Mathematical Analysis of Poiseuille Flow of Casson Fluid past Porous Medium

In this article, the influence of microstructure in the Casson fluid flow through a porous medium is investigated, 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-channel/pipes or multiple channels/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 channel width and pipe radius. The porosity of the flow medium slumps with the rise of the periodof the channels and pipes distribution from 1 to 2, and it decreases very slowly with the further rise of the period H of the channels and pipes from 2 to 11.