Heat transfer by fully developed flow and viscous heating in a vertical channel with prescribed wall heat fluxes

An analysis of combined forced and free convection in a vertical parallel-plate channel with prescribed wall heat fluxes is performed by considering a fully developed flow and by taking into account the effect of viscous dissipation. It is shown that the condition of fully developed flow cannot be accomplished if a streamwise change of the wall heat fluxes occurs. An analytical solution of the momentum balance and energy balance equations is found by a perturbation method. In particular, the forced convection flow with viscous heating is treated as the base heat transfer process. Then, the effect of buoyancy is accounted for by expressing the fluid velocity and temperature as power series with respect to the ratio between the Grashof number and the Reynolds number.