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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.

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A laminar Couette-Poiseullie flow of a Newtonian fluid is considered and heat transfer characteristics are analyzed, attention being given to the effect of viscous dissipation for the thermal boundary condition that both the plates being kept at specified and at different constant heat fluxes. The momentum equation is solved to obtain the velocity profile in such a way that it consists of the velocity of the upper moving plate and in turn the energy equation is solved to yield temperature distribution and Nusselt number. Interesting results are observed based on the influence of various parameters which are in terms of Brinkman number, dimensionless velocity and heat flux ratio.