Viscosity dissipation and mixed convection flow in a vertical double-passage channel with permeable fluid

The method of regular perturbation is used to analyse the fully developed flow and heat transfer in a vertical two-way channel containing a permeable liquid. The Brinkman model is used for flow through porous media. The energy equation contains a viscosity term and a Darcy dissipation term. The fully conductive thin partition is divided into two stages; the wall is uniformly heated; and the effects of the porous parameter σ and the mixed convection parameter λ on the velocity and temperature distribution near the hot and cold walls are investigated. The results show that these effects mainly depend on the position of the baffle. Analytical solutions are first used to resolve the simpler problems of either a negligible Brinkman number or a negligible Grashof number. Then, using a perturbation series method, the combined effects of buoyant forces and viscous dissipation are examined. The velocity field and the temperature field in the cases under study were assessed.