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

Document Type : Research Paper

Authors

1 Applied Mathematics and Economics Programme, School of Applied Sciences and Mathematics, Universiti Teknologi Brunei,‎ Jalan Tungku Link, Bandar Seri Begawan, BE1410, Brunei Darussalam

2 UTM Centre for Industrial and Applied Mathematics, Ibnu Sina Institute for Scienntific and Industrial Research, Universiti Teknologi Malaysia,‎ ‎81310 Johor Bharu, Johor, Malaysia‎

3 Ship & Offshore Extreme Technology Industry-Academic Co-operation Research Center, Inha university, 100 Inha-ro, Incheon, 22212, South Korea

4 School of Mathematics, Computer Science and Engineering, Liverpool Hope University, Hope Park, Liverpool L16 9JD, United Kingdom‎

5 Department of Mathematical Sciences, Universiti Teknologi Malaysia, 81310 Johor Bharu, Johor, Malaysia‎

6 Department of Mathematics, National Institute of Technology, Yupia – 791112, Arunachal Pradesh, India‎

Abstract

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 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 1 to 2 and it drops very slowly when the period of the pipes/channels rises from 2 to 11.

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Main Subjects

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