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Bulletin of Pure and Applied Sciences- Math& Stat. (Started in 1982)
eISSN: 2320-3226
pISSN: 0970-6577
Impact Factor: 4.895 (2017)
DOI: 10.5958/2320-3226
Editor-in-Chief:  Prof. Dr. Lalit Mohan Upadhyaya
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Article Details

Bulletin of Pure and Applied Sciences- Math& Stat. (Started in 1982)
Year : 2020, Volume & Issue : BPAS-Maths & Stat 39E(1), JAN-JUN 2020
Page No. : 58-76, Article Type : Original Aticle
Article DOI : 10.5958/2320-3226.2020.00005.3 (Communicated, edited and typeset in Latex by Lalit Mohan Upadhyaya (Editor-in-Chief). Received March 29, 2019 / Revised February 18, 2020 / Accepted March 13, 2020. Online First Published on June 30, 2020)

Creeping flow of a viscous fluid past a pair of porous separated spheres

T.S.L. Radhika1 , T. Raja Rani2 and Divy Dwivedi3
Author’s Affiliation : 1,3. BITS Pilani- Hyderabad Campus, Hyderabad, Telangana - 500078, India. 2. Research Fellow, University of Portsmouth, U.K. 2. Military Technological College, Muscat, Oman. 1. E-mail: [email protected] , 2. Email: [email protected]

Corresponding Author : T.S.L. Radhika,
E-Mail:-[email protected]


Abstract

In this paper we consider the problem of creeping or the Stokes' flow of a viscous fluid past a pair of porous separated spheres with the problem formulation done in the bipolar coordinate system. Stokesian approximation of the Navier-Stokes equations for the Newtonian fluid model is taken to describe the fluid flow in the region exterior to the porous spheres, while the classical Darcy's law is for the flow inside the porous spheres. An analytical solution to this problem is found wherein the expressions for stream function, pressure and velocity are derived in terms of the Legendre functions, the hyperbolic trigonometric functions and the Gegenbauer functions. Also, the expression for the drag experienced by each of the spheres is found and we carry out numerical evaluations to compute the values of drag in the cases where the two spheres are of equal radii and the case where they are of unequal radii. The plots of streamlines and pressure contours are presented and discussed.

Keywords

Porous separated spheres, Bipolar, Gegenbauer functions, Legendre function, Stream function, Drag. 2020 Mathematics Subject Classification: 76S05, 76S99.
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