Effect of viscous dissipation on mixed convection in a vertical channel with boundary conditions of the third kind

Abstract

The effect of viscous dissipation on fully-developed mixed convection is analyzed for the laminar flow in a parallel-plate vertical channel whose walls exchange heat with an external fluid. Both conditions of equal and of different reference temperatures of the external fluid are considered. First, the simpler cases of either negligible Brinkman number or negligible Grashof number are solved analytically. Then, the combined effects of buoyancy forces and of viscous dissipation are analyzed by a perturbation series method. In the examined cases, the velocity field, the temperature field and the Nusselt numbers are evaluated.