Numerical investigation of conjugate natural convection heat transfer in a square porous cavity heated partially from left sidewall (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.
Natural convection heat transfer in a porous rectangular partially active heated wall is numerically investigated using finite element method. Three different cases of heating and cooling zone had been taken in the consideration along the vertical walls while the others are considered to be adiabatic. The governing equations are obtained by the applying of Darcy Model and Boussinesq approximation. Finite element method is used to solve the dimensionless governing equations with the specified boundary conditions. The investigated parameters in the present study are the modified Rayleigh number (10 # Ra # 10), aspect ratio 3 (0.5 # A# 2), finite wall thickness (0.02 # D# = 0.5) and the thermal conductivity ratio (0.1# K # 10). The results r are presented in terms of streamlines, isotherms and Nusselt number. The results indicate that as the aspect ratio, finite wall thickness increase, Nusselt number decrease. Also, as the modified Rayleigh number increases, the Nusselt number will increase. Case 1 and 2 gave approximately the same effects of heat transfer rate while case 3 give lower rate of heat transfer rate.
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.
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.
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 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 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.
A numerical study of non-Darcian natural convection heat transfer in a rectangular enclosure filled with porous medium saturated with viscous fluid was carried out. The effects of medium Rayleigh number, porosity, particle to fluid thermal conductivity ratio, Darcy number and enclosure aspect ratio on heat transfer were examined to demonstrate the ability Porosity Dimensionless temperature Viscosity (N.s/m 2 ) Density (kg/m 3 ) Dimensionless time Dimensionless stream function Dimensionless vorticity Subscripts d Dispersive e Effective f Fluid m Medium s Solid st Stagnant
Computational Thermal Sciences: An International Journal, 2019
Numerical results of two-dimensional steady natural convection in a square cavity filled with porous medium by adopting a two-temperature model of heat transfer are presented. The left wall is linearly heated (by increasing or decreasing the wall temperature); the right wall is uniformly cooled while the horizontal top and bottom walls are considered insulated. A developed program (based on the finite-volume method and the semi-implicit method for pressure-linked equations algorithm) was utilized to numerically solve the governing Navier-Stokes equations with the associated boundary conditions. The controlling parameters on the fluid flow and heat transfer for this investigation are the interphase heat transfer coefficient (H), porosity-scaled conductivity ratio (γ), Rayleigh number (Ra), and Darcy number (Da) at Pr = 0.70.