Abstract
Unsteady flow over an infinite permeable rotating cone in a rotating fluid in the presence of an applied magnetic field has been investigated. The unsteadiness is induced by the time-dependent angular velocity of the body, as well as that of the fluid. The partial differential equations governing the flow have been solved numerically by using an implicit finite-difference scheme in combination with the quasi-linearization technique. For large values of the magnetic parameter, analytical solutions have also been obtained for the steady-state case. It is observed that the magnetic field, surface velocity, and suction and injection strongly affect the local skin friction coefficients in the tangential and azimuthal directions. The local skin friction coefficients increase when the angular velocity of the fluid or body increases with time, but these decrease with decreasing angular velocity. The skin friction coefficients in the tangential and azimuthal directions vanish when the angular velocities of fluid and the body are equal but this does not imply separation. When the angular velocity of the fluid is greater than that of the body, the velocity profiles reach their asymptotic values at the edge of the boundary layer in an oscillatory manner, but the magnetic field or suction reduces or suppresses these oscillations.
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References
Hide, R., Roberts, P.H., ‘The origin of the main geomagnetic field’, in: Physics and Chemistry of the Earth. Vol. 4, Pergamon Press, New York, 1961, pp. 27–98.
Dieke, R.H., ‘Internal rotation of the sun’, in: L. Goldberg (Ed.) Annual Reviews of Astronomy and Astrophysics. Vol. 8, Annual Review Inc., New York, 1970, pp. 297–328.
Bodewadt, U.T., ‘Die Drehstromung Uber festern Grand’, ZAMM 20 (1940) 241–253.
Von Karman, Th., ‘Uber laminare und turbulente Reibung’, ZAMM 1 (1921) 233–252.
King, W.S. and Lewellen, W.S., ‘Boundary layer similarity solutions for rotating flow with or without magnetic interaction’, Phys. Fluids 7 (1964) 1674–1680.
King, W.S. and King, W.S., ‘The boundary layer of a conducting vortex flow over a disk with an axial magnetic field’, in: Ostrach, S. and Scanlan, R.H. (eds) Development in Mechanics, Vol. 2, 1965, pp. 107–125.
Stewartson, K. and Troesch, B.A., ‘On a pair of equations occurring in swirling viscous flow with an applied magnetic field’, ZAMP 28 (1977) 951–963.
Nath, G. and Venkatachala, B.J., ‘The effect of suction on boundary layer for rotating flows with or without magnetic field’, Proc. Ind. Acad. Sci. 85 (1977) 332–337.
Sparrow, E.M. and Cess, R.D., ‘Magneto-hydrodynamic flow and heat transfer about a rotating disk’, J. Appl. Mech. 29 (1962) 181–187.
Tarek, M.A., Mishkawy, El., Hazem, A.A. and Adel, A.M., ‘Asymptotic solution for the flow due to an infinite rotating disk in the case of small magnetic field’, Mech. Res. Comm. 25 (1998) 271–278.
Rogers, M.H. and Lance, G.N., ‘The rotationally symmetric flow of a viscous fluid in the presence of an infinite rotating disk’, J. Fluid Mech. 7 (1960) 617–631.
Bien, F. and Penner, S.S.: ‘Velocity profiles in steady and unsteady rotating flow for a finite cylindrical geometry’, Phys. Fluids 13 (1970) 1665–1671.
Kuo, H.L., ‘Axi-symmetric flows in the boundary layer of a maintained vortex’, J. Atmos. Sci. 28 (1971) 20–41.
Millsaps, K. and Nydahl, J.E., ‘Heat transfer in a laminar cyclone’, ZAMM 53 (1973) 241–246.
Tien, C.L. and Tsuji, I.J., ‘A theoretical analysis of laminar forced flow and heat transfer about a rotating cone’, J. Heat Transfer 87 (1965) 184–190.
Koh, T.C.Y. and Price, J.F., ‘Non-similar boundary layer heat transfer of a rotating cone in forced flow’, J. Heat Transfer 89 (1967) 139–145.
Wang, C.Y., ‘Boundary layers on rotating cones, disks and axi-symmetric surfaces with concentrated heat source’, Acta Mechanica 81 (1990) 245–251.
Vira, N.R. and Fan, D.N., ‘Heat transfer from a cone spinning in a co-rotating fluid’, J. Heat Transfer 103 (1981) 815–817.
Ece, M.C., ‘An initial boundary layer flow past a translating and spinning rotational symmetric body’, J. Eng. Math. 26 (1992) 415–428.
Ozturk, A. and Ece, M.C., ‘Unsteady forced convection heat transfer from a translating and spinning body’, J. Heat Transfer 117 (1995) 318–323.
Berker, R., ‘A new solution of the Navier-Stokes equations for the motion of a fluid confined between two parallel plates rotating about the same axis’, Arch. Mech. 31 (1979) 265–280.
Porter, S.V. and Rajagopal K.R., ‘Swirling flow between rotating plates’, Arch. Rat. Mech. Anal. 86 (1984) 305–315.
Lai, C.Y., Rajagopal, K.R. and Szeri, S.Z., ‘Asymmetric flow between parallel rotating disks’, J. Fluid Mech. 146 (1984) 203–225.
Lai, C.Y., Rajagopal, K.R. and Szeri, S.Z., ‘Asymmetric flow above a rotating disk’, J. Fluid Mech. 157 (1985) 471–492.
Inouye, K. and Tate, A., ‘Finite-difference version quasi-linearization applied to boundary layer equations’, AIAA J. 12 (1974) 558–560.
Varga, R.S., Matrix Iterative Analysis, Springer, New York, 2000, pp. 220.
Eringen, A.C. and Maugin, S.A., Electrodynamics in Continua, Vol. 2, Springer, Berlin 1990.
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Roy, S., Takhar, H. & Nath, G. Unsteady MHD Flow on a Rotating Cone in a Rotating Fluid. Meccanica 39, 271–283 (2004). https://doi.org/10.1023/B:MECC.0000022847.28148.98
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DOI: https://doi.org/10.1023/B:MECC.0000022847.28148.98