Variable Property Effects on Convection in a Heat Generating Porous Medium

Abstract

Convection heat transfer in a fluid-saturated porous medium has many applications, such as in oil and gas production, grain storage, and geothermal energy. A number of numerical studies have been carried out using Darcy's law to formulate the natural convection heat transfer mathematically in enclosures of internally heat-generating porous media. This paper uses Irmay's momentum equation for radial and axial equations that include inertia terms with models an internally heat-generating porous medium in a short, vertical circular cylinder (R = 2m, H = 4m). The cylinder side and top are isothermal and at the same temperature (T{sub {infinity}}). The bottom surface of the cylinder is adiabatic. The variations in density and viscosity with temperature and inertia are investigated. For slow flows, the effect of inertia would be expected to be small. For large temperature variations, the effects of variable dynamic viscosity and density are expected to be large. The density and the dynamic viscosity of air were represented by the relationships {rho} = {rho}{sub {infinity}} (1 {minus} (T {minus} T{sub {infinity}})/T) and v = v{sub {infinity}} (1 + 2(T {minus} T{sub {infinity}})/T{sub {infinity}}). These relationships for {rho} and v are accurate for air between 20 and 200C.