Free Convection in a Porous Square Enclosure with Localized Sinusoidally Varying Temperature Profile on the Bottom Wall

Alhadj Hisseine Issaka Ali^{1, 2,} , Cheikh Mbow¹, Samba Dia¹, Mahamoud Youssouf Khayal³ and A.C. Beye¹

¹Department of Physics, Cheikh Anta Diop University of Dakar, Dakar, Senegal

²Department of Hydrocarbons Exploitation, Higher National Petroleum Institute of Mao, Mao, Chad

³Department of Technical Sciences, University of N’Djamena, N’Djamena, Chad

Cite this paper:
Alhadj Hisseine Issaka Ali, Cheikh Mbow, Samba Dia, Mahamoud Youssouf Khayal and A.C. Beye. Free Convection in a Porous Square Enclosure with Localized Sinusoidally Varying Temperature Profile on the Bottom Wall. International Journal of Physics. 2017; 5(5):162-170. doi: 10.12691/ijp-5-5-4

Abstract

This current study focuses on the simulation of free 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 localized temperature varying sinusoidally with the space while the upper horizontal wall and rest of the bottom walls are insulated. 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, amplitude and length of source heating on the dynamic and thermal fields are investigated. On the other hand, the effects of the amplitude on the horizontal velocity distribution and the mean horizontal temperature distribution(y=0.5) were presented and discussed. It emerges from this study that the increasing of the amplitude and Rayleigh-Darcy number intensify the flow and the global heat transfer in our physical domain.

Keywords:
free convection porous media finite difference method sinusoidal temperature localized heating

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