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

Abstract

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.