Heat and Mass Transfer

, 44:921 | Cite as

Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet

  • A. Ishak
  • R. Nazar
  • I. Pop


An analysis is made for the steady two-dimensional magneto-hydrodynamic flow of an incompressible viscous and electrically conducting fluid over a stretching vertical sheet in its own plane. The stretching velocity, the surface temperature and the transverse magnetic field are assumed to vary in a power-law with the distance from the origin. The transformed boundary layer equations are solved numerically for some values of the involved parameters, namely the magnetic parameter M, the velocity exponent parameter m, the temperature exponent parameter n and the buoyancy parameter λ, while the Prandtl number Pr is fixed, namely Pr = 1, using a finite difference scheme known as the Keller-box method. Similarity solutions are obtained in the presence of the buoyancy force if n = 2m−1. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. It is found that both the skin friction coefficient and the local Nusselt number decrease as the magnetic parameter M increases for fixed λ and m. For m = 0.2 (i.e. n = −0.6), although the sheet and the fluid are at different temperatures, there is no local heat transfer at the surface of the sheet except at the singular point of the origin (fixed point).


Heat Transfer Rate Buoyancy Force Mixed Convection Magnetic Parameter Heat Transfer Characteristic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

a, b



magnetic field


uniform magnetic field


skin friction coefficient


dimensionless stream function


acceleration due to gravity


local Grashof number


thermal conductivity


velocity exponent parameter


magnetic parameter


temperature exponent parameter


local Nusselt number


Prandtl number


heat transfer from the stretching sheet


local Reynolds number


fluid temperature


temperature of the stretching sheet


ambient temperature

u, v

velocity components along the x and y directions, respectively


velocity of the stretching sheet

x, y

Cartesian coordinates along the surface and normal to it, respectively

Greek symbols


thermal diffusivity


thermal expansion coefficient


similarity variable


buoyancy or mixed convection parameter


dimensionless temperature


dynamic viscosity


kinematic viscosity


fluid density


electrical conductivity


skin friction


stream function



condition at the stretching sheet

condition at infinity


differentiation with respect to η



The authors wish to express their very sincere thanks to the reviewers for their valuable time spent reading this paper and for their valuable comments and suggestions. This work is supported by a research grant (SAGA project code: STGL–013–2006) from the Academy of Sciences Malaysia. Prof. I. Pop also wishes to thank the Royal Society (London) for partial financial support to enable collaboration on this research.


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversiti Kebangsaan MalaysiaSelangorMalaysia
  2. 2.Faculty of MathematicsUniversity of ClujClujRomania

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