Summary
Nonsimilar solution of the unsteady laminar incompressible magneto-hydrodynamic boundary layer flow and heat transfer for an electrically conducting fluid over two-dimensional and axisymmetric bodies in the presence of an applied magnetic field has been obtained. The effects of surface mass transfer, Joule heating and viscous dissipation are included in the analysis. Numerical computation have been carried out for the flow over a circular cylinder and a sphere using an implicit finite difference scheme in combination with a quasi-linearization technique. It is observed that magnetic field and suction cause the location of vanishing skin friction to move downstream while, the effect of injection is just the opposite. The effect of magnetic field on the skin friction is more pronounced as compared to its effect on the heat transfer. On the other hand, the heat transfer is strongly affected by the viscous dissipation and the effect is more for larte times. However, heat transfer responds comparatively less to the fluctuations of the free stream than the skin friction.
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References
Schlichting, H.: Boundary layer theory. New York: McGraw-Hill 1979.
Dewey, C. F., Gross, J. F.: Exact solutions of the laminar boundary layer equations. In: Advances in Heat Transfer, vol. 4, p. 317. New York: Academic Press 1967.
Sparrow, E. M., Quack, H., Boerner, C. J.: Local non-similarity boundary layer solutions. A.I.A.A. J.8, 1936–1942 (1970).
Sparrow, E. M., Yu, H. S.: Local non-similarity thermal boundary layer solutions. Trans. A.S.M.E. J. Heat Transfer93, 328–334 (1971).
Kao, T., Elrod, H. G.: Rapid calculation of heat transfer in non-similar laminar incompressible boundary-layers. A.I.A.A. J.14, 1746–1749 (1976).
Nath, G.: An approximate method for the solution of a class of non-similar laminar boundary-layer equations. Trans. A.S.M.E. J. Fluids Engg.98, 292–296 (1976).
Smith, A. M. O., Clutter, D. W.: Solutions of incompressible laminar boundary layer equations, A.I.A.A. J.1, 2062–2064 (1963).
Terril, R. M.: Laminar boundary-layer flow near separation with or without suction. Philos. Trans. Roy. Soc. London253A, 55–58 (1960).
Riley, N.: Unsteady laminar boundary layers. SIAM Review17, 274–289 (1975).
Telionis, D. P.: Review — Unsteady boundary layers, separated and attached. Trans. A.S.M.E. J. Fluids Engg.101, 29–42 (1979).
Ram, P. C.: Recent developments of heat and mass transfer in hydro-magnetic flows. Int. J. Energy Res.15, 691–713 (1991).
Meena, B. K., Nath, G.: Non-similar incompressible laminar boundary layer with magnetic field. Proc. Indian Acad. Sci.87A (2), 55–64 (1978).
Surma Devi, C. D., Nath, G.: Unsteady non-similar laminar boundary-layer flows with heat and mass transfer. Acta Technical CSAV28 (2), 225–239 (1983).
Inouye, K., Tate, A.: Finite-difference version of quasi-linearization applied to boundary-layer equations. A.I.A.A. J.12, 558–560 (1974).
Williams, J. C.: Mathematical criterion for unsteady boundary-layer separation. A.I.A.A. J.18, 335–343 (1980).
Ingham, D. B.: Unsteady separation. J. Comput. Phys.53, 90–96 (1984).
Cebeci, T. (ed.): Numerical and Physical aspects of aerodynamic flows, pp. 265–277, New York: Springer 1984.
Sarpkaya, T.: Brief reviews of some time-dependent flows. Trans. A.S.M.E., J. Fluids Engg114, 283–298 (1992).
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Sathyakrishna, M., Roy, S. & Nath, G. Unsteady two-dimensional and axisymmetric MHD boundary-layer flows. Acta Mechanica 150, 67–77 (2001). https://doi.org/10.1007/BF01178545
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DOI: https://doi.org/10.1007/BF01178545