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Unsteady two-dimensional and axisymmetric MHD boundary-layer flows

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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

  1. Schlichting, H.: Boundary layer theory. New York: McGraw-Hill 1979.

    Google Scholar 

  2. 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.

    Google Scholar 

  3. Sparrow, E. M., Quack, H., Boerner, C. J.: Local non-similarity boundary layer solutions. A.I.A.A. J.8, 1936–1942 (1970).

    Google Scholar 

  4. Sparrow, E. M., Yu, H. S.: Local non-similarity thermal boundary layer solutions. Trans. A.S.M.E. J. Heat Transfer93, 328–334 (1971).

    Google Scholar 

  5. 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).

    Google Scholar 

  6. 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).

    Google Scholar 

  7. Smith, A. M. O., Clutter, D. W.: Solutions of incompressible laminar boundary layer equations, A.I.A.A. J.1, 2062–2064 (1963).

    Google Scholar 

  8. Terril, R. M.: Laminar boundary-layer flow near separation with or without suction. Philos. Trans. Roy. Soc. London253A, 55–58 (1960).

    Google Scholar 

  9. Riley, N.: Unsteady laminar boundary layers. SIAM Review17, 274–289 (1975).

    Google Scholar 

  10. Telionis, D. P.: Review — Unsteady boundary layers, separated and attached. Trans. A.S.M.E. J. Fluids Engg.101, 29–42 (1979).

    Google Scholar 

  11. Ram, P. C.: Recent developments of heat and mass transfer in hydro-magnetic flows. Int. J. Energy Res.15, 691–713 (1991).

    Google Scholar 

  12. Meena, B. K., Nath, G.: Non-similar incompressible laminar boundary layer with magnetic field. Proc. Indian Acad. Sci.87A (2), 55–64 (1978).

    Google Scholar 

  13. 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).

    Google Scholar 

  14. Inouye, K., Tate, A.: Finite-difference version of quasi-linearization applied to boundary-layer equations. A.I.A.A. J.12, 558–560 (1974).

    Google Scholar 

  15. Williams, J. C.: Mathematical criterion for unsteady boundary-layer separation. A.I.A.A. J.18, 335–343 (1980).

    Google Scholar 

  16. Ingham, D. B.: Unsteady separation. J. Comput. Phys.53, 90–96 (1984).

    Google Scholar 

  17. Cebeci, T. (ed.): Numerical and Physical aspects of aerodynamic flows, pp. 265–277, New York: Springer 1984.

    Google Scholar 

  18. Sarpkaya, T.: Brief reviews of some time-dependent flows. Trans. A.S.M.E., J. Fluids Engg114, 283–298 (1992).

    Google Scholar 

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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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