Solutions for MHD viscous flow due to a shrinking sheet by Hankel‐Padé method

Abstract

Purpose

In this paper, an analysis is performed to find the solution of a nonlinear ordinary differential equation that appears in a model for MHD viscous flow caused by a shrinking sheet.

Design/methodology/approach

The cases of two dimensional and axisymmetric shrinking have been discussed. When the sheet is shrinking in the x‐direction, the analytical solutions are obtained by the Hankel‐Padé method. Comparison to exact solutions reveals reliability and high accuracy of the procedure, even in the case of multiple solutions. The case of sheet shrinking in the y‐direction is also considered, with success.

Findings

When the sheet shrinks in the x‐direction, the analytical solutions are obtained by Hankel‐Padé method. Also, when the sheet shrinks in the y‐direction, the obtained results with Hankel‐Padé method are presented.

Practical implications

Comparison to exact solutions reveals reliability and high accuracy of the procedure and convincingly could be used to obtain multiple solutions for certain parameter domains of this case of the governing nonlinear problem.

Originality/value

The numerical solutions are given for both two‐dimensional and axisymmetric shrinking sheets by using Hankel‐Padé method. It is clear that the Hankel‐Padé method is, by far, more simple, straightforward and gives reasonable results for large Hartman numbers and suction parameters.

Citation

Abbasbandy, S. and Roohani Ghehsareh, H. (2013), "Solutions for MHD viscous flow due to a shrinking sheet by Hankel‐Padé method", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 23 No. 2, pp. 388-400. https://doi.org/10.1108/09615531311293533