Effect of eccentricity on natural convection in fluid-saturated porous media in an elliptical annulus

Energetic Physics Laboratory, Faculty of Exact Sciences, Constantine University 1, Algeria

^a Corresponding author: mdjezzar@umc.edu.dz

Received: 14 April 2014
Accepted: 6 December 2014

Abstract

In this paper, we summarize a numerical study of two-dimensional natural convection in an annular elliptical space fluid-saturated porous, by solving numerically the mass balance equations, momentum and energy, using Darcy’s law, Boussinesq approximation, vorticity-stream function formulation and the finite volumes method for the discretization of partial derivative equations. Both walls delimiting the annular space are maintained at two uniform different temperatures. The external parameters considered are the eccentricity of the inner elliptic wall (0.55, 0.688, 0.86, 0.9 and 0.999) and Rayleigh-Darcy number (Ra_m = 500). The results indicate that there are two main modes of natural convection: natural convection with only two cells and with more cells, their description is given in detail. The average equivalent conductivity is presented in terms of external parameters and allows us to see that it increases when the internal wall eccentricity increases.