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

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 Um (as an experimentally accessible quantity) is prescribed. It is shown that under these conditions both upward (Um > 0) and downward (Um < 0) laminar flow solutions may exist as long as Um does not exceed a maximum value Um,max. The velocity field can either be unidirectional or bidirectional. Moreover, bidirectional flow configurations are possible also for Um = 0. A remarkable feature of the problem is that for Um < Um,max even two solution branches (dual solutions) exist, which merge when Um approaches its maximum value Um,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.