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Analytical solutions of temperature distributions and the Nusselt numbers in forced convection are reported for flow through infinitely long parallel plates, where the upper plate moves in the flow direction with constant velocity and the lower plate is kept stationary. The flow is assumed to be laminar, both hydro-dynamically and thermally fully developed, taking into account the effect of viscous dissipation of the flowing fluid. Both the plates being kept at specified and at different constant heat fluxes are considered as thermal boundary conditions. The solutions obtained from energy equation are in terms of Brinkman number, dimensionless velocity and heat flux ratio. These parameters greatly influence and give complete understanding on heat transfer rates that has potentials for designing and analyzing energy equipment and processes. 113 Figure 4. Nusselt number versus q 2 /q 1 , at U * = −1.0, −0.5, 0.0, 0.5, and 1.0, at various Br q1 . Vertical lines are asymptotes. (a) Br q1 = −0.01; (b) Br q1 = −0.10; (c) Br q1 = 0.00; (d) Br q1 = 0.01; (e) Br q1 = 0.10; (f) Br q1 = 0.50.