Analysis of Transient Three-Dimensional Natural Convection in Porous Media

Abstract

Transient multidimensional natural convection in porous media has been studied using a numerical method based on the simplified marker and cell technique with local cancellation of low order, diffusional truncation errors. The conservation equations and boundary conditions were phrased in terms of the primitive variables, velocity and temperature. Differences in temperature between the fluid and the solid matrix are considered. Heat transfer between the solid and liquid phases was modelled by representing the porous medium as an assemblage of spherical particles, and solving the conduction problem within the spheres at every time step. Nusselt numbers at walls were calculated from the temperature and velocity profiles. Numerical results for heat transfer through fluid saturated porous media heated from below are in good agreement with published experiments. Consideration of heat transfer between the solid and fluid phase leads to Nusselt numbers that vary with the thermophysical properties of the solid material, even when the Rayleigh number and fluid thermophysical properties are kept constant. This is also observed in experiments. The calculations also show convective instabilities of the right period at high Rayleigh numbers.