Numerical analysis of natural convection in parallel, convergent, and divergent open‐ended channels (original) (raw)
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Journal of Thermal Analysis and Calorimetry, 2020
In this study, a two-dimensional investigation on natural convection inside a porous cavity at pore-scale is performed using the lattice Boltzmann method with the focus on the effects of pores geometry. The model is independent of the shape, density, porosity, and arrangements of the pores, because the image of the porous cavity is binarized and given to the code as input. The influences of pores geometry, Rayleigh number, porosity, and pore/liquid thermal diffusivity ratio are studied. A D2Q9 multi-relaxation time and a D2Q9 single-relaxation time lattice Boltzmann model are used for the flow and energy equations, respectively, with two separate distribution functions approach. For this purpose, pores with square, circular, and star shapes are considered. The Rayleigh number is varied in the range of 10 3 to 10 6 for three different porosity values (0.43, 0.71, 0.85) and pore/liquid thermal diffusivity ratios of 6, 70, and 788, with water and air as working fluids. Local variations of hot wall Nusselt number revealed that the star, circular, and square pores have the highest peak values of the local Nusselt number, respectively. By contrast, the lowest local values occur in the porous cavity with circular pores. In the examined porous media, the maximum increase in the hot wall averaged Nusselt number is equal to 24.3% occurring at = 0.71 , when pores are varied from circular to star shapes at Ra = 10 4. Moreover, using the star pores with a porosity value of 0.43, the averaged Nusselt number on the hot wall is increased by 184.46% compared to the empty cavity at Ra = 10 3. Besides, it is shown that increasing the thermal diffusivity ratio higher than 70 has little effect on the hot wall averaged Nusselt number.
A modification of a Nusselt number correlation for forced convection in porous media
International Communications in Heat and Mass Transfer, 2010
We report numerical simulations of forced convection heat transfer rates of a steady laminar flow in a twodimensional model of porous media to elucidate the differences observed between the numerical predictions of ) [Int. J Heat Mass Trans. 44, 1153-1159 and Gamrat et al. (2008) [Int. J Heat Mass Trans. 51, 853-864]. A modification in the correlation given by is proposed to make the results of the three numerical studies comparable and in agreement with the experimental data.
Natural convection heat transfer in a differentially heated and vertically partially layered porous cavity filled with a nanofluid is studied numerically based on double-domain formulation. The left wall, which is adjacent to the porous layer, is isothermally heated, while the right wall is isothermally cooled. The top and bottom walls of the cavity are thermally insulated. Impermeable cavity walls are considered except the interface between the porous layer and the nanofluid layer. The Darcy-Brinkman model is invoked for the porous layer which is saturated with the same nanofluid. Equations govern the conservation of mass, momentum, and energy with the entity of nanoparticles in the fluid filling the cavity and that are saturated in the porous layer are modeled and solved numerically using under successive relaxation upwind finite difference scheme. The contribution of five parameters are studied, these are; nanoparticle volume fraction u (0-0.1), porous layer thickness Xp(0-0.9), Darcy number Da (10 À7 -1), aspect ratio A (1, 2, 4), and Rayleigh number Ra (10 3 -10 6 ). The nanofluid is considered to be composed of copper nanoparticles and water as a base fluid. The results have shown that with the aid of a nanofluid, the convective heat transfer can be enhanced even at a low permeable porous medium. It is found that when Ra 10 5 , there is a critical porous layer thickness Xp at which the Nusselt number is maximum. Otherwise, the Nusselt number Nu decreases rapidly with Xp. Correlations of Nu with the other parameters are established and tested for A ¼ 2.
The effect of aspect ratio on heat transfer in a square cavity filled with a porous medium
IOP Conference Series: Materials Science and Engineering, 2020
Two dimensional mathematical model of an enclosure filled with a porous medium and heated from the lower end with various values of the width to height ratio (aspect ratio) has been studied in the present article. A two dimensional free convection model has been solved numerically using finite difference technique to evaluate the streamlines, isotherm lines, and the average Nusslet number. The set values where; Rayleigh number of 106, Prandtl number of 0.72, and aspect ratio ranging from 1:4 to 4:1. The model has been validated and the results showed that the aspect ratio has a clear effect on the average Nusselt number and that increasing the flow rate for aspect ratio form 1:4 to 4:1.
Acta Mechanica, 2007
The problem of natural convection flow in a cavity filled with a water near its maximum density saturated porous medium and subjected to thermal non-equilibrium condition is investigated numerically in the present article. The natural convection flow in the horizontally heated rectangular cavity is assumed to be two-dimensional. A parabolic relationship of the density-temperature is used in Darcy's model. The dimensionless governing equations were solved using the finite volume method, and the results are presented to show the effect of the governing parameters. The numerical results are presented in the form of variations of the average Nusselt number with the Rayleigh number with different values of the heat transfer coefficient parameter H, and the thermal conductivity parameter K r . It is found that by increasing H and K r the shape of the isotherms of the solid phase appear to be similar to those of the water due to the enhancement of the thermal communications between the two phases. The results for the average Nusselt number of the thermal equilibrium model, which is the maximum possible value, can be achieved for high values of H Â K r . The numerical results reveal the dependence of the total (solid + fluid) average Nusselt number on the aspect ratio, and the maximum values of the average Nusselt number are found for the cavities of aspect ratio A % 0.5.
Numerical Study of Heat Transfer Coefficient in Porous Media
2009
⎯ In this study, convective heat transfer in a porous flat plate channel flow is simulated by a direct numerical method. The solid materials consist of uniform distributed blocks, which resemble the porous medium within the channel. The solid materials are assumed to be isothermal and the channel walls are under adiabatic conditions. The Navier–Stokes equations are solved directly in the fluid region without the assumption of volume averaging. The two energy transport equations are solved for the solid and fluid flow separately. The results indicate that the mean bulk temperature across the channel develops faster if the channel aspect ratio gets smaller. On the other hand, the Nusselt number has the highest value at the channel inlet and gradually approaches to a minimum or developing condition at a distance which depends on the value of the aspect ratio.
International Journal of Heat and Mass Transfer, 2006
Natural convection flows in a square cavity filled with a porous matrix has been studied numerically using penalty finite element method for uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls. Darcy-Forchheimer model is used to simulate the momentum transfer in the porous medium. The numerical procedure is adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 10 3 6 Ra 6 10 6 , Darcy number Da, 10 À5 6 Da 6 10 À3 , and Prandtl number Pr, 0.71 6 Pr 6 10) with respect to continuous and discontinuous thermal boundary conditions. Numerical results are presented in terms of stream functions, temperature profiles and Nusselt numbers. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating case for all Rayleigh numbers but average Nusselt number shows overall lower heat transfer rate for non-uniform heating case. It has been found that the heat transfer is primarily due to conduction for Da 6 10 À5 irrespective of Ra and Pr. The conductive heat transfer regime as a function of Ra has also been reported for Da P 10 À4 . Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes the power law correlations between average Nusselt number and Rayleigh numbers are presented.
International Journal of Heat and Mass Transfer, 1987
In this work, the applicability of the Boussinesq approximation is investigated for natural convection in a fluid-saturated porous cavity with vertical walls maintained at two different temperatures and horizontal walls completely insulated. Numerical calculations are performed for two different fluids of practical interest, water and air, in a wide range of Rayleigh numbers and aspect ratios. Flow and temperature fields and heat transfer rates obtained through the evaluation of a model that includes fluid temperature dependent properties, are presented. One of the most important conclusions is that the Nusselt number evaluated through the Boussinesq approximation can be substantially different from the Nusselt number obtained with this model.
Transport in Porous Media, 2019
Natural convection in a porous enclosure in the presence of thermal dispersion is investigated. The Fourier-Galerkin (FG) spectral element method is adapted to solve the coupled equations of Darcy's flow and heat transfer with a full velocity-dependent dispersion tensor, employing the stream function formulation. A sound implementation of the FG method is developed to obtain accurate solutions within affordable computational costs. In the spectral space, the stream function is expressed analytically in terms of temperature, and the spectral system is solved using temperature as the primary unknown. The FG method is compared 1 to finite element solutions obtained using an in-house code (TRACES), OpenGeoSys and COMSOL Multiphysics ®. These comparisons show the high accuracy of the FG solution which avoids numerical artifacts related to time and spatial discretization. Several examples having different dispersion coefficients and Rayleigh numbers are tested to analyze the solution behavior and to gain physical insight into the thermal dispersion processes. The effect of thermal dispersion coefficients on heat transfer and convective flow in a porous square cavity has not been investigated previously. Here, taking advantage of the developed FG solution, a detailed parameter sensitivity analysis is carried out to address this gap. In the presence of thermal dispersion, the Rayleigh number mainly affects the convective velocity and the heat flux to the domain. At high Rayleigh numbers, the temperature distribution is mainly controlled by the longitudinal dispersion coefficient. Longitudinal dispersion flux is important along the adiabatic walls while transverse dispersion dominates the heat flux toward the isothermal walls. Correlations between the average Nusselt number and dispersion 2 coefficients are derived for three Rayleigh number regimes.
COMPUTATIONAL INVESTIGATION OF CONJUGATE HEAT TRANSFER IN CAVITY FILLED WITH SATURATED POROUS MEDIA
The conjugate natural convection heat transfer in a partially heated porous enclosure had been studied numerically. The governing dimensionless equations are solved using finite element method. Classical Darcy model have been used and the considering dimensionless parameters are modified Rayleigh number (10 ≤ Ra ≤ 10 3), finite wall thickness (0.02 ≤ D ≤ 0.5), thermal conductivity ratio (0.1 ≤ Kr ≤ 10), and the aspect ratio (0.5 ≤ A≤ 10). The results are presented in terms of streamlines, isotherms and local and average Nusselt number. The results indicate that heat transfer can be enhanced by increasing the modified Rayleigh number, and thermal conductivity ratio. Wall thickness effects on the heat transfer mechanism had been studied and it is found that; as the Wall thickness increases, the conduction heat transfer mechanism will be dominated. Also, increasing aspect ratio will increase the stream function and reduced the heat transfer rate.