Shahid Chamran University of AhvazJournal of Applied and Computational Mechanics2383-45368420221001Theoretical Study on Poiseuille Flow of Herschel-Bulkley Fluid in Porous Media124612691684010.22055/jacm.2021.36921.2928END.S.SankarApplied Mathematics and Economics Programme, School of Applied Sciences and Mathematics, Universiti Teknologi Brunei, Jalan Tungku Link, Bandar Seri Begawan, BE1410, Brunei Darussalam0000-0002-2039-5922K.K.ViswanathanUTM Centre for Industrial and Applied Mathematics, Ibnu Sina Institute for Scienntific and Industrial Research, Universiti Teknologi Malaysia, 81310 Johor Bharu, Johor, MalaysiaShip & Offshore Extreme Technology Industry-Academic Co-operation Research Center, Inha university, 100 Inha-ro, Incheon, 22212, South Korea0000-0003-4470-4774Atulya K.NagarSchool of Mathematics, Computer Science and Engineering, Liverpool Hope University, Hope Park, Liverpool L16 9JD, United Kingdom0000-0001-5549-6435Nurul AiniBinti JaafarDepartment of Mathematical Sciences, Universiti Teknologi Malaysia, 81310 Johor Bharu, Johor, Malaysia0000-0003-4346-6786A. VanavKumarDepartment of Mathematics, National Institute of Technology, Yupia – 791112, Arunachal Pradesh, India0000-0002-9123-9230Journal Article20210315This 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<span lang="EN-SG"> 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</span> 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.https://jacm.scu.ac.ir/article_16840_39277d65173045e342bc8310d166a88c.pdf