A Variant of the Classical Von Kármán Flow for a Couple Stress Fluid
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Abstract
We present an attempt to study the influence of couple stresses on the flow induced by an infinite disk rotating with a constant angular velocity. The governing equations of motion in three dimensions are treated analytically yielding the derivation of exact solutions which differ from those corresponding to the classical Von Kármán's flow. The analysis reveals that a boundary layer structure develops near the surface of the disk, whose far-field behaviour is distinct from the near-wall solution. The velocity and vorticity components for various values of the dimensionless parameters, associated with the flow, are presented graphically. -
References
[1] Cochran W G 1930 Proc. Cambridge Phil. Soc. 30 365 doi: 10.1017/S0305004100012561 [2] Berker R 1982 Int. J. Eng. Sci. 20 217 [3] Rajagopal K R 1988 Int. J. Eng. Sci. 22 451 [4] Erdogan M E 1977 Rev. Roum. Mec. Appl. 22 171 [5] Erdogan M E 1976 ASME J. Appl. Mech. 43 203 [6] Rajagopal K R and Parter S V 1984 Arch. Rat. Mech. Anal. 89 305 [7] Turkyilmazoglu M 2009 Int. J. Non-Linear Mech. 44 209 [8] Siddiqui A M, Farooq A A 2011 Int. J. Appl. Math. Mech. 38 71 [9] Farooq A A 2012 Int. J. Appl. Math. Mech. 8 96 [10] Stokes V K 1966 Phys. Fluids 9 1709 [11] Mekheimer Kh S 2008 Phys. Lett. A 372 4271 [12] Srinvasacharya D, Srinivasacharya N and Odelu O 2009 Int. Comm. Heat Mass Transfer. 36 180 -
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