Solutions for MHD viscous flow due to a shrinking sheet by Hankel-Pade´ method

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-Pade´ 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-Pade´ method. Also, when the sheet shrinks in the y-direction, the obtained results with Hankel-Pade´ 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-Pade´ method. It is clear that the Hankel-Pade´ method is, by far, more simple, straightforward and gives reasonable results for large Hartman numbers and suction parameters

Flow, Boundary layers, Viscosity, Boundary layer flow, Magnetohydrodynamic flow, Pade´ approximation, Hankel-Pade´ method