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Drag on a permeable sphere placed in a micropolar fluid with non-zero boundary condition for microrotations

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper concerns an analytical study of an infinite expanse of uniform flow of steady axisymmetric creeping flow of an incompressible micropolar fluid around the permeable sphere assuming a nonhomogeneous boundary condition for microrotation vector. It is assumed that microrotation vector is proportional to the rotation rate of velocity vector. The stream function solutions for the flow fields are obtained in the terms of modified Bessel’s functions and Gegenbauer functions. Continuity of normal velocity, no-slip condition, non-zero microrotation vector on the sphere, uniform velocity at infinity are the different boundary conditions used to determine the flow fields explicitly. The microrotation component, pressure field, bounds of permeability parameter and drag force experienced by the permeable sphere are calculated. Dependence of the drag force on different fluid parameters is presented graphically and discussed. It is found that drag force decreases with increasing spin parameter. Several cases of interest are deduced from the present analysis.
Rocznik
Strony
97--109
Opis fizyczny
Bibliogr. 21 poz, rys.
Twórcy
autor
  • Department of Mathematics, Jaypee University of Engineering & Technology
autor
  • Department of Mathematics, Jaypee University of Engineering & Technology Guna, M.P, India
Bibliografia
  • [1] Darcy H., Les Fontaines Publiques, De La Ville De Dijon, Paris, Victor Dalmont, 1856.
  • [2] Wolfersdorf L.V., Stokes flow past a sphere with permeable surface, Journal of Applied Mathematics and Mechanics 1989, 69, 111-112.
  • [3] Leonov A.I., The slow stationary flow of a viscous fluid about a porous sphere, Journal of Applied Mathematics and Mechanics 1962, 26, 564-566.
  • [4] Zeng, Yu, Wu, Wang-Yi, A new exact solution of the Stokes equation, Chinese Sci. Bull. 1990, 35(14), 1172-1176.
  • [5] Joseph D.D., Tao L.N., The effect of permeability on the slow motion of a porous sphere in a viscous liquid, Journal of Applied Mathematics and Mechanics 1964, 44, 361-364.
  • [6] Birikh, R., Rudakoh R., Slow motion of a permeable sphere in viscous fluid, Fluid Dynamics 1982, 17(5), 792-793.
  • [7] Happel J., Brenner H., Low Reynolds Number Hydrodynamics, Martinus Nijhoff, Publishers, Hague 1983.
  • [8] Padmavathi B.S., Amarnath T., Palaniappan D., Stokes flow past a permeable sphere-nonaxisymetric case, Journal of Applied Mathematics and Mechanics 1994, 74, 290-292.
  • [9] Usha R., Creeping flow with concentric permeable spheres in relative motion, Journal of Applied Mathematics and Mechanics 1995, 75, 644-646.
  • [10] Vasudeviah M., Malathi V., Slow viscous flow past a spinning sphere with permeable surface, Mechanics Research Communications 1995, 22(2), 191-200.
  • [11] Eringen A.C., Theory of micropolar fluids, J. Math. Mech. 1966, 16, 1-18.
  • [12] Ramkisoon H., Majumdar S.R., Drag on an axially symmetric body in the Stokes flow of micropolar fluid, Physics of Fluids 1976, 19, 16-21.
  • [13] Rao S.K.L., Rao, P. B., Slow stationary flow of a micropolar fluid past a sphere, J.Engg. Maths. 1971, 4, 209-217.
  • [14] Srinivasacharya D., Rajyalakshmi I., Creeping flow of micropolar fluid past a porous sphere, App. Mathematics and Computation 2004, 153, 843-854.
  • [15] Ramkissoon H., Flow of micropolar fluid past a Newtonian fluid sphere, Journal of Applied Mathematics and Mechanics 1985, 12, 635-637.
  • [16] Haffmann K.H., Marx D., Botkin N., Drag on spheres in micropolar fluids with non-zero boundary conditions for microrotations, J. Fluid. Mech. 2007, 590, 319-330.
  • [17] Gupta B.R., Deo S., Stokes flow of micropolar fluid past a porous sphere with non-zero boundary condition for microrotations, International Journal of Fluid Mechanics Research 2010, 37(5), 424-434.
  • [18] Jaiswal B.R., Gupta B.R., Drag on Reiner-Rivlin liquid sphere placed in micropolar fluid with non-zero boundary condition for microrotations, Int. J. of Appl. Math. and Mech. 2014, 10(7), 90-103.
  • [19] Gupta B.R., Dev S., Axisymmetric creeping flow of micropolar fluid over a sphere coated with a thin fluid film, Journal of Applied Fluid Mechanics 2013, 6(2), 149-155.
  • [20] Aparna P., Murthy J.V.R., Nagaraju G., Slow steady rotation of a permeable sphere in an incompressible couple stress fluid, International Journal of Mathematical Archive 2015, 6(2), 1-9.
  • [21] Aparna P., Murthy J.V.R., Uniform flow of an incompressible micropolar fluid past a permeable sphere, International Electronic Engineering Mathematical Society 2010, 8, 1-10.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-221ac2de-4675-4d58-a366-f24e16270f56
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