Theoretical Study on Poiseuille Flow of Herschel-Bulkley Fluid in Porous Media

Abstract

This theoretical study analyses the effects of geometrical and fluid parameters on the flow metrices in the Hagen-Poiseuille and plane-Poiseuille flows of Herschel-Bulkley fluid through porous medium which is considered as (i) single pipe/single channel and (ii) multi–pipes/multi-channels when the distribution of pores size in the flow medium are represented by each one of the four probability density functions: (i) Uniform distribution, (ii) Linear distribution of Type-I, (iii) Linear distribution of Type-II and (iv) Quadratic distribution. It is found that in Hagen-Poiseuille and plane-Poiseuille flows, Buckingham-Reiner function increases linearly when the pressure gradient increases in the range 1 - 2.5 and then it ascends slowly with the raise of pressure gradient in the range 2.5 - 5. In all of the four kinds of pores size distribution, the fluid’s mean velocity, flow medium’s porosity and permeability are substantially higher in Hagen-Poiseuille fluid rheology than in plane-Poiseuille fluid rheology and, these flow quantities ascend considerably with the raise of pipe radius/channel width and a reverse characteristic is noted for these rheological measures when the power law index parameter increases. The flow medium’s porosity decreases rapidly when the period of the pipes/channels distribution rises from 1 to 2 and it drops very slowly when the period of the pipes/channels rises from 2 to 11.