Analysis of Combined Forced and Free Flow in a Vertical Channel With Viscous Dissipation and Isothermal-Isoflux Boundary Conditions

In the last years, several analyses of combined forced and free convection in vertical channels have appeared in the literature. Most of the interest in this subject is due to its applications, for instance, in the design of cooling systems for electronic devices and in the field of solar energy collection. Fully developed and laminar mixed convection in a parallel-plate vertical channel is investigated in the case of non-negligible viscous heating. The channel walls are subjected to asymmetric boundary conditions: One wall experiences a constant and uniform heat flux, while the other is kept at a uniform and constant temperature. The velocity field and the temperature field are evaluated analytically by means of perturbation expansions with respect to a buoyancy parameter, i.e., the ratio between the Grashof number and the Reynolds number. The Nusselt numbers and the friction factors are obtained as functions of the buoyancy parameter.