Forced convection in bidisperse porous media incorporating viscous dissipation

Highlights: • Forced convection in a bidisperse parallel-plate channel is studied incorporating viscous dissipation. • The analysis emphasizes on the effects of bidispersivity and viscous dissipation on the thermal performance. • Critical Brinkman numbers arising from the cold wall cases lead to the singularity in Nusselt numbers. • The bidispersivity plays a significant role in balancing the wall heat flux and the heat generated by viscous dissipation. Forced convective heat transfer in a parallel-plate channel filled with a bidisperse porous medium (BDPM) is studied analytically incorporating viscous dissipation, in which the constant wall heat flux condition is taken into account. The flow is assumed to be hydrodynamically and thermally fully developed and is described by a two-velocity one-temperature formulation. Exact solutions are obtained for the temperature distributions of both f- and p-phases and the Nusselt number. The analysis emphasizes on the effects of bidispersivity and viscous dissipation on the thermal performance. It is found that the existing critical Brinkman numbers, which arise from the cold wall case only, lead to the singularity in Nusselt numbers. More importantly, the bidispersivity plays a significant role in balancing the heat flux at the wall and the heat generated by viscous dissipation. For both cases with and without viscous dissipation, the Nusselt numbers become independent of the bidispersivity when the Darcy number ratio increases.