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International Journal of Fluid Mechanics Research
ESCI SJR: 0.206 SNIP: 0.446 CiteScore™: 0.5

ISSN 印刷: 2152-5102
ISSN オンライン: 2152-5110

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International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v42.i2.60
pages 170-189

Stokes Flow of Micropolar Fluid Past a Non-Newtonian Liquid Spheroid

Bharat Raj Jaiswal
Department of Mathematics, AKS University, Satna 485001, M.P., India
Bali Ram Gupta
Department of Mathematics, JaypeeUniversity of Engineering and Tech., Guna 473226, M. P., India.

要約

This paper deals with the problem of creeping, steady, axisymmetric Stokes flow of a viscous incompressible micropolar fluid past a Reiner−Rivlin liquid spheroid whose shape deviates a bit from that of a sphere. The polar equation of the deformed sphere is considered for the present study. The stream function solution for the flow outside the liquid spheroid is obtained in terms of modified Bessel functions and Gegenbauer functions, and for the flow inside the liquid spheroid, the stream function solution is obtained by expanding the stream function in terms of S. The flow fields are determined explicitly by matching the boundary conditions at the interface of the micropolar fluid and the liquid spheroid, and uniform velocity at infinity. As an example, the case of an oblate liquid spheroid is considered, and force experienced by it is evaluated. The dependence of drag coefficient on the deformation parameter ε, dimensionless parameter S, viscosities µ1 and µ2, and vortex viscosity κ is discussed for the oblate spheroid and presented graphically. Previous well-known results are then also deduced from the present analysis. It is found that the drag on the oblate spheroid increases with the increase in deformation parameter and cross-viscosity.


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