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Motion of a permeable shell in a spherical container filled with non-Newtonian fluid

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Abstract

This paper presents an analytical study of creeping motion of a permeable sphere in a spherical container filled with a micro-polar fluid. The drag experienced by the permeable sphere when it passes through the center of the spherical container is studied. Stream function solutions for the flow fields are obtained in terms of modified Bessel functions and Gegenbauer functions. The pressure fields, the micro-rotation components, the drag experienced by a permeable sphere, the wall correction factor, and the flow rate through the permeable surface are obtained for the frictionless impermeable spherical container and the zero shear stress at the impermeable spherical container. Variations of the drag force and the wall correction factor with respect to different fluid parameters are studied. It is observed that the drag force, the wall correction factor, and the flow rate are greater for the frictionless impermeable spherical container than the zero shear stress at the impermeable spherical container. Several cases of interest are deduced from the present analysis.

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Abbreviations

a :

radius of inner sphere

b :

radius of outer sphere

μ :

dynamic viscosity

κ :

vertex viscosity

ω :

microrotation vector

α, β, γ:

gyro viscosity coefficient

p :

pressure

υ θ :

micro-rotation component

ψ :

stream function

D :

drag force

W :

wall correction factor

Q :

flow rate

Kn-1/2(λr), In-1/2(λr):

modified Bessel functions

G n (ζ), H n (ζ):

Gegenbauer functions

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Authors and Affiliations

  1. Department of Mathematics, Jaypee University of Engineering and Technology, Madhya Pradesh, 473226, India

    V. Mishra & B. R. Gupta

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  1. V. Mishra
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  2. B. R. Gupta
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Correspondence to B. R. Gupta.

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Mishra, V., Gupta, B.R. Motion of a permeable shell in a spherical container filled with non-Newtonian fluid. Appl. Math. Mech.-Engl. Ed. 38, 1697–1708 (2017). https://doi.org/10.1007/s10483-017-2287-8

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  • DOI: https://doi.org/10.1007/s10483-017-2287-8

Keywords

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2010 Mathematics Subject Classification

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