Convective flow of two immiscible viscous and couple stress permeable fluids through a vertical channel

Abstract

An analytical solution is presented for fully developed laminar flow between vertical parallel plates filled with 2 immiscible viscous and couple stress fluids in a composite porous medium. The flow in the porous medium is modeled using the Brinkman equation. The viscous and Darcy dissipation terms are included in the energy equation. The transport properties of the fluids in both regions are assumed to be constant. The continuity conditions for the velocity, temperature, shear stress, and the heat flux at the interfaces between the couple stress permeable fluid layer and the viscous fluid layer are assumed. The influence of physical parameters on the flow, such as the couple stress parameter, porous parameter, Grashof number, viscosity ratio and conductivity ratio, are evaluated, and a set of graphical results is presented. An interesting and new approach is incorporated to analyze the flow for strong, weak, and comparable porosity conditions with the couple stress fluid parameter. © TÜB?TAK.