The effect of thermal asymmetry on laminar forced convection heat transfer in an annular porous channel with a Darcy dissipation of fluid kinetic energy was investigated numerically. The cylindrical surfaces 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 the Darcy, Peclet and Reynolds numbers, the thermal asymmetry may lead to a reversal of the heat flux along the channel at least at one of the channel walls. The corresponding Nusselt number becomes zero and subsequently experiences a discontinuity, thereby jumping from infinite negative to infinite positive, or vice versa. This feature is observed in the region of thermal development. In the fully developed heat transfer region, the Nusselt numbers can be positive or negative for the same inlet conditions, depending on the heat source strength. In the case of a plug flow, the analytical expressions for the Nusselt numbers have been obtained.