Variable Viscosity on Magnetohydrodynamic Fluid Flow and Heat Transfer over an Unsteady Stretching Surface with Hall Effect

S Shateyi,Ss Motsa

doi:10.1155/2010/257568

Abstract

The problem of magnetohydrodynamic flow and heat transfer of a viscous, incompressible, and electrically conducting fluid past a semi-infinite unsteady stretching sheet is analyzed numerically. The problem was studied under the effects of Hall currents, variable viscosity, and variable thermal diffusivity. Using a similarity transformation, the governing fundamental equations are approximated by a system of nonlinear ordinary differential equations. The resultant system of ordinary differential equations is then solved numerically by the successive linearization method together with the Chebyshev pseudospectral method. Details of the velocity and temperature fields as well as the local skin friction and the local Nusselt number for various values of the parameters of the problem are presented. It is noted that the axial velocity decreases with increasing the values of the unsteadiness parameter, variable viscosity parameter, or the Hartmann number, while the transverse velocity increases as the Hartmann number increases. Due to increases in thermal diffusivity parameter, temperature is found to increase.

Highlights

Fluid and heat flow induced by continuous stretching heated surfaces is often encountered in many industrial disciplines
We remark that all the Successive Linearisation Method (SLM) results presented in this paper were obtained using N 30 collocation points
The skin friction increases as β1 increases. We observe in this table that the local Nusselt number −θ 0 decreases as the fluid variable viscosity parameter β1 increases

Summary

Introduction

Fluid and heat flow induced by continuous stretching heated surfaces is often encountered in many industrial disciplines. Mukhopadhyay 14 presented solutions for unsteady boundary layer flow and heat transfer over a stretching surface with variable fluid viscosity and thermal diffusivity in presence of wall suction. Mahmoud investigated the influence of radiation and temperature-dependent viscosity on the problem of unsteady MHD flow and heat transfer of an electrically conducting fluid past an infinite vertical porous plate taking into account the effect of viscous dissipation. Tsai et al examined the simultaneous effects of variable viscosity, variable thermal conductivity, and Ohmic heating on the fluid flow and heat transfer past a continuously moving porous surface under the presence of magnetic field. Abd El-Aziz 21 investigated the effect of Hall currents on the flow and heat transfer of an electrically conducting fluid over an unsteady stretching surface in the presence of a strong magnet. The effects of different parameters on velocity and temperature fields are investigated and analyzed with the help of their graphical representations along with the energy

Mathematical Formulation

A11 A12 A13

Results and Discussion

Conclusion