Mixed convection with viscous dissipation in a vertical channel filled with a porous medium

Abstract

The fully developed laminar mixed convection flow in a vertical plane parallel channel filled with a porous medium and subject to isoflux ÷ isothermal wall conditions is investigated assuming that (i) the Darcy law and the Boussinesq approximation hold, (ii) the effect of viscous dissipation is significant, and (iii) the average flow velocity U m (as an experimentally accessible quantity) is prescribed. It is shown that under these conditions both upward (U m > 0) and downward (U m < 0) laminar flow solutions may exist as long as U m does not exceed a maximum value U m, max. The velocity field can either be unidirectional or bidirectional. Moreover, bidirectional flow configurations are possible also for U m = 0. A remarkable feature of the problem is that for U m < U m, max even two solution branches (dual solutions) exist, which merge when U m approaches its maximum value U m, max. The mechanical and thermal characteristics of the flow configurations associated with the dual solutions are investigated in the paper analytically and numerically in detail.