Mixed convection flow in vertical channel with boundary conditions of third kind in presence of heat source/sink

The effects of viscous dissipation and heat source/sink on fully developed mixed convection for the laminar flow in a parallel-plate vertical channel are investigated. The plate exchanges heat with an external fluid. Both conditions of equal and different reference temperatures of the external fluid are considered. First, the simple cases of the negligible Brinkman number or the negligible Grashof number are solved analytically. Then, the combined effects of buoyancy forces and viscous dissipation in the presence of heat source/sink are analyzed by a perturbation series method valid for small values of the perturbation parameter. To relax the conditions on the perturbation parameter, the velocity and temperature fields are solved by using the Runge-Kutta fourth-order method with the shooting technique. The velocity, temperature, skin friction, and Nusselt numbers at the plates are discussed numerically and presented through graphs.