Non-uniform porosity and thermal dispersion effects on natural convection about a heated horizontal cylinder in an enclosed porous medium

A numerical solution has been obtained for transient two-dimensional natural convection from a heated horizontal cylinder embedded in an enclosed porous medium. Non-Darcian effects are taken into consideration in the momentum equation, while the thermal dispersion effect is taken into consideration in the energy equation. The wall effect on porosity is approximated by an exponential function and its effect on thermal dispersion is modeled by a dispersive length. The governing equations in terms of the stream function, vorticity, and temperature are expressed in a body-fitted coordinate system, which were solved numerically by the finite difference method. Results are presented for the streamlines and isotherms, tangential velocity and temperature distributions, as well as the average Nusselt numbers at different values of Rayleigh number, dimensionless particle diameter, and Prandtl number. The non-uniform porosity effect tends to increase the temperature gradient near the wall while the thermal dispersion effect increases the effective thermal conductivity, both resulting in an increase in surface heat flux. The effect of thermal dispersion on natural convection in porous media at low to moderate Rayleigh number is small. With nonuniform porosity and thermal dispersion effects taken into consideration, the predicted average Nusselt numbers are found to be in better agreement with experimental data.