Analysis of double slip model for a partially filled porous microchannel-An exact solution

Forced convective flow in a microchannel partially filled with a porous medium is analytically modeled with the velocity slips at the solid walls and the porous-fluid interfaces. The inertial effect in the porous medium is taken into account. Explicit solutions for the velocity distribution for a partially filled porous channel are obtained. A flow heterogeneity coefficient based on the flow characteristics of the porous medium is proposed, which is used for evaluating the flow characteristics of a partially filled porous channel. The effects of the Darcy number, porosity, inertial constant, Reynolds number, Knudsen number, and the interfacial velocity slip coefficient on the flow characteristics are analyzed. It is shown that the friction factor decreases with an increase in the Darcy number, and the Knudsen number, and a decrease in the dimensionless porous thickness. The flow heterogeneity coefficient increases with an increase in the dimensionless porous thickness and the Darcy number, and a decrease in f⋅Re2 and the Knudsen number. The present work is useful for better understanding of boundary and interfacial velocity slip for high velocity flow in a porous-fluid micro-gap. This work also provides an accurate benchmark for various numerical schemes, which involve porous/fluid interactions.