On the boundary conditions at the interface between a porous layer and a fluid layer

Abstract

In this paper, hydrodynamic and thermal boundary conditions at the interface between a porous layer and a fluid layer are investigated through a theoretical study. Concerning hydrodynamic boundary conditions at the porous-plain media interface, three kinds of boundary conditions have been suggested and used by previous investigators. They are slip-velocity condition, continuous shear stress condition with continuous velocity condition and slip-shear-stress condition with continuous velocity condition. Using the three boundary conditions, we obtain analytical solutions for velocity distribution for the composite system consisting of the porous layer and the fluid layer. The heat transfer at the porous-plain media interface is analytically and numerically investigated. A volume-averaged energy equation, which governs the energy transport in the fluid layer, is newly proposed together with the two-equation model due to the non-uniformity of the temperature distribution parallel to the interface in the fluid layer. Under the assumption of the local thermal equilibrium, analytical solutions based on the one-equation model are obtained with a continuous boundary condition with or without a slip-heat-flux condition. When the local thermal equilibrium is not valid, the analytical solutions are solved for temperature distribution using the newly proposed energy equation together with the two-equation model with continuous heat flux and temperature conditions in the sense of the volume averaging and an additional boundary condition obtained from the energy balance in the porous layer. To determine the most appropriate hydrodynamic and thermal boundary conditions, we introduce an ideal composite system consisting of a fluid layer and an ideal porous layer, which is shaped like a rectangular microchannel. For the ideal composite system, velocity distributions and temperature distributions are obtained by numerically solving the Navier-Stokes equation and the energy equa...