Published May 24, 2012 | Version 10567

MHD Falkner-Skan Boundary Layer Flow with Internal Heat Generation or Absorption

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This paper examines the forced convection flow of incompressible, electrically conducting viscous fluid past a sharp wedge in the presence of heat generation or absorption with an applied magnetic field. The system of partial differential equations governing Falkner - Skan wedge flow and heat transfer is first transformed into a system of ordinary differential equations using similarity transformations which is later solved using an implicit finite - difference scheme, along with quasilinearization technique. Numerical computations are performed for air (Pr = 0.7) and displayed graphically to illustrate the influence of pertinent physical parameters on local skin friction and heat transfer coefficients and, also on, velocity and temperature fields. It is observed that the magnetic field increases both the coefficients of skin friction and heat transfer. The effect of heat generation or absorption is found to be very significant on heat transfer, but its effect on the skin friction is negligible. Indeed, the occurrence of overshoot is noticed in the temperature profiles during heat generation process, causing the reversal in the direction of heat transfer.

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References

  • V.M.Falkner and S.W.Skan, "Some approximate solutions of the boundary layer equations", Philos.Mag.vol.12, pp.865-896, 1931.
  • D.R.Hartree, "On an equation occurring in Falkner and Skan-s approximate treatment of the equations of the boundary layer", Proc.Cambridge Philos.Soc., vol.33, pp.223-239, 1937.
  • E. R. G. Eckert, "Die Berechnungs/des Warmeuberganges in der Laminaren Grenzschicht um stomter Korper", VDI- Forschungsheft, vol.416, pp.1-24, 1942.
  • K.Stewartson, "Further solutions the Falkner-Skan equation", Proc. Cambridge Phil. Soc., vol. 50, pp.454-465, 1954.
  • J.C.Y.Koh and J.P.Harnett, "Skin friction and heat transfer for incompressible laminar flow over a porous wedge with suction and variable wall temperature", Int.J.Heat Mass Transfer, vol.2, pp.185-198, 1961.
  • K. K. Chen and P. A. Libby, " Boundary layers with small departure from the Falkner-Skan profile", J. Fluid Mech. vol.33, pp.273-282, 1968.
  • H. T.Lin and L. K. Lin, "Similarity solutions for laminar forced convection heat transfer from wedges to fluids of any Prandtl number", Int. J. Heat Mass Transfer, vol.30, pp.1111-1118, 1987.
  • T.Watanabe, "Thermal boundary layer over a wedge with uniform suction and injection in forced flow", Acta Mechanica, vol.83, pp.119- 126, 1990.
  • K.Vajravelu and J.Nayfeh, "Hydromagnetic convection at a cone and a wedge. Int Commun Heat and Mass Transfer", vol.19, pp.701-710, 1992. [10] N.G.Kafoussias and N.D.Nanousis, "Magnetohydrodynamic laminar boundary layer flow over a wedge with suction or injection", Canadian Journal of Physics, vol.75, pp.733-745, 1997. [11] S.Abbasbandy and T.Hayat, "Solution of the MHD Falkner-Skan flow by Homotopy Analysis Method", Commun.Nonlinear Sci.Numer.Simul. vol.14, pp.3591-3598, 2009. [12] K. Inouye and A. Tate, "Finite difference version of quasilinearization applied to boundary layer euations", A.I.A.A.J., vol.12, pp.558-560, 1974. [13] R. S. Varga, "Matrix Iterative Analysis," Prentice-Hall, New Jersy, 2000. [14] F. M. White, Viscous Fluid Flow, 3rd Edition, Mc. Graw-Hill, New York, 2006.