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 divided by 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,U- 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,U-max even two solution branches (dual solutions) exist, which merge when U-m approaches its maximum value U-m,U- 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.