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ABSTRACT: Coupled laminar natural convection with radiation in air-filled square enclosure heated from below and cooled from above is
studied numerically for a wide variety of radiative boundary conditions at the sidewalls. A numerical model based on the finite
difference method was used for the solution of mass, momentum and energy equations. The surface-to-surface method was used
to calculate the radiative heat transfer. Simulations were performed for two values of the emissivities of the active and
insulated walls (ɛ1=0.05 or 0.85, ɛ2=0.05 or 0.85) and Rayleigh numbers ranging from 103 to 2.3×106 . The influence of those parameters on the flow and temperature patterns and heat transfer rates are analyzed and discussed
for different steady-state solutions. The existing ranges of these solutions are reported for the four different cases considered.
It is founded that, for a fixed Ra, the global heat transfer across the enclosure depends only on the magnitude of the emissivity
of the active walls. The oscillatory behavior, characterizing the unsteady-state solutions during the transitions from bicellular
flows to the unicellular flow are observed and discussed.
Heat and Mass Transfer 04/2012; 42(3):214-225. · 0.90 Impact Factor
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International Journal of Heat and Fluid Flow. 01/2008; 29:1360-1368.
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ABSTRACT: Thermal buoyant air inside a modified Rayleigh–Bénard (RB) cavity bounded by a lower flat plate and an inverted-V upper plate has been investigated numerically using the finite-volume method. The second-order-accurate QUICK and SIMPLE schemes were used for the discretization of the convective terms and the pressure–velocity coupling in the set of conservation equations, respectively. The problem under study is controlled by two parameters: (1) the Rayleigh number ranging from 103 to 106 and (2) the relative height of the vertical sidewalls d. In reference to the latter, it varies from one limiting case corresponding to the standard RB cavity (a rectangle with d = 1) to another limiting case represented by an isosceles triangular cavity where d = 0. The numerical results for the velocity and temperature fields are presented in terms of streamlines, isotherms, local and mean heat fluxes. An additional effort was devoted to determine the critical Ra values characterizing the transition from symmetrical to asymmetrical buoyant airflow responsive to incremental changes in Ra. For purposes of engineering design, a general correlation equation for the Nusselt number in terms of the pertinent Ra and d was constructed using nonlinear multiple regression theory. Copyright © 2007 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Fluids 06/2007; 56(4):453 - 465. · 1.18 Impact Factor
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ABSTRACT: This article addresses the buoyant air circulation inside attic spaces of houses and buildings with sloped roofs and horizontally suspended ceilings. In order to counteract the excessive heat transmission through the roof that takes place during the wintertime, when the attic is heated at the base, this study attached an array of baffles onto the top inclined walls to alter the flow characteristics of the buoyant air. To perform the computational analysis, the finite volume method is the vehicle for the discretization of the conservation equations. The Boussinesq approximation is not invoked, and all thermophysical properties are considered as temperature-dependent. Simulations are performed for several values of baffles length and the Rayleigh number. The influence of these parameters upon the flow and temperature patterns is analyzed and discussed. A comparison of the thermal performance between baffled attics and non-baffled attics is presented. The results show that the presence of baffles provides an important energy savings for heating and helps keep the attic at a desired temperature.
Heat Transfer Engineering 02/2007; 28(2):103-111. · 0.89 Impact Factor
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Numerical Heat Transfer Applications 01/2006; Part A: Applications(Vol. 49):175-193. · 2.49 Impact Factor
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ABSTRACT: The Wilson plot is a technique to estimate the film coefficients in several types of heat transfer processes and to obtain general heat transfer correlations. This method is an outstanding tool in practical applications and in laboratory research activities that involve analysis of heat exchangers. Moreover, the application of this method is simple enough to be taught in laboratory practices for students at university and doctoral level of physics and engineering. Therefore, an experimental apparatus has been designed and built in our laboratory that allows the students to carry out experiments based on the application of the Wilson plot method. In this note, the principles of the method are explained, the experimental apparatus is described and representative results of the experimental data taken from the apparatus and the application of the Wilson plot method are shown.
European Journal of Physics 04/2005; 26(3):N1. · 0.82 Impact Factor
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Experimental Heat Transfer 04/2005; 18(2):81-86. · 0.54 Impact Factor
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ABSTRACT: The present investigation deals with the numerical computation of laminar natural convection with and without surface-to-surface radiation in a class of right-angled triangular cavities filled with air. The vertical walls are uniformly heated and the inclined walls are uniformly cooled while the upper connecting walls are adiabatic. The aperture angle φ located at the lower vertex of the triangular cavities between the vertical and the inclined walls identifies the shape of each cavity. This kind of cavity finds application in the miniaturization of cabinets housing electronic components constrained by space and/or weight severely. With a view at enhancing the heat transfer rates and/or reducing the size of cabinets, the influence that surface radiation exerts upon natural convection should be scrutinized. To this end, the finite volume method is implemented to perform the computational analysis of the above-described problem(s). Numerical results are reported for the local quantities, the velocity and temperature fields encompassing aperture angles φ that extend from 15° to 45° at two extreme Rayleigh numbers, Ra = 103 and 106. Additionally, the two global quantities, the mean convective Nusselt number and the mean radiative Nusselt number are reported in tabulated and graphical forms for the same controlling parameters. Overall, it was found that the competition between surface radiation and natural convection in right-angled triangular cavities filled with air plays a preponderant role. Finally, the analysis culminates with the construction of a comprehensive correlation equation for the total Nusselt number in terms of the controlling parameters which should be useful for engineering analysis and design. This correlation equation will undoubtedly provide a fast evaluation avenue to judge the cavity thermal performance.
International Journal of Heat and Mass Transfer.
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ABSTRACT: A numerical study of three-dimensional natural convection in an attic space with heated horizontal base and cooled upper walls is presented. Every previous study pertinent to this subject as of today has assumed that the flow in attics is two-dimensional and restricted to triangular cavities. This problem is examined for fixed aspect ratios holding width to height of 2 and depth to height of 3.33 and Rayleigh numbers ranging from 104 to 8 × 105. The coupled system of conservation equations, subject to the proper boundary conditions, along with the equation of state assuming the air behaves as a perfect gas are solved with the finite volume method. In the conservation equations, the second-order-accurate QUICK scheme was used for the discretization of the convective terms and the SIMPLE scheme for the pressure-velocity coupling. It is categorically found that the flow in the attic is 3D. From the physics of the problem, two steady-state solutions are possible. The symmetrical solution prevails for relatively low Rayleigh numbers. However, as the Ra is gradually increased, a transition occurs at a critical value RaC. Above this value of RaC, an asymmetrical solution exhibiting a pitchfork bifurcation arises and eventually becomes steady. Results are presented detailing the occurrence of the pitchfork bifurcation and the resulting flow patterns are described.
International Journal of Heat and Fluid Flow.
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ABSTRACT: This paper re-examines the venerable lumped model of unsteady heat conduction by means of a detailed study of the exact temperature distributions in bodies of elementary geometry (i.e., large slab, long cylinder and sphere). The space-mean temperature is used as a vehicle for demonstrating that the lumped calculation directly follows as a particular case from the infinite series solution of the general distributed model. In this manner, several methods to find a limit Biot number can be established as simpler alternatives to the traditional procedure. Additionally, the discussion offers a different perspective of this classical subject of heat conduction theory, gaining more insight on the limiting behavior of unsteady temperature distributions.
International Journal of Thermal Sciences 42(10):921-930. · 2.14 Impact Factor
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ABSTRACT: This paper discusses the thermal calculation of composite, metallic fins of variable thickness. In the simpler case of a constant-thickness (rectangular profile), the complete procedure involves first the analytical solution of the two-dimensional, two-material conduction problem, under the form of an infinite series of orthogonal eigenfunctions. Then the limit as Bi → 0 is sought, also analytically, which simplifies the series to its first term and permits to express the fin efficiency in closed form. This limit is equivalent to the usual 1D, Murray–Gardner, or thin-fin, approximation of ordinary, single-material fins, provided that an averaged thermal conductivity is used.For variable thickness (tapered profile), no analytical solutions have been found, so that resort should be made to numerical methods. Since the adoption of dimensional parameters is advisable in that context, the paper first reviews the industrial application of composite fins and selects a comprehensive set of material pairs of interest. Subsequently, two arbitrary but representative geometries and a reasonable range of dimensions and convection coefficients are fixed, thus assembling a rather exhaustive matrix of case-studies. Numerical calculations are compared to approximate results, in order to ascertain two facts: whether a single parameter exists (thermal length) that allows an accurate prediction of fin efficiency, and whether this parameter can be expressed in terms of an averaged thermal conductivity. Well within the bounds of usual engineering accuracy, the answer to both questions is affirmative. Therefore, calculation methods of ordinary fins and composite, constant-thickness fins are shown to be applicable to the most general case. Error bounds and specific recommendations for practical problems are also given.
International Journal of Heat and Mass Transfer 51:2153-2166. · 2.41 Impact Factor
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ABSTRACT: Heat exchange devices are essential components in complex engineering systems related to energy generation and energy transformation in industrial scenarios. The calculation of convection coefficients constitutes a crucial issue in designing and sizing any type of heat exchange device. The Wilson plot method and its different modifications provide an outstanding tool for the analysis and design of convection heat transfer processes in research laboratories. The Wilson plot method deals with the determination of convection coefficients based on measured experimental data and the subsequent construction of appropriate correlation equations. This paper is to present an overview of the Wilson plot method along with numerous modifications introduced by researches throughout the years to improve its accuracy and to extend its use to a multitude of convective heat transfer problems. Undoubtedly, this information will be useful to thermal design engineers.
Applied Thermal Engineering.
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ABSTRACT: Laminar flows in parallel-plate channels are usually caused by a combination of small channel dimensions and low fluid velocities. As a consequence, the heat transfer coefficients in these channels are extremely low. The present study avoids inward protruding fins attached to the channel walls and instead focuses on the opposite arrangement. That is, molding the walls of parallel-plate channels with arrays of transverse cavities pointing outward. Two configurations were studied, one with symmetrically opposing cavities onto the bottom and upper walls and another with non-symmetric or staggered cavities onto the two parallel walls. A 120-cm-long channel contains two series of 3, 6 and 12 transverse cavities having ratios of cavity depth to cavity print diameter δ/D of 0.125, 0.25, 0.375, and 0.5. Computations are performed for Reynolds numbers based on the hydraulic diameter ranging from 1000 to 2500 for air (Pr = 0.7). The finite-volume method is used to perform the computational analysis with embedded second-order-accurate QUICK and SIMPLE schemes. It is found that the cavity/channel assemblies can achieve heat transfer enhancements of about 30% relative to the smooth channel, with pressure loss increases of 19%. In all cases examined, the outcome of the numerical simulation reveals that the heat transfer enhancement overcomes the pressure drop accretion.
International Journal of Heat and Mass Transfer.
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ABSTRACT: This paper addresses turbulent natural convection of air confined in an isosceles triangular enclosure representing conventional attic spaces of houses and buildings with pitched roofs and horizontally suspended ceilings. The values to be considered are H = 0.86 m and 2.73 m for the height while the values 1.72 m and 5.46 m were assigned to the width, W, such as the aspect ratio H/W remains 0.5. The third dimension of the cavity is considered long enough for the flow to be considered 2D. The base wall is heated at 20 °C and the inclined walls are cooled at 0 °C. This combination of factors leads to large Rayleigh numbers equal to 1.58 × 109 and 5 × 1010. Turbulence is modeled by a low-Reynolds-number k–ε model. The system of governing equations, subject to the proper boundary conditions is solved with the finite volume method. Second-order-accurate QUICK and SIMPLE schemes were used for the discretization of the convective terms and the pressure–velocity coupling, respectively. The velocity and temperature distributions were calculated at different locations in the cavity and their mean quantities are presented. The local and average Nusselt numbers and the wall shear stresses are also presented. Since to the knowledge of the authors, no previous results on turbulent thermal convection in this geometry exist, the validation of the numerical code was performed by comparing velocity and temperature profiles against recent experimental measurements, obtained for a square cavity. Satisfactory agreement was observed.
International Journal of Heat and Fluid Flow.
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ABSTRACT: Thermal performance of micro-pin fins of variable diameter and rough surface is calculated by means of an approximate procedure based on truncated power series. The geometric effect of roughness is modeled after Bahrami et al. [9], which greatly increases the intricacy of the fin equation, preventing its analytical solution even by symbolic computer codes. The approximate series solution is developed firstly by estimating an adequate number of terms based on convergence to the (known) exact solution of smooth pin fins of the same geometry. Then, residual convergence for an increasing number of terms is studied for the rough fin. Three selected geometries are analyzed, of hyperbolic, trapezoidal and concave parabolic profiles. Influence of surface roughness is evaluated for a wide range of heat transfer conditions; results are discussed in terms of the two primary quantities of interest in fin design, viz., efficiency and effectiveness. Due to the easiness of the present methodology, it can be safely applied to other geometric arrangements involving straight and annular fins.
International Journal of Thermal Sciences 49(1):23-35. · 2.14 Impact Factor
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ABSTRACT: Thermal modelling of large pulverized fuel utility boilers has reached a very remarkable development, through the application of CFD techniques and other advanced mathematical methods. However, due to the computational requirements, on-line monitoring and simulation tools still rely on lumped models and semiempirical approaches, which are often strongly simplified and not well connected with sound theoretical basis. This paper reviews on-line modelling techniques, aiming at the improvement of their capabilities, by means of the revision and modification of conventional lumped models and the integration of off-line CFD predictions. The paper illustrates the coherence of monitoring calculations as well as the validation of the on-line thermal simulator, starting from real operation data from a case-study unit. The outcome is that it is possible to significantly improve the accuracy of on-line calculations provided by conventional models, taking into account the singularities of large combustion systems and coupling off-line CFD predictions for selected scenarios.
Applied Thermal Engineering.
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ABSTRACT: A novel approximate solution has been devised for predicting the thermal entry length in duct flows for situations of either isothermal or isoflux walls and fully developed velocity distribution. The conventional partial differential energy equation does not need to be solved in the region of thermal development of the duct. This is a unique feature of the proposed solution, which has not been fully discussed in the literature before. Computed values of the thermal entry length for circular pipes and parallel plates are in good agreement with results obtained by more elaborate traditional techniques. These are the geometries most commonly used in fluid flow and heat transfer devices.
International Journal of Heat and Fluid Flow.
