CONVECTION IN A HORIZONTAL ANNULAR POROUS LAYER WITH NON-LINEAR DENSITY EFFECTS

This paper presents a theoretical study of heat transfer and flow by natural convection in an annular layer of porous material saturated with cold water and subjected to different thermal boundary conditions. The governing equations are solved, within the Boussinesq and Darcy approximations, using an implicit finite difference method. The results obtained for streamlines and isotherms, velocity and temperature profiles, and local and global Nusselt numbers are analysed in terms of R, the radius of the cavity, (R) over capa, a nonlinear Rayleigh number, and gamma, an inversion parameter, relating the temperature for maximum density to the wall temperature. It is found that the essential effect of density inversion is to create multicellular flows and to reduce the fluid velocities as well as the convective heat transfer. The problem of a common fluid without density inversion is recovered as a special case of this study.