Mathematical analysis of Poiseuille flow of Casson fluid past porous medium

This article investigates the influence of microstructure in the Casson fluid flow through porous medium, by extending the Buckingham-Reiner’s one dimensional model to plane-Poiseuille flow and Hagen-Poiseuille flow geometries. While analyzing the flow characteristics in single chael/pipes or multiple chaels/pipes of different width/radius, four different probability density functions are used to model the pores widths/radii distributions. It is found that when the pressure gradient increases, the Buckingham-Reiner function raises slowly in the plane-Poiseuille flow, whereas in Hagen-Poiseuille flow, it rises rapidly. In all kinds of distribution of pores, the fluid’s mean velocity and porosity of the flow medium are considerably higher in the Hagen-Poiseuille flow than in the plane-Poiseuille flow and this behavior is reversed for the permeability of the flow medium. The fluid’s mean velocity, porosity and permeability of the flow medium increases appreciably with the rise of the chael width and pipe radius. The porosity of the flow medium slumps with the rise of the period of the chaels and pipes distribution from 1 to 2 and it decreases very slowly with the further rise of the period H of the chaels and pipes from 2 to 11.