ORIGINAL PAPER
Slowly Vibrating Axially Symmetric Bodies-Transverse Flow
 
 
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Department of Mathematics, B.S.N.V. Post Graduate College, K.K.V., University of Lucknow, Station Road, Charbagh, Lucknow-226001, U.P., India
 
 
Online publication date: 2021-01-29
 
 
Publication date: 2021-03-01
 
 
International Journal of Applied Mechanics and Engineering 2021;26(1):226-250
 
KEYWORDS
ABSTRACT
Stokes drag on axially symmetric bodies vibrating slowly along the axis of symmetry placed under a uniform transverse flow of the Newtonian fluid is calculated. The axially symmetric bodies of revolution are considered with the condition of continuously turning tangent. The results of drag on sphere, spheroid, deformed sphere, egg-shaped body, cycloidal body, Cassini oval, and hypocycloidal body are found to be new. The numerical values of frictional drag on a slowly vibrating needle shaped body and flat circular disk are calculated as particular cases of deformed sphere.
 
REFERENCES (15)
1.
Stokes G.G. (1851): On the effect of the internal friction of fluids on pendulums.– Trans. Comb. Philos. Soc., vol.9, p.8.
 
2.
Kanwal R.P. (1955): Rotatory and longitudinal oscillations of axi-symmetric bodies in a viscous fluid.– J. Fluid Mech., vol.9, No.4, pp.631-636.
 
3.
Payne L.E. and Pell W.H. (1960): The Stokes flow problem for a class of axially symmetric bodies.– J. Fluid Mech., vol.7, No.4, pp.529-549.
 
4.
Kanwal R.P. (1964): Drag on an axially symmetric body vibrating slowly along its axis in a viscous fluid.– J. Fluid Mech., vol.19, No.4, pp.631-636.
 
5.
Proudman I. and Pearson J.R.A. (1957): Expansions at small Reynolds numbers for flow past a sphere and a circular cylinder.– J. Fluid Mech., vol.2, pp.237-262.
 
6.
Chwang A. T. and Wu T.Y. (1975): Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows.– J. Fluid Mech., vol.67, No.4, pp.787-815.
 
7.
Datta S. and Srivastava D.K. (1999): Stokes drag on axially symmetric bodies: a new approach.– Proceedings Math. Sci., Ind. Acad. Sci., vol.109, No.4, pp.441-452.
 
8.
Srivastava D.K. (2001): Stokes drag on axially symmetric bodies: a note.– Nepali Math. Sci. Report, vol.19, No.1 and No.2, pp.29-34.
 
9.
Srivastava D.K., Yadav R.R. and Yadav S. (2012): Steady Stokes flow around deformed sphere: class of oblate axi-symmetric bodies.– Int. J. of Appl. Math and Mech., vol.9, No.20, pp.16-44.
 
10.
Srivastava D.K., Yadav R.R. and Yadav S. (2013): Steady Stokes flow around deformed sphere: class of prolate axi-symmetric bodies.– Int. J. of Appl. Math and Mech., vol.9, No.20, pp.16-44.
 
11.
Lamb H. (1945): Hydrodynamics.– 6th ed., New York: Dover.
 
12.
Landau L.D. and Lifshitz E.M. (1959): Fluid Mechanics.– New York: Addison-Wesley.
 
13.
Happel J. and Brenner H. (1983): Low Reynolds Number Hydrodynamics.– Nijhoff, Dordrecht, The Nederlands.
 
14.
Kohr M. and Pop I. (2004): Viscous Incompressible Flow for Low Reynolds Numbers.– WIT Press, Southampton (UK), Boston.
 
15.
Sangtae Kim and Seppo J. Karrila (2005): Microhydrodynamics: Principles and Selected Applications.– Courier Corporation.
 
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ISSN:1734-4492
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