This paper presents a numerical study on heat transfer by laminar flows in a two-dimensional channel. The channel is filled with a porous material which is assumed to be non-uniform across the channel, especially near the channel walls where the permeability of the porous material increases drastically to simulate the complexity at the interface between the porous media and the solid walls. Degrees of the non-uniformity of the porous material are described in this study by a parameter β. Heat sources, either constant temperature or constant heat flux, are located on the channel walls, so that heat transfer from the sources into the channel flow is greatly affected by the condition at the wall-porous media interfaces. The temperature distribution near the heat source region and the Nusselt numbers are calculated for different β values. The sensitivity of the non-uniformity of the porous media near the channel walls on the overall heat transfer is assessed. It is found that a higher non-uniformity of the porous material near the channel wall can actually enhance the heat transfer from the sources to the channel flow, as the flow velocity near the wall has been significantly increased due to the higher permeability of the porous material in the near-wall region.