A two-field model for natural convection in a porous annulus at high Rayleigh numbers

Abstract

This work studies the natural convection in a vertical porous annulus for Rayleigh numbers up to 8×10 4. A model is deduced within a simple context of the mixture theory in which the following effects are included: (1) The solid and the fluid may be at different temperatures depending upon the flow regime and the permeability of the porous matrix. (2) Density, heat conductivity and viscosity of the fluid depend on temperature. (3) The porosity of the rigid solid matrix varies near the cavity walls. (4) Heat conduction in the fluid phase is accompanied with thermal dispersion. (5) Forchheimer inertial, Brinkman viscous and convective terms are considered in the momentum balance of the fluid phase. The resulting model is used to evaluate the heat transfer in a porous medium, the matrix of which is composed of equal spheres of well-specified diameters. Inner and outer walls of concentric cylinders are maintained at different temperatures and the two horizontal walls are adiabiatic. Numerical predictions of the Nusselt number are compared with available experimental data. For high Rayleigh and Darcy numbers (porous media of high permeability) all these effects have to be considered in the mathematical model. Thermal dispersion has a significant effect on the heat transfer through the solid–fluid composite.