Effects of heterogeneity in forced convection in a porous medium: Parallel-plate channel, asymmetric property variation, and asymmetric heating

The effects of variation (in the transverse direction) of permeability and thermal conductivity on fully developed forced convection in a parallel pla te channel or circular duct filled with a saturated porous medium is invest igated analytically on the basis of a Darcy model. Previous work on the cas e of symmetric property variation and symmetric hearing is now supplemented by a study of the case of asymmetric property variation, for both symmetri c and asymmetric hearing. Isoflux and isotemperature boundary conditions ar e treated in turn. For the isoflux case, it is found that both permeability variation and conductivity variation lead to a reduction in the value of t he Nusselt number Nu based on mean properties, but for the isotemperature c ase the situation is more complicated. For the isoflux case and permeabilit y variation only: Nu is independent of the degree of asymmetric hearing as represented by a flux ratio tau, but in the case of conductivity variation Nu is strongly dependent on t and the degree of conductivity variation. In the case of isotemperature boundary conditions no fully developed solution exists when both the property variation and the heating are asymmetric.