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 (Ram = 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.

In this paper, we have numerically studied the phenomenon of unidimensional convectionconduction equation in a channel, cylinder and sphere immersed in a solar pond. Then we have studied bidimensional case in a heat exchanger, which undergoes an external heat flow provided by solar pond. We carried out the discretization of the mathematical model by finite differences method (explicit scheme). Calculation codes in Fortran language have been created for the temperature distribution in all these geometries. We presented the numerical results in terms of temperature profile functions, one-and twodimensional, in laminar flow regime, for various parameters. We also present a study by COMSOL of the same phenomenon on these geometries. This study can be presented by two methods, the first using the physical model and the second using the mathematical part of COMSOL.