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.

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