Document Type : Research Paper

Authors

• D.S. Sankar ¹
• K.K. Viswanathan ^{2, 3}
• Atulya K. Nagar ⁴
• Nurul Aini Binti Jaafar ⁵
• A. Vanav Kumar ⁶

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.

Keywords

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

Main Subjects

• Nonlinear Dynamics

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.