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 ۱ - ۲.۵ and then it ascends slowly with the raise of pressure gradient in the range ۲.۵ - ۵.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 quantitiesascend 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 ۱ to ۲ and it drops very slowly when the period of the pipes/channels rises from ۲ to ۱۱.

Keywords:

Mathematical analysis , Porous medium , Permeability , Porosity , Mean velocity.‎