×

zbMATH — the first resource for mathematics

An oscillating hydromagnetic non-Newtonian flow in a rotating system. (English) Zbl 1060.76130
Summary: We obtain an exact solution of an oscillatory boundary layer flow bounded by two horizontal flat plates, one of which is oscillating in its own plane and the other is at rest. The fluid and the plates are in a state of solid body rotation with constant angular velocity about the \(z\)-axis normal to the plates. The fluid is assumed to be second-grade, incompressible, and electrically conducting. A uniform transverse magnetic field is applied. During the mathematical analysis, it is found that the steady part of the solution is identical to that of viscous fluid. The structure of the boundary layers is also discussed. Several known results are found as particular cases of the solution of the problem considered.

MSC:
76W05 Magnetohydrodynamics and electrohydrodynamics
76A05 Non-Newtonian fluids
76U05 General theory of rotating fluids
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Hartman, I, Hg-dynamics, 1. kgl. danske videnskabernes selskab, Math. fys. medd., 15, (1937)
[2] Rossow, V.J, On flow of electrically conducting fluids over a flat plate in the presence of transverse magnetic field, Nacatn, 3971, (1957)
[3] Davidson, J.H; Kulacki, F.A; Dun, P.F, Convective heat transfer with electric and magnetic fields, (), 9.1-9.49
[4] Gupta, A.S, Magnetohydrodynamic Ekman layer, Acta mech., 13, 155, (1972) · Zbl 0246.76118
[5] Debnath, L, On unsteady magnetohydrodynamic boundary layers in a rotating system, Zamm, 52, 623, (1972) · Zbl 0257.76098
[6] Soundalgekar, V.M; Pop, I, On hydromagnetic flow in a rotating fluid past an infinite porous wall, Zamm, 53, 718, (1973)
[7] Mazumder, B.S; Gupta, A.S; Data, N, The flow and heat transfer in the hydromagnetic Ekman layer on a porous plate with Hall effects, Int. J. heat mass transfer, 19, 523, (1976) · Zbl 0321.76047
[8] Mazumder, B.S, An exact solution of oscillatory Couette flow in a rotating system, ASME J. appl. mech., 58, 1104, (1991) · Zbl 0825.76879
[9] Ganapathy, R, A note on oscillatory Couette flow in a rotating system, ASME J. appl. mech., 61, 208, (1994) · Zbl 0800.76509
[10] Singh, K.D, An oscillatory hydromagnetic flow in a rotating system, Zamm, 80, 6, 429, (2000) · Zbl 0959.76094
[11] Tanner, R.I, Engineering rheology, (1988), Clarendon Press Oxford · Zbl 1171.76301
[12] Rajagopal, K.R, A note on unsteady unidirectional flows of a non-Newtonian fluid, Int. J. non-linear mech., 17, 5/6, 369, (1982) · Zbl 0527.76003
[13] Rivlin, R.S; Ericksen, J.L, Stress deformation relation for isotropic materials, J. rat. mech. anal., 4, 323, (1955) · Zbl 0064.42004
[14] Dunn, J.E; Fosdick, R.L, Thermodynamics, stability and boundedness of fluids of complexity 2 and fluids of second grade, Arch. rat. mech. anal., 56, 191, (1974) · Zbl 0324.76001
[15] Fosdick, R.L; Rajagopal, K.R, Anomalous features in the model of second order fluids, Arch. rat. mech. anal., 70, 145, (1979) · Zbl 0427.76006
[16] Pai, S.I, Magnetogasdynamics and plasma dynamics, (1962), Springer Berlin · Zbl 0102.41702
[17] Telionis, D.P, Unsteady viscous flows, (1981), Springer-Verlag New York · Zbl 0484.76054
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.