MHD boundary layer flow and heat transfer over a stretching sheet with induced magnetic field

In this paper, the problem of steady magnetohydrodynamic boundary layer flow and heat transfer of a viscous and electrically conducting fluid over a stretching sheet is studied. The effect of the induced magnetic field is taken into account. The transformed ordinary differential equations are solved numerically using the finite-difference scheme known as the Keller-box method. Numerical results are obtained for various values of the magnetic parameter, the reciprocal magnetic Prandtl number and the Prandtl number. The effects of these parameters on the flow and heat transfer characteristics are determined and discussed in detail. When the magnetic field is absent, the closed analytical results for the skin friction are compared with the exact numerical results. Also the numerical results for the heat flux from the stretching surface are compared with the results reported by other authors when the magnetic field is absent. It is found that very good agreement exists.

[1]  I. Pop,et al.  MHD stagnation‐point flow towards a shrinking sheet , 2011 .

[2]  G. Nath,et al.  Unsteady three-dimensional boundary layer flow due to a stretching surface , 1993 .

[3]  A. Gupta,et al.  Magnetohydrodynamic stagnation-point flow towards a stretching sheet , 2001 .

[4]  G. Carrier,et al.  The magnetohydrodynamic flow past a flat plate , 1959, Journal of Fluid Mechanics.

[5]  T. V. Davies.  The magneto-hydrodynamic boundary layer in the two-dimensional steady flow past a semi-infinite flat plate. I. Uniform conditions at infinity , 1963, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[6]  I. Pop,et al.  A note on MHD flow over a stretching permeable surface , 1998 .

[7]  Chao-Yang Wang,et al.  The three‐dimensional flow due to a stretching flat surface , 1984 .

[8]  Tiegang Fang,et al.  Closed-form exact solutions of MHD viscous flow over a shrinking sheet , 2009 .

[9]  C. Wang,et al.  Viscous flow due to a shrinking sheet , 2006 .

[10]  A. Gupta,et al.  HYDROMAGNETIC FLOW AND HEAT TRANSFER OVER A STRETCHING SHEET , 1979 .

[11]  B. K. Dutta.  Heat transfer from a stretching sheet in hydromagnetic flow , 1988 .

[12]  H. E. Wilhelm,et al.  Integration of the Magnetohydrodynamic Boundary‐Layer Equations by Meksyn's Method , 1974 .

[13]  M. Ezzat,et al.  Magnetohydrodynamic boundary layer flow past a stretching plate and heat transfer , 2004 .

[14]  H. Chuang.  Effects of transpiration on MHD boundary layers , 1976 .

[15]  V. Rossow.  On flow of electrically conducting fluids over a flat plate in the presence of a transverse magnetic field , 1957 .

[16]  M. Glauert.  A study of the magnetohydrodynamic boundary layer on a flat plate , 1961, Journal of Fluid Mechanics.

[17]  Eugen Magyari,et al.  Exact solutions for self-similar boundary-layer flows induced by permeable stretching walls , 2000 .

[18]  H. Andersson.  MHD flow of a viscoelastic fluid past a stretching surface , 1992 .

[19]  M. Cobble.  Magnetofluiddynamic flow with a pressure gradient and fluid injection , 1977 .

[20]  I. Pop,et al.  UNSTEADY MIXED CONVECTION BOUNDARY LAYER FLOW DUE TO A STRETCHING VERTICAL SURFACE , 2006 .

[21]  M. Thiyagarajan,et al.  Steady nonlinear hydromagnetic flow and heat transfer over a stretching surface of variable temperature , 2006 .

[22]  S. Venkateswaran,et al.  Three-Dimensional Unsteady Flow With Heat and Mass Transfer Over a Continuous Stretching Surface , 1988 .

[23]  Ali J. Chamkha,et al.  Unsteady three-dimensional MHD-boundary-layer flow due to the impulsive motion of a stretching surface , 2001 .

[24]  B. C. Sakiadis.  Boundary‐layer behavior on continuous solid surfaces: II. The boundary layer on a continuous flat surface , 1961 .

[25]  D. Ingham.  Impulsively started viscous flow past a finite flat plate with and without an applied magnetic field , 1973 .

[26]  F. Goldsworthy.  Magnetohydrodynamic flows of a perfectly conducting, viscous fluid , 1961, Journal of Fluid Mechanics.

[27]  D. Ingham.  Flow Past an Impulsively Started Semi-infinite Flat Plate in the Presence of a Magnetic Field , 1977 .

[28]  P. S. Gupta,et al.  Heat and mass transfer on a stretching sheet with suction or blowing , 1977 .

[29]  B. K. Dutta,et al.  Temperature field in flow over a stretching sheet with uniform heat flux , 1985 .

[30]  L. Crane.  Flow past a stretching plate , 1970 .

[31]  M. Nandeppanavar,et al.  Heat transfer in MHD viscoelastic boundary layer flow over a stretching sheet with non-uniform heat source/sink , 2009 .

[32]  Tasawar Hayat,et al.  The application of homotopy analysis method for MHD viscous flow due to a shrinking sheet , 2009 .

[33]  P. Bradshaw,et al.  Physical and Computational Aspects of Convective Heat Transfer , 1984 .

[34]  Ali J. Chamkha,et al.  Flow and heat transfer on a stretching surface in a rotating fluid with a magnetic field , 2003 .

[35]  G. Nath,et al.  Analytical solution of unsteady three-dimensional MHD boundary layer flow and heat transfer due to impulsively stretched plane surface , 2009 .

[36]  I. A. Hassanien,et al.  Flow and heat transfer in a power-law fluid over a nonisothermal stretching sheet , 1998 .

[37]  T. Hayat,et al.  MHD rotating flow of a viscous fluid over a shrinking surface , 2007 .

[38]  G. Nath,et al.  Unsteady flow over a stretching surface with a magnetic field in a rotating fluid , 1998 .

[39]  H. Takhar,et al.  MHD flow and heat transfer over a stretching surface with prescribed wall temperature or heat flux , 1990 .

[40]  Lord Rayleigh,et al.  LXXXII. On the motion of solid bodies through viscous liquid , 1911 .