MHD Falkner-Skan Boundary Layer Flow with Internal Heat Generation or Absorption
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.
[1] V.M.Falkner and S.W.Skan, "Some approximate solutions of the
boundary layer equations", Philos.Mag.vol.12, pp.865-896, 1931.
[2] 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.
[3] E. R. G. Eckert, "Die Berechnungs/des Warmeuberganges in der
Laminaren Grenzschicht um stomter Korper", VDI- Forschungsheft,
vol.416, pp.1-24, 1942.
[4] K.Stewartson, "Further solutions the Falkner-Skan equation", Proc.
Cambridge Phil. Soc., vol. 50, pp.454-465, 1954.
[5] 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.
[6] 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.
[7] 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.
[8] T.Watanabe, "Thermal boundary layer over a wedge with uniform
suction and injection in forced flow", Acta Mechanica, vol.83, pp.119-
126, 1990.
[9] 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.
[1] V.M.Falkner and S.W.Skan, "Some approximate solutions of the
boundary layer equations", Philos.Mag.vol.12, pp.865-896, 1931.
[2] 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.
[3] E. R. G. Eckert, "Die Berechnungs/des Warmeuberganges in der
Laminaren Grenzschicht um stomter Korper", VDI- Forschungsheft,
vol.416, pp.1-24, 1942.
[4] K.Stewartson, "Further solutions the Falkner-Skan equation", Proc.
Cambridge Phil. Soc., vol. 50, pp.454-465, 1954.
[5] 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.
[6] 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.
[7] 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.
[8] T.Watanabe, "Thermal boundary layer over a wedge with uniform
suction and injection in forced flow", Acta Mechanica, vol.83, pp.119-
126, 1990.
[9] 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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:59624", author = "G.Ashwini and A.T.Eswara", title = "MHD Falkner-Skan Boundary Layer Flow with Internal Heat Generation or Absorption", abstract = "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.", keywords = "Heat generation / absorption, MHD Falkner- Skan
flow, skin friction and heat transfer", volume = "6", number = "5", pages = "566-4", }