Influence of thickness on porous lining when the inclined channel walls are bounded by a deformable porous layer

Abstract

This paper deals with the viscous fluid flow in an inclined channel bounded by a deformable porous layer. The coupled phenomenon of fluid movement and solid deformation in the porous layer was considered. The governing equations were obtained for the fluid velocity, solid displacement and temperature distribution in the deformable porous medium. Analytical solutions were obtained for solid displacement, fluid velocity, velocity in the free flow region and temperature distributions. The results were analysed for different physical parameters using graphs. The results revealed that the effect of the thickness of the porous layer was significant on solid displacement and fluid velocity. The solid displacement decreased by increasing the volume fraction of the fluid and the thickness of the porous layer. Since the drag coefficient was the ratio of fluid viscosity to the permeability of the porous material, it follows that the enhancement in drag reduces the permeability of the bounding porous layer. The flow in the blood vessels (capillaries) is surrounded by a tissue layer which is modelled as a deformable porous medium.