MHD stagnation-point flow of an upper-convected Maxwell fluid over a stretching surface T. Hayat a , Z. Abbas a, * , M. Sajid b a Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan b Theoretical Plasma Physics Division, PINSTECH, P.O. Nilore, Islamabad 44000, Pakistan Accepted 2 January 2007 Abstract The present analysis comprises the steady two-dimensional magnetohydrodynamic flow of an upper-convected Max- well fluid near a stagnation-point over a stretching surface. The governing non-linear partial differential equation for the flow are reduced to an ordinary differential equation by using similarity transformations. The analytic solution of nonlinear system is constructed in the series form using Homotopy analysis method. Convergence of the obtained series is discussed explicitly. The effects of the sundry parameters on the velocity profile is shown through graphs. The values of skin-friction coefficient for different parameters is tabulated. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Stagnation-point flow; Maxwell fluid; MHD flow; Stretching sheet; HAM solution 1. Introduction Nature is abundant with examples of flows involving non-Newtonian fluids. Such flows have been attracting the attention of investigators for a long time. This attraction has been growing considerably especially during the past few decades. Undoubtedly, the resulting equations of non-Newtonian fluids are non-linear, higher order and much more complicated than the Navier–Stokes equations. Hence, progress is limited until recent times since closed form solutions are not available to many problems of practical interests. The flows of non-Newtonian fluids occur in a wide variety of applications: from oil and gas well drilling to well completion operations, from industrial processes involving waste fluids, synthetic fibres, foodstuffs to extrusion of molten plastic, and as well as in some flows of polymer solutions. The large variety of fluids and industrial applications has been a major motivation for researchers in non-Newtonian flows. The flow characteristics of non-Newtonian fluids are quite different in comparison to Newtonian fluids. In order to obtain a thorough cognition of non-Newtonian fluids and their various applications, it is necessary to study their flow behaviors. In the literature, the vast majority of non-Newtonian fluid models are concerned with the fluids of grade two or three. But these fluid models do not predict the effects of stress relaxation. A subclass of rate type fluids namely the Maxwell model can predict the stress relaxation and therefore, have become more popular. Some recent studies 0960-0779/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.chaos.2007.01.067 * Corresponding author. Tel.: +92 51 2275341. E-mail address: za_qau@yahoo.com (Z. Abbas). Chaos, Solitons and Fractals 39 (2009) 840–848 www.elsevier.com/locate/chaos