Natural convection in a square cavity filled with a porous medium: Effects of various thermal boundary conditions (original) (raw)
Related papers
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.
This paper investigates the combined effects of thermal radiation and heat generation on natural convection in a square cavity filled with porous medium using finite-difference technique in staggered grid distribution. In the present study, the cavity is assumed to have isothermal vertical walls and adiabatic horizontal walls. The hydrodynamic field in the porous medium is modelled according to the general model involving Brinkman and Forchheimer terms. Here, parametric study for a wide range of Rayleigh number (Ra), Darcy number (Da), thermal radiation parameter (N R ), heat generation parameter (He) is done, which shows consistent performance of the numerical approach used for obtaining the solutions as streamlines, isotherms, velocity profiles, temperature profiles, local Nusselt numbers and the average Nusselt numbers. For the purpose of numerical simulation, Pr = 1 and = 0.4 are considered in this work. The results are also computed for vertical velocity and temperature profiles for non-porous case by taking = 1.0 and Da = 10 4 . Heat transfer rates at the heated walls are presented in terms of local Nusselt number. The effect of increasing the thermal radiation parameter is to enhance the vertical velocity. Average Nusselt number increases with increase in the thermal radiation parameter whereas reverse effect is observed in the case of heat generating parameter increase.
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.
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.
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.
Natural convection in porous cavity with sinusoidal bottom wall temperature variation
International Communications in Heat and Mass Transfer, 2005
Numerical study of natural convection in a porous cavity is carried out in the present paper. Natural convection is induced when the bottom wall is heated and the top wall is cooled while the vertical walls are adiabatic. The heated wall is assumed to have spatial sinusoidal temperature variation about a constant mean value which is higher than the cold top wall temperature. The non-dimensional governing equations are derived based on the Darcy model. The effects of the amplitude of the bottom wall temperature variation and the heat source length on the natural convection in the cavity are investigated for Rayleigh number range 20-500. It is found that the average Nusselt number increases when the length of the heat source or the amplitude of the temperature variation increases. It is observed that the heat transfer per unit area of the heat source decreases by increasing the length of the heated segment. D
Influence of thermal radiation on natural-convection flow in a square cavity filled with a porous medium of uniform porosity having isothermal vertical walls and adiabatic horizontal walls, has been studied numerically by using finite-difference method with staggered grid distribution. The simulation is performed by considering both Darcian and non-Darcian models. Governing momentum and energy equations are solved numerically to obtain velocity and temperature fields for various values of different physical parameters. It is seen that increasing the thermal radiation parameter enhances the local Nusselt number on the left vertical wall whereas the reverse effects are observed due to increase in the heat generating parameter when Ra = 10 9 . The temperature at the mid-horizontal plane decreases with increase in the value of Rayleigh number up to a certain distance from the left vertical wall and beyond that distance the opposite trend is observed. The temperature at the mid-horizontal plane increases with increase in the value of heat generating parameter.
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.
2015
Unsteady natural convection and heat transfer in a square cavity partially filled with porous media using a thermal<br> non-equilibrium model is studied in this paper. The left vertical wall is<br> maintained at a constant hot temperature Th and the right vertical wall<br> is maintained at a constant cold temperature Tc, while the horizontal<br> walls are adiabatic. The governing equations are obtained by applying<br> the Darcy model and Boussinesq approximation. COMSOL's finite<br> element method is used to solve the non-dimensional governing<br> equations together with specified boundary conditions. The governing<br> parameters of this study are the Rayleigh number (Ra = 10^5, and Ra = 10^6 ), Darcy namber (Da = 10^−2, and Da = 10^−3),<br> the modified thermal conductivity ratio (10^−1 ≤ γ ≤ 10^4), the inter-phase heat transfer coefficien (10^−1 ≤ H ≤ 10^3) and the<br> time dependent (0.001 ≤ τ ≤ 0.2). The results pre...
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.