Similarity solutions to rotating Couette flow of non-Newtonian fluids in the presence of a magnetic field
Authors:
J. P. Pascal and H. Pascal
Journal:
Quart. Appl. Math. 54 (1996), 345-358
MSC:
Primary 76A05; Secondary 76W05
DOI:
https://doi.org/10.1090/qam/1388021
MathSciNet review:
MR1388021
Full-text PDF Free Access
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Abstract: We study the rotating Couette flow of conducting power law fluids in the presence of a magnetic field. We analyze the coupled effects of the rheology and the magnetic field on the angular velocity and shear stress distributions for the case when an infinite long cylinder rotates in an unbounded fluid. For shear thickening fluids our exact similarity solutions exhibit traveling wave characteristics determining the existence of a moving shear front. We investigate the electrorheological effect on the propagation of the shear disturbances front.
A. Acrivos et al., Momentum and heat transfer in laminar boundary layer flow of non-Newtonian fluids past external surfaces, A.I.Ch.E.J. 6, 312–317 (1960)
K. G. Batchelor, An introduction to fluid dynamics, Cambridge Univ. Press, London and New York, 1967
D. Bershader (ed.), The Magnetohydrodynamics of Conducting Fluids, Symposium, Stanford University Press, 1959
F. N. Frenkel and W. R. Sears (eds.), Magnetofluid dynamics, Rev. Modern Phys. 32 (1960)
R. Gorla et al., Effects of transverse magnetic field on mixed convection in wall plume of power law fluids, Internat. J. Engrg. Sci. (7) 31, 1035–1045 (1993)
D. Gray, The laminar plume above a line heat source in a transverse magnetic field, Appl. Sci. Research 33, 437–451 (December 1977)
N. Kapur and C. Srivastava, Similar solutions of the boundary layer equations for power law fluids, Z. Angew. Math. Phys. 14, 385–389 (1963)
M. Katagini, Flow formation in Couette motion in magnetohydrodynamics, J. Phys. Soc. Japan 17, 393 (1962)
R. Landshoff (ed.), Magnetohydrodynamics, Symposium, Stanford University Press, 1960
H. K. Moffatt, Report on the NATO Advanced Study Institute on magnetohydrodynamic phenomena in rotating fluids, J. Fluid Mech. 57, 635 (1973)
S. Pai, Viscous Flow Theory, D. Van Nostrand Company Inc., 1956
H. Pascal, Similarity solutions to some unsteady flows of non-Newtonian fluids of power law behavior, Internat. J. Non-Linear Mech. 27, 759–771 (1992)
R. K. Rathy, Hydrodynamic Couette’s flow with suction and injection, Z. Angew. Math. Phys. (7) 43 (1963)
C. Roger and W. F. Ames, Nonlinear Boundary Value Problems in Science and Engineering, Academic Press Inc., New York, 1989
J. P. Pascal and H. Pascal, Pressure diffusion in unsteady non-Darcian flows through porous media, European J. Mech. B Fluids 14, 75–90 (1995)
J. P. Pascal and H. Pascal, On some non-linear shear flows of non-Newtonian fluids, Internat. J. Non-Linear Mech. 30, 487–500 (1995)
K. Sarweswar and M. Ram, Stagnation points flows of non-Newtonian power law fluids, Z. Angew. Math. Phys. 19, 84–144 (1966)
R. Schowalter, The application of boundary layer theory to power law pseudoplastic fluids, similar solutions, A.I.Ch.E.J. 6, 24–28 (1960)
G. W. Sutton and A. Sherman, Engineering Magnetohydrodynamics, McGraw-Hill, 1965
A. Acrivos et al., Momentum and heat transfer in laminar boundary layer flow of non-Newtonian fluids past external surfaces, A.I.Ch.E.J. 6, 312–317 (1960)
K. G. Batchelor, An introduction to fluid dynamics, Cambridge Univ. Press, London and New York, 1967
D. Bershader (ed.), The Magnetohydrodynamics of Conducting Fluids, Symposium, Stanford University Press, 1959
F. N. Frenkel and W. R. Sears (eds.), Magnetofluid dynamics, Rev. Modern Phys. 32 (1960)
R. Gorla et al., Effects of transverse magnetic field on mixed convection in wall plume of power law fluids, Internat. J. Engrg. Sci. (7) 31, 1035–1045 (1993)
D. Gray, The laminar plume above a line heat source in a transverse magnetic field, Appl. Sci. Research 33, 437–451 (December 1977)
N. Kapur and C. Srivastava, Similar solutions of the boundary layer equations for power law fluids, Z. Angew. Math. Phys. 14, 385–389 (1963)
M. Katagini, Flow formation in Couette motion in magnetohydrodynamics, J. Phys. Soc. Japan 17, 393 (1962)
R. Landshoff (ed.), Magnetohydrodynamics, Symposium, Stanford University Press, 1960
H. K. Moffatt, Report on the NATO Advanced Study Institute on magnetohydrodynamic phenomena in rotating fluids, J. Fluid Mech. 57, 635 (1973)
S. Pai, Viscous Flow Theory, D. Van Nostrand Company Inc., 1956
H. Pascal, Similarity solutions to some unsteady flows of non-Newtonian fluids of power law behavior, Internat. J. Non-Linear Mech. 27, 759–771 (1992)
R. K. Rathy, Hydrodynamic Couette’s flow with suction and injection, Z. Angew. Math. Phys. (7) 43 (1963)
C. Roger and W. F. Ames, Nonlinear Boundary Value Problems in Science and Engineering, Academic Press Inc., New York, 1989
J. P. Pascal and H. Pascal, Pressure diffusion in unsteady non-Darcian flows through porous media, European J. Mech. B Fluids 14, 75–90 (1995)
J. P. Pascal and H. Pascal, On some non-linear shear flows of non-Newtonian fluids, Internat. J. Non-Linear Mech. 30, 487–500 (1995)
K. Sarweswar and M. Ram, Stagnation points flows of non-Newtonian power law fluids, Z. Angew. Math. Phys. 19, 84–144 (1966)
R. Schowalter, The application of boundary layer theory to power law pseudoplastic fluids, similar solutions, A.I.Ch.E.J. 6, 24–28 (1960)
G. W. Sutton and A. Sherman, Engineering Magnetohydrodynamics, McGraw-Hill, 1965
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© Copyright 1996
American Mathematical Society
