Natural convection in an inclined porous cavity with variable porosity and thermal dispersion effects

The variable porosity and thermal dispersion effects on natural convection in an inclined porous cavity are investigated numerically. The wall effect on porosity is approximated by an exponential function and its effect on thermal dispersion is modeled in terms of a dispersive length. Numerical results show that both variable porosity and thermal dispersion effects increase the temperature gradient adjacent to the wall resulting in the enhancement of surface heat flux. These effects become important when the dimensionless particle diameter is increased. The variable porosity effect increases the fluid velocity near the wall, consequently enhancing convective heat transfer. The Prandtl number effect on the Nusselt number is small for Prandtl number greater than one, but increases as the Prandtl number decreases below one. The effect of thermal conductivity ratio on the Nusselt number is greater at low Rayleigh numbers where conduction heat transfer is predominant. A comparison between theoretical and experimental results shows that the calculated Nusselt numbers which take into account variable porosity and thermal dispersion effects have the best agreement with experimental data.