# Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet

- First Online:

- Received:
- Accepted:

DOI: 10.1007/s00231-007-0322-z

- Cite this article as:
- Ishak, A., Nazar, R. & Pop, I. Heat Mass Transfer (2008) 44: 921. doi:10.1007/s00231-007-0322-z

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- 423 Downloads

## Abstract

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* = 2*m*−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).

### List of symbols

*a*,*b*constants

*B*(*x*)magnetic field

*B*_{0}uniform magnetic field

*C*_{f}skin friction coefficient

*f*dimensionless stream function

*g*acceleration due to gravity

*Gr*_{x}local Grashof number

*k*thermal conductivity

*m*velocity exponent parameter

*M*magnetic parameter

*n*temperature exponent parameter

*Nu*_{x}local Nusselt number

*Pr*Prandtl number

*q*_{w}heat transfer from the stretching sheet

*Re*_{x}local Reynolds number

*T*fluid temperature

*T*_{w}(*x*)temperature of the stretching sheet

*T*_{∞}ambient temperature

*u*,*v*velocity components along the

*x*and*y*directions, respectively*U*(*x*)velocity of the stretching sheet

*x*,*y*Cartesian coordinates along the surface and normal to it, respectively

### Greek symbols

- α
thermal diffusivity

- β
thermal expansion coefficient

- η
similarity variable

- λ
buoyancy or mixed convection parameter

- θ
dimensionless temperature

- μ
dynamic viscosity

- ν
kinematic viscosity

- ρ
fluid density

- σ
electrical conductivity

- τ
_{w} skin friction

- ψ
stream function

### Subscripts

*w*condition at the stretching sheet

- ∞
condition at infinity

### Superscript

- ′
differentiation with respect to η