Numerical Simulation for Conjugate Natural Convection in a Partially Heated Rectangular Porous Cavity (original) (raw)
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The conjugate natural convection heat transfer in a partially heated square porous enclosure had been studied numerically. The governing dimensionless equations are solved using COMSOL Multiphysics and Darcy model assumed to be used. The considering dimensionless parameters are modified Rayleigh number, finite wall thickness, thermal conductivity ratio and the heat source length. The results are presented in terms of streamlines, isotherms and local and average Nusselt number. The results indicate that; the heat transfer can be enhanced by increasing the modified Rayleigh number. When the heat source length increases, the local Nusselt number of fluid phase increases, while, a reverse behavior of the local Nusselt number along the heat source is found. As the Rayleigh number increase, the local Nusselt number for both fluid and solid phase increases, therefore, the heat transfer rate will be enhanced. On the other hand, when the thermal conductivity ratio increase, the local Nusselt number for the fluid phase increases, and the local Nusselt number along the heated wall decreases.
Effect of partially thermally active wall on natural convection in porous enclosure
International Information and Engineering Technology Association, 2018
A numerical investigation is presented to illustrate the impact of aspect ratio in a conjugate heat transfer enclosure filled with porous media and partially heated from vertical walls. The left and right walls are partially heated and cooled, respectively. The remaining partitions of the vertical walls in addition to the top and bottom walls are considered to be adiabatic. the present work is limited to two different cases: Top-Bottom (case 1) and Bottom-Top (case 2). The dimensionless Navier-Stokes governing equations are solved using the finite element method. The parameters of interest are the modified Rayleigh number 10 ≤ Ra ≤ 10 3 , the finite wall thickness 0.02 ≤ D ≤ 0.5, 0.1 ≤ Kr ≤ 10 and the aspect ratio 0.5 ≤ A ≤ 10. The results are presented in term of streamlines, isotherms and average Nusselt number for fluid phase and along the solid hot wall. The results indicated that the locations of partially active walls have great influence on heat transfer rate. I was shown that Bottom-Top arrangement gives better heat transfer rate compared to that of Top-Bottom. It was also found that by increasing the Rayleigh number, the rate of heat transfer increased. In contrast, increasing the wall thickness and aspect ratio reduced the heat transfer rate.
International Journal of Thermal Sciences, 2007
Steady conjugate natural convection-conduction heat transfer in a two-dimensional porous enclosure with finite wall thickness is studied numerically in the present article. The horizontal heating is considered, where the vertical boundaries are isothermal at different temperatures with adiabatic horizontal boundaries. The Darcy model is used in the mathematical formulation for the porous layer and finite volume method is used to solve the dimensionless governing equations. The governing parameters considered are the Rayleigh number (10 Ra 1000), the wall to porous thermal conductivity ratio (0.1 K r 10) and the ratio of wall thickness to its height (0.02 D 0.5). The results are presented to show the effect of these parameters on the heat transfer and fluid flow characteristics. The results including the streamlines and isotherm patterns and the local and average Nusselt number for different values of the governing parameters. It is found, in most of the cases that either increasing the Rayleigh number and the thermal conductivity ratio or decreasing the thickness of the bounded wall can increase the average Nusselt number for the porous enclosure (Nu p ). In special cases at low Ra and high conductive walls, the values of Nu p are increasing with the increase of the wall thickness.
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.
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.
The effects of nonuniform heating and a finite wall thickness on natural convection in a square porous cavity based on the local thermal nonequilibrium (LTNE) model are studied numerically using the finite difference method (FDM). The finite-thickness horizontal wall of the cavity is heated either uniformly or nonuniformly, and the vertical walls are maintained at constant cold temperatures. The top horizontal insulated wall allows no heat transfer to the surrounding. The Darcy law is used along with the Boussinesq approximation for the flow. The results of this study are obtained for various parametric values of the Rayleigh number, thermal conductivity ratio, ratio of the wall thickness to its height, and the modified conductivity ratio. Comparisons with previously published work verify good agreement with the proposed method. The effects of the various parameters on the streamlines, isotherms, and the weighted-average heat transfer are shown graphically. It is shown that a thicker bottom solid wall clearly inhibits the temperature gradient which then leads to the thermal equilibrium case. Further, the overall heat transfer is highly affected by the presence of the solid wall. The results have possible applications in the heat-storage fluid-saturated porous systems and the applications of the high power heat transfer.
International Journal of Heat and Mass Transfer, 2007
In this paper natural convection flows in a square cavity filled with a porous matrix has been investigated numerically when the bottom wall is uniformly heated and vertical wall(s) are linearly heated whereas the top wall is well insulated. Darcy-Forchheimer model without the inertia term is used to simulate the momentum transfer in the porous medium. Penalty finite element method with bi-quadratic rectangular elements is used to solve the non-dimensional governing equations. Numerical results are presented for a 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, 0.2 6 Pr 6 100) in terms of stream functions and isotherm contours, and local and average Nusselt numbers.
The conjugate natural convection heat transfer in a partially heated square porous enclosure had been studied numerically. The governing dimensionless equations are solved using COMSOL Multiphysics and Darcy model assumed to be used. The considering dimensionless parameters are modified Rayleigh number, finite wall thickness, thermal conductivity ratio and the heat source length. The results are presented in terms of streamlines, isotherms and local and average Nusselt number. The results indicate that; the heat transfer can be enhanced by increasing the modified Rayleigh number. When the heat source length increases, the local Nusselt number of fluid phase increases, while, a reverse behavior of the local Nusselt number along the heat source is found. As the Rayleigh number increase, the local Nusselt number for both fluid and solid phase increases, therefore, the heat transfer rate will be enhanced. On the other hand, when the thermal conductivity ratio increase, the local Nusselt number for the fluid phase increases, and the local Nusselt number along the heated wall decreases.
CONJUGATE HEAT TRANSFER IN A POROUS CAVITY HEATED BY A TRIANGULAR THICK WALL
The conjugate natural convection-conduction heat transfer in a square domain composed of a cavity heated by a triangular solid wall is studied under steady state condition. The vertical and horizontal walls of the triangular solid are kept isothermal and at the same hot temperature T h. The other boundaries surrounding the porous cavity are kept adiabatic except the right vertical wall, where it is kept isothermally at the lower temperature T c. Equations governing the heat transfer in the triangular wall and heat and fluid flow, based on the Darcy model, in the fluid-saturated porous medium together with the derived relation of the interface temperature are solved numerically using the second order central differences finite difference scheme with the successive over relaxation (SOR) method. The investigated parameters are the Rayleigh number Ra (100-1000), solid to fluid saturated porous medium thermal conductivity ratio Kr (0.1–10), and the triangular wall thickness D (0.05-1). The results are presented in the conventional form; contours of streamlines and isotherms and the local and average Nusselt numbers. An uncommon behavior of the heat transfer in the porous medium with the triangular wall thickness D is observed and accounted.
International Communications in Heat and Mass Transfer, 2008
Numerical investigations of steady natural convection flow through a fluid-saturated porous medium in a rectangular enclosure with a sinusoidal varying temperature profile on the bottom wall were conducted. All the walls of the enclosure are insulated except the bottom wall which is partially heated and cooled. The governing equations were written under the assumption of Darcy-law and then solved numerically using finite difference method. The problem is analyzed for different values of the Rayleigh number Ra in the range 10 ≤ Ra ≤ 1000, aspect ratio parameter AR in the range 0.25 ≤ AR ≤1.0 and amplitude λ of the sinusoidal temperature function in the range 0.25 ≤ λ ≤ 1.0. It was found that heat transfer increases with increasing of amplitude λ and decreases with increasing aspect ratio AR. Multiple cells were observed in the cavity for all values of the parameters considered.