Jñānābha‎, Vol. 48 (1) (2018), 92-101

SLOW ROTATION OF A SPHERICAL CAVITY ENCLOSING A CONCENTRIC POROUS SPHERE OF VARIABLE PERMEABILITY

Mukesh Awasthi1, Sunil Datta2 & Nidhi Pandya3
1Faculty of Mathematical & Statistical Sciences,SRMU, Lucknow-Deva Road, Uttar Pradesh,INDIA
2;3Department of Mathematics & Astronomy, University of Lucknow, Lucknow, 226007, INDIA


Abstract 


In this paper we present an analytical investigation of slow motion generated by rotation of a spherical container about a concentric porous sphere of variable permeability (kr2−n ,r being the polar distance). The exterior space is filled with viscous fluid. Stokes and Brinkman equations are employed to obtain the flow fields respectively in the region exterior to the porous sphere and inside it. The torque on the sphere is evaluated and wall correction factor are obtained. Graphs to show the effects of various parameters on torque, wall correction factor and velocity are presented and discussed. It is concluded that in general increasing index n the effects decrease. 


Keywords and phrases. Variable permeability, porous sphere, slow rotation, spherical cavity, torque, wall effect. 

2010 Mathematics Subject Classification. 76D07, 74F10.

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