Forced convection heat transfer between parallel plates kept at unequal wall temperatures has been studied assuming laminar, incompressible, steady flow of a Newtonian fluid of constant thermophysical properties. Unequal wall temperatures have been characterized by an asymmetry parameter It has been shown that the heat transferred from the walls monotonically varies with the axial distance even though the Nusselt number (at one of the walls) does not vary continuously due to asymmetry. It has been found that a modified Nusselt number varies continuously with the asymmetry parameter. Plots to obtain heat transferred from each wall have been presented which serve the purpose of mean Nusselt number Non-dimensional heat transferred from the two walls is independent of the asymmetry parameter. The down stream boundary condition applicable for the thermal field when the walls are kept at unequal temperatures has been brought out which becomes necessary when solving elliptic form of conservation of thermal energy equation. say, when axial conduction is included. (C) 2010 Elsevier Ltd All rights reserved.