Variable Viscosity on Magnetohydrodynamic Fluid Flow and Heat Transfer over an Unsteady Stretching Surface with Hall Eff
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Research Article Variable Viscosity on Magnetohydrodynamic Fluid Flow and Heat Transfer over an Unsteady Stretching Surface with Hall Effect S. Shateyi1 and S. S. Motsa2 1
School of Mathematical and Natural Sciences, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa 2 Department of Mathematics, University of Swaziland, Private Bag 4, Kwaluseni M201, Swaziland Correspondence should be addressed to S. Shateyi, [email protected] Received 16 July 2010; Accepted 16 August 2010 Academic Editor: Vicentiu D. Radulescu Copyright q 2010 S. Shateyi and S. S. Motsa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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.
1. Introduction Fluid and heat flow induced by continuous stretching heated surfaces is often encountered in many industrial disciplines. Applications include extrusion process, wire and fiber coating, polymer processing, foodstuff processing, design of various heat exchangers, and chemical processing equipment, among other applications. Stretching will bring in a unidirectional orientation to the extrudate, consequently the quality of the final product considerably depends on the flow and heat transfer mechanism. To that end, the analysis of momentum and thermal transports within the fluid on a continuously stretching surface is important for
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Boundary Value Problems
gaining some fundamental understanding of such processes. Since the pioneering study by Crane 1 who presented an exact analytical solution for the steady two-dimensional flow due to a stretching surface in a quiescent fluid, many studies on stretched surfaces have been done. Dutta et al. 2 and Grubka and Bobba 3 studied the temperature field in the flow over a stretching surface subject to a uniform heat flux. Elbashbeshy 4 considered the case of a
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