using Reynold's model viscosity, in partially filled annulus. ...
In this study, entropy production in flow along with heat transport of non-Newtonian fluid via porous medium, is analyzed. For fluid flow via porous medium, a modified Darcy resistance term, is taken in the momentum equation for third-grade fluid. Temperature-dependent viscosity is considered using Vogel’s model viscosity. Using adequate transformations, the momentum and heat transport equation are reduced to non-dimensional form and solved analytically invoking homotopy analysis method on MATHEMATICA software. Effects of parameters arising in the study are depicted by graphs on velocity distribution, temperature distribution, and entropy production with Bejan number and discussed. For validity of current findings, the values of velocity and temperature are computed for particular values of the parameters and equated with previously published results, excellent agreement achieved. Furthermore, skin-friction coefficient and Nusselt number values are expressed in tabular form for various values of relevant parameters and discussed. It is noticed that slip parameters and reduce the entropy generation number . Also noticed that skin friction coefficient upsurges with rising velocity slip parameter value while, effect of temperature slip parameter is observed to lessen Nusselt number in the absolute sense. HIGHLIGHTS Entropy production in third grade non-Newtonian fluid flow and heat transfer in a channel via porous medium is investigated in the presence of a heat source. Slip boundary conditions are applied. The resulting governing equations are solved analytically using the homotopy analysis method (HAM). Maximum entropy production observed near the lower wall of channel and Bejan number attains maximum value in middle of the channel. GRAPHICAL ABSTRACT
... The performance of thermal machines such as air conditioners, heat pumps, and energy plants is measured due to entropy generation. Bejan [38] for the first time addressed the entropy generation problem. Alkanhal et al. [39] investigate entropy generation for magnetohydrodynamic flow of nanofluids with convective heat transfer. ...
... In many engineering applications the heat and mass transformation are important demand; however, the efficiency of these systems decreases due to irreversibility generation which can be indicated by entropy. [47][48][49] Entropy can be generated due to transfer of heat, transfer of mass, viscosity of the fluid, and magnetohydrodynamic and many researchers try to investigate in these areas to understand how to decrease these irreversibility's and hence decreases the efficiency losses of the system. [50][51][52][53] The effect of entropy generation and combined diffusive in a lid driven cavity filled with nanofluid was numerically studied by Mondal and Mahapatra. ...
The current work extensively investigates double‐diffusive of nano‐encapsulated phase change material in a thermal storage system partially filled with porous foam. The generation of irreversibilities and the influence of Soret/Dufour and magnetohydrodynamic effects are also considered. The circular cold cavity contains a corrugated hot cylinder covered by an annular foam. The considered parameters are Rayleigh number (10³–10⁵), fusion temperature (0.1–0.9), Stefan number (0.1–0.9), volume concentration of nanoparticles (0–0.05), Darcy number (10⁻⁴–10⁻¹). Hartmann number (0–80) and the undulations of the inner (3–9). The numerical analysis has exploited the finite element approximations. The results indicate that Rayleigh and Hartmann numbers greatly influence the fluid flow, isotherms, concentrations and the melting/solidification region. The fusion has also a great influence on the melting/solidification region while there is no evident influence on the flow, isotherms and the concentrations where both Nusselt and Sherwood numbers change with around 5% with the change of the fusion temperature and Stefan number. In contrast, both values are decreased by around 30% by decreasing the Da number from 0.1 to 10⁻⁴. Furthermore, the change of the undulations number has very low influence on heat transfer, mass transfer and the melting/solidification region.
... In fundamental physics, it relates to key areas such as nonlinear dynamics and nonequilibrium thermodynamics related to fluid instabilities [1][2][3][4]. In industry, these transitions are crucial for manufacturing processes using transport phenomena [5][6][7][8][9]. Rayleigh-Bénard convection-a classic example of thermal convection-has been extensively studied both theoretically and experimentally for many years [10][11][12][13][14][15][16][17]. ...
In this study, we evaluated the nonlinear dynamics of convection flow using the thermodynamic variational principle, focusing on scenarios where multiple external forces, such as a thermal gradient and rotational field, are applied to a shallow annular pool. We observed that with the increase in the thermal gradient, the flow changed from an axial flow to a rotational oscillatory flow with the wave amplitudes aligned. Further increasing the temperature difference led to a rotational oscillatory flow characterized by alternating wave generation and annihilation. Our analysis of the flow, considering heat fluxes orthogonal to the thermal gradient, allowed us to describe the flow state as a phase at equilibrium. The state transition of the flow was accompanied by a discontinuous jump in the heat flux, which occurred at the intersection of the entropy production curves. The first transition occurred at a temperature difference ΔT=12.4 K Marangoni number,Ma=1716 and the second at ΔT = 16.3 K Ma=2255. Analysis based on entropy production could accurately predict the observed transition points.
In this paper, the analysis of the 2nd law of thermodynamics characteristics of assisted mixed convection heat transfer coupled with fluid flow within a vertical convergent isothermal channel is numerically carried out. The numerical model is undertaken for 2D, laminar and steady flow using finite volume approach and air as working fluid. The analysis focused on two pertinent geometric situations namely the variation of the minimal distance (Dmin) of the convergent channel while keeping the convergence angle fixed, and the change of the latter (2°, 10°, and 20°) while Dmin kept unchanged. Whereas, Dmax was used as the characteristic length. The measurements are performed for the following buoyancy-assisted cases: upward/downward flow within hot/cold walls. Several buoyancy parameters are considered ranging from 0.1 to 10 at Reynolds number equal to 100. The effect the aforementioned geometric parameters on entropy production and its distribution is investigated. The results revealed that the energy degradation is dominated by heat transfer irreversibility. Also, this latter is more influenced by Dmin variations.
In light of the rising demand for improved heat transfer in thermal systems, this work offers a unique technique for boosting heat transfer capacity and reducing entropy generation using a ternary nanofluid. Moreover, constant pressure gradient, magnetic field, Joule heating, and thermal radiation also contribute to the flow dynamics. The 2D mathematical model is solved numerically using a finite difference method and the simulations are done in MATLAB. The obtained results show that ternary nanoparticles not only increase the thermal rates but are also helpful in maintaining the irreversibility of a system. It is also observed that the heat transfer of the base fluid increased by 7.5%, 8.3%, and 8.5% on adding TiO, CuOTiO, and MgOCuOTiO nanoparticles, respectively.
Magnetohydrodynamic flow efficiency and irreversibility improvement research are multiple problems that arise when electroosmosis forces affect Buongiorno’s nanofluid in a complicated peristaltic tapered channel. Thermal energy and temperature gradients cause nanoparticles to migrate randomly, affecting flow efficiency and irreversibility. Sometimes the infected veins generate complex peristaltic waves on its walls. The mathematical model that characterizes the motion of Jeffrey magnetohydrodynamic Buongiorno’s nanofluid inside a complex tapered peristaltic channel, considering the effects of electroosmotic forces, is discussed. The long wavelength and low Reynolds numbers approximation is considered. The approximate solution of the nonlinear system of partial differential formulas is obtained using the Adomian decomposition method. Also, the irreversibility of the system and entropy generation are being studied. Flow characteristics with biophysical and thermal parameters are plotted and discussed. The improvement in the interstitial distances that make up the nanofluid in turn enhances the Bejan numbers. So, one of the important results is that when the increment of Brownian motion and thermophoresis of the nanoparticles, the Bejan numbers are raised significantly. Both the Jeffrey parameter and Debye–Huckel parameter work to upsurge the loss of kinetic energy within the molecules, which reduces the temperatures inside the nanofluid and thus reduces the entropy rate, in contrast to the rest of the parameters that raise the kinetic energy inside the molecules that make up the nanofluid.
Purpose
The heat transport phenomenon in which energy transfers due to temperature differences is an important topic of interest for scientists in recent times. It is because of its wide range of applications in numerous domains such as electronics, heat dispersion, thermoregulation, cooling mechanism, the managing temperature in automotive mobile engines, climate engineering, magnetoresistance devices, etc. On account of such considerations, the magnetohydrodynamic (MHD) entropy rate for nanomaterial ( CoFe 2 O 4 / C 2 H 6 O 2 ) and hybrid nanomaterial ( CoFe 2 O 4 + MoS 4 / C 2 H 6 O 2 ) is analyzed. The Darcy–Forchheimer relation is utilized to describe the impact of a porous medium on a stretched sheet. Two nanoparticles molybdenum ( MoS 4 ) and cobalt ferrite ( CoFe 2 O 4 ) are combined to make hybrid nanomaterial ( CoFe 2 O 4 + MoS 4 / C 2 H 6 O 2 ). Heat flux corresponds to the Cattaneo–Christov model executed through heat transfer analysis. The influence of dissipation and heat absorption/generation on energy expression for nanomaterial ( CoFe 2 O 4 + MoS 4 / C 2 H 6 O 2 ) and hybrid nanomaterial ( CoFe 2 O 4 + MoS 4 / C 2 H 6 O 2 ) is described.
Design/methodology/approach
Nonlinear partial differential expressions have been exchanged into dimensionless ordinary differential expressions using relevant transformations. Newton’s built-in shooting method is employed to achieve the required results.
Findings
Concepts of fluid flow, energy transport and entropy optimization are discussed. Computational analysis of local skin friction and Nusselt number against sundry parameters for nanomaterial ( CoFe 2 O 4 / C 2 H 6 O 2 ) and hybrid nanomaterial ( CoFe 2 O 4 + MoS 4 / C 2 H 6 O 2 ) is engrossed. Larger magnetic field parameters decay fluid flow and entropy generation, while an opposite behavior is observed for temperature. Variation in magnetic field variables and volume fractions causes the resistive force to boost up. Intensification in entropy generation can be seen for higher porosity parameters, whereas a reverse trend follows for fluid flow. Heat and local Nusselt numbers rise with an increase in thermal relaxation time parameters.
Originality/value
No such work is yet published in the literature.
The study of fluid flow in cylindrical shapes under the effect of electric fields is of utmost importance because of its vast applications in industrial, agricultural, and biomedical domains, as well as in drilling machines, equipment, transport brakes, and vehicles. The purpose of this research is to analyze the influence of Hall impacts, slippage effects, and thermal relaxation time on the magnetohydrodynamic flow near an extended cylinder or flat plate. An assessment of entropy generation is carried out. Results are determined by the process of elongating a planar surface and a cylindrical object. The velocity field and entropy production are greater in the case of a stretched cylinder compared to a stretching flat plate. The choice of an appropriate stretching surface may have an impact on the thermal conductivity of the boundary layer. Velocity, temperature, and entropy are influenced by several factors including the Eckert number, thermal relaxation time, transverse curvature, magnetic field, Hall effect, molecular slip, and mixed convection parameters. These characteristics influence the movement of fluid, the transfer of heat, the measure of disorder (entropy), and the Bejan number. The variables mentioned cause changes in skin friction and Nusselt values. The Hall effect has advantages in reducing friction and enhancing heat transfer in industrial and technical processes.
The gas-liquid supersonic separator is a convergent-divergent nozzle in which condensation and phase change at speeds higher than sound are the characteristics of this device. The fluid flow, mass, and heat transfer in supersonic separators are not understood well due to the complicated interaction of the supersonic flow and phase change. In this research, the virial gas equation of state and a mathematical model have been used to accurately predict spontaneous condensation using nucleation and droplet growth theories. The droplet average radius and pressure distribution obtained from the numerical model are well consistent with the experimental data. The results showed that with a 3.5% decrease in inlet temperature at a constant pressure, the average radius of the outlet droplets increased by more than 40%. Also, with about a 40% increase in inlet pressure at a constant temperature, the maximum liquid mass fraction increased by more than 90%. Therefore, low temperature and high pressure at the inlet are necessary to improve the separation efficiency. Also, the lowest entropy generation rate due to temperature changes is related to the highest pressure and the lowest temperature, and the lowest entropy generation rate due to pressure changes is related to the lowest temperature and pressure. The Bejan number calculation showed that irreversibility is affected by the effects of fluid friction compared to heat transfer.
Purpose
The current work investigates an unsteady squeezed flow of hybrid-nanofluid between two parallel plates in occurrence with a uniform transverse magnetic field. Water is used as base fluid mixed with Graphene Oxide (GO) and Copper (Cu) nanoparticles. The flow considered here is under slip boundary conditions.
Design/methodology/approach
The governing PDEs are transmuted into ODEs by applying an appropriate similarity transformation and then solved numerically using the 4th order R-K method with shooting technique. Graphical illustrations for velocity, temperature, entropy generation ( N G ), Bejan number ( B e ), streamline etc. are presented and discussed in detail from the physical point of view. The nature of the Nusselt number is also studied numerically through contour plots for different flow parameters.
Findings
There is no funding obtained for the research work.
Social implications
This kind of study may be used in various fields including polymer processing, lubrication apparatus, compression including hydrodynamical machines compression, food processing etc.
Originality/value
It is observed that very little investigation has yet been made about the movement of hybrid nanofluid between two analogous plates.
This chapter highlights nanofluids containing nanoparticles dispersed within a base fluid. The emphasis is on understanding the dynamic behavior, particularly nanoparticle's exceptional thermal transport properties. The most prominent feature, enhanced thermal conductivity compared to base fluids, is explored in detail. This chapter also explores nanoparticle material properties, size distribution, and interfacial phenomena. Beyond thermal conductivity, the chapter explores the rheological behavior of nanofluids. The influence of nanoparticle characteristics on viscosity, including potential shear-thinning or thickening effects, is discussed. This chapter explores how the introduction of nanoparticles modifies flow dynamics within nanofluids. This includes alterations to flow velocity profiles, boundary layer thickness, and flow stability. The interplay between nanoparticle type, concentration, and size with these flow characteristics is comprehensively analyzed. Finally, the chapter highlights the immense potential of nanofluids in various engineering applications, with a specific focus on their role in enhancing heat transfer efficiency. Promising examples include microelectronics cooling, where nanofluids can significantly improve heat dissipation in miniaturized devices, application in solar collectors to optimize energy absorption and conversion, as well as their potential use in engine thermal management for improved engine performance and fuel efficiency.
The significance of the present article is to enhance the thermal management and energy efficiency of complex engineering infrastructures such as energy storage systems, modern electric vehicles, thermal insulations, heavy‐duty machinery, and production units. This research aims to understand the intricate relationship between the thermal conductivity performance of ternary () hybrid nanomaterial and entropy generation to optimize material design and efficacy. A synergetic combination of three distinct nanomaterials silicon dioxide, ferric oxide, and titanium oxide with ethylene glycol and water in the ratio 3:2 as a base solvent is comprised of contributing unique thermophysical properties. To elucidate the impact of this hybrid composition on thermal conductivity, various factors are analyzed. The advanced computational technique of Artificial intelligent feed‐forward neural network (AIFFNN) is utilized. The problem governed the system of PDEs, which is transformed into ODEs by dimensionless similarity. Adams method provided the dataset which is filtered and embedded into Marquardt–Levenberg Algorithm (LMA). The study examines the role of nanomaterial constituents, morphology, and boundary conditions on thermal performance and entropy generation. Graphical analysis of velocity, temperature, and entropy is provided with respect to varying parameters, including surface absorption ( λ ), magnetic strength (Tesla M ), radiation parameter ( Rd ), Brownian motion ( Br ), and Eckert number ( Ec ). The findings have practical significance for optimizing material design in engineering and industrial applications.
The present study employs the predictor homotopy analysis method (PHAM) to investigate the behaviour of incompressible, steady ternary hybrid nanofluid flow through a converging or diverging channel (non‐parallel plates). The study aims to capture multiple solutions containing various shapes of nanoparticles, including spherical (Alumina [Al 2 O 3 ]), platelet‐like (Graphene [Gr]), and cylindrical (carbon nanotube [CNT]). The impact of physical parameters (such as Reynolds number, nanoparticle volume fractions, and heat source/sink parameters) on critical physical quantities has been studied. The study also considers the backflow regime, which results in multiple flow patterns in converging plates but is absent in diverging ones. Additionally, the article deals with a second‐law analysis assuming several parameters, and PHAM is used to investigate the temporal stability of both solution branches. The results show the existence of a stable branch with positive eigenvalues. Stability analysis confirms that the upper branch of the solution is physically significant. The study contributes to understanding the behaviour of nanofluid flow and its applications in various fields.
The present research employs a neural network, specifically the Levenberg-Marquardt algorithm, to characterize the entropy optimization performance in the electro-magneto-hydrodynamic flow of a Casson tetra hybrid nanofluid over a rotating disk. The problem was formulated mathematically using equations for momentum, continuity, and temperature. The dimensional partial differential equations governing the system are transformed into ordinary differential equations and solved numerically. The results were presented of the flow parameters in both tabular and graphical formats. This trained neural network is then utilized to predict the heat flow velocity and Nusselt number of the rotating disk. The developed model was evaluated using mean square error, error analysis, and regression analysis, thereby confirming the consistency, accuracy and reliability of the designed technique. The best validation performance for skin friction and the Nusselt number for the Casson tetra-hybrid nanofluid flow across a rotating disk is 8752e-05 at epoch 95 and 0.00033239 at epoch 37. Training, validation, testing, and all performance metrics of the ANN model are close to unity. As magnetic field strength increases, temperature profiles rise in di-hybrid, ternary-hybrid, and tetra-hybrid nanoparticle scenarios. Tetra-hybrid nanofluids are considered superior fluids when compared to di-hybrid, ternary-hybrid, and tetra-hybrid nanofluids. This optimization method holds promise for diverse applications in biotechnology, microbiology, and medicine, offering significant potential for various fields.
In this study, we aim to investigate the entropy production in the magnetohydrodynamic (MHD) flow of hybrid nanofluids over permeable rotating disks. We will analyze the entropy production within a three‐dimensional MHD flow of Ag‐MgO nanofluid over a rotating porous disk with variable fluid properties. Our analysis will incorporate time‐dependent radial stretching and slip effects on velocities and temperature. Moreover, the study will take into account exponentially temperature‐dependent viscosity and nonlinear thermal radiation. The study uses self‐similar transformations to convert the coupled nonlinear partial differential equations into a set of nonlinear ordinary differential equations. Numerically solving these equations involves using a shooting technique and relies on the 4th‐order Runge–Kutta–Fehlberg method. The rotation of the disk introduces a parameter that accelerates fluid motion. The study explores heat transfer rate, skin friction, and entropy production quantified by the Bejan number. Various factors, including magnetic field intensity, disk rotation, thermal radiation, and variable viscosity, influence this quantification. The outcomes of the study can enhance system efficiency through suitable parameter choices, deepening our understanding of entropy generation and system performance under varying factors. This research is important for improving heat transfer processes, reducing energy waste, and improving the design and operation of advanced fluid systems in engineering applications. The results could lead to innovations in thermal management, energy conservation, and sustainable engineering practices.
Purpose
Analyzing and reducing entropy generation is useful for enhancing the thermodynamic performance of engineering systems. This study aims to explore how polymers and nanoparticles in the presence of Lorentz forces influence the fluid behavior and heat transfer characteristics to lessen energy loss and entropy generation.
Design/methodology/approach
The dispersion model is initially used to examine the behavior of polymer additives over a magnetized surface. The governing system of partial differential equations (PDEs) is subsequently reduced through the utilization of similarity transformation techniques. Entropy analysis is primarily performed through the implementation of numerical computations on a non-Newtonian polymeric FENE-P model.
Findings
The numerical simulations conducted in the presence of Lorentz forces provide significant insights into the consequences of adding polymers to the base fluid. The findings suggest that such an approach minimizes entropy in the flow region. Through the utilization of polymer-MHD (magnetohydrodynamic) interactions, it is feasible to reduce energy loss and improve the efficiency of the system.
Originality/value
This study’s primary motivation and novelty lie in examining the significance of polymer additives as agents that reduce entropy generation on a magnetic surface. The author looks at how nanofluids affect the development of entropy and the loss of irreversibility. To do this, the author uses the Lorentz force, the Soret effect and the Dufour effect to minimize entropy. The findings contribute to fluid mechanics and thermodynamics by providing valuable insights for engineering systems to increase energy efficiency and conserve resources.
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