Abstract
This current study focuses on the simulation of natural convection in square cavity filled with a porous medium considered homogenous, isotropic and saturated by a Newtonian fluid obeying the law of Darcy and the hypothesis of Boussinesq. The lower horizontal wall of the enclosure is subjected to a temperature varying sinusoidally with the space while the upper horizontal wall is maintained adiabatic. The vertical walls are kept cold isotherm. In order to generalize the results, all governing equations are put into dimensionless form, discretized by the Finite Difference Method and solved by the relaxed Gauss Seidel (SUR) Algorithm. A code has been proposed in Fortran 95, in order to solve numerically the equations of the problem. The study parameters are the Rayleigh-Darcy number (Ra) and the amplitude (Ar) of the hot wall temperature. The effects of the Rayleigh-Darcy number and amplitude on the dynamic and thermal field, the horizontal velocity distribution and the mean horizontal temperature distribution (y = 0.5) were presented and discussed. It emerges from this study that the increases of the amplitude and Rayleigh-Darcy number intensify the flow and the global transfer of heat in our physical domain.
Highlights
This current study focuses on the simulation of natural convection in square cavity filled with a porous medium considered homogenous, isotropic and saturated by a Newtonian fluid obeying the law of Darcy and the hypothesis of Boussinesq
The lower horizontal wall of the enclosure is subjected to a temperature varying sinusoidally with the space while the upper horizontal wall is maintained adiabatic
We have carried out a numerical study of natural convection in a square cavity filled with a porous medium and saturated by an incompressible Newtonian fluid
Summary
Nowadays convection transfer in a porous medium saturated by a fluid is a pa-. The problem of convection in fluid saturated porous media has been widely studied in the past decades for its applications in thermal, electronics, and engineering [1]-[17]. The problem of natural convection in a porous cavity whose walls are maintained at different temperatures or heat fluxes is classic problem in porous media. Numerous research projects, both theoretical and experimental, have been carried out on this type of cavity [1]. An excellent review of these studies can be found in the books of Nield and Bejan [2], Kaviany (2004) [3], Vafai (2005) [4], Ingham and Pop [5] search field
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