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

This theoretical study analyses the effects of geometrical and fluid parameters on the flow metrics 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.