Heat transfer with laminar forced convection in a porous channel exposed to a thermal asymmetry

The effect of thermal asymmetry on laminar forced convection heat transfer in a plane porous channel with Darcy dissipation has been investigated numerically. The parallel plates making the channel boundaries were kept at constant, but different temperatures. The thermal asymmetry thus imposed on the system, results in an asymmetric temperature field and different heat fluxes across the channel boundaries. Depending on Darcy, Peclét and Reynolds number, the thermal asymmetry may lead to a reversal of the heat flux at a certain position along the flow at least at one of the channel walls. The corresponding Nusselt numbers become zero and might experience discontinuities thereby jumping from infinite positive to infinite negative, or vice versa. This feature is observed not only in the region of thermal development, but also in the fully developed region. In the fully developed region, an analytical expressions for the Nusselt numbers were obtained. From these expressions, analytical equations were deduced for the calculations of the axial positions along the channel where the Nusselt numbers become zero, or experiences discontinuity.