MHD stagnation‐point flow towards a shrinking sheet

Y.Y. Lok (Faculty of Manufacturing Engineering, Universiti Teknikal Malaysia Melaka, Durian Tunggal, Malaysia and Mathematics Section, School of Distance Education, Universiti Sains Malaysia, Pulau Pinang, Malaysia)
A. Ishak (School of Mathematical Sciences, Universiti Kebangsaan Malaysia, Bangi, Malaysia and Faculty of Science, Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur, Malaysia)
I. Pop (Faculty of Mathematics, University of Cluj, Cluj, Romania)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Publication date: 11 January 2011



The purpose of this paper is to theoretically investigate the steady two‐dimensional magnetohydrodynamic (MHD) boundary layer flow over a shrinking sheet. The effects of stretching and shrinking parameter as well as magnetic field parameter near the stagnation point are studied.


A similarity transformation is used to reduce the governing partial differential equations to a set of nonlinear ordinary differential equations which are then solved numerically using Keller‐box method.


The solution is unique for stretching case; however, multiple (dual) solutions exist for small values of magnetic field parameter for shrinking case. The streamlines are non‐aligned and a reverse flow is formed near the surface due to shrinking effect.

Practical implications

The flow due to a stretching or shrinking sheet is relevant to several practical applications in the field of metallurgy, chemical engineering, etc. For example, in manufacturing industry, polymer sheets and filaments are manufactured by continuous extrusion of the polymer from a die to a windup roller, which is located at a finite distance away. In these cases, the properties of the final product depend to a great extent on the rate of cooling which is governed by the structure of the boundary layer near the stretching surface.


The present results are original and new for the MHD flow near the stagnation‐point on a shrinking sheet. For shrinking case, the velocity on the boundary is towards a fixed point which would cause a velocity away from the sheet. Therefore, this paper is important for scientists and engineers in order to become familiar with the flow behaviour and properties of such MHD flow and the way to predict the properties of this flow for the process equipments.



Y.Y. Lok, A. Ishak and I. Pop (2011) "MHD stagnation‐point flow towards a shrinking sheet", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 21 No. 1, pp. 61-72

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