STAGNATION POINT FLOW TOWARDS A STRETCHING/ SHRINKING SHEET IN A MICROPOLAR FLUID WITH A CONVECTIVE SURFACE BOUNDARY CONDITION Nor Azizah Yacob 1 and Anuar Ishak 23 * 1. Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Pahang, 26400 Bandar Jengka, Pahang, Malaysia 2. Centre for Modelling & Data Analysis, Faculty of Science and Technology, School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia 3. Faculty of Science, Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia The problem of a steady laminar two-dimensional stagnation point flow towards a stretching/shrinking sheet in a micropolar fluid with a convective surface boundary condition is studied. The governing partial differential equations are transformed into ordinary differential equations using a similarity transformation, before being solved numerically using the Runge–Kutta–Fehlberg method with shooting technique. The effects of the material parameter and the convective parameter on the fluid flow and heat transfer characteristics are disscussed. It is found that the skin friction coefficient and the heat transfer rate at the surface decrease with increasing values of the material parameter. Moreover, dual solutions are found to exist for the shrinking case, while for the stretching case, the solution is unique. Keywords: micropolar fluid, convective boundary condition, heat transfer, similarity solution INTRODUCTION T he boundary layer flow over moving or stretching surfaces has important applications in engineering processes, such as polymer extrusion, drawing of copper wires, continu- ous stretching of plastic films and artificial fibres, hot rolling, wire drawing, glass-fibre, metal extrusion, and metal spinning (Xu and Liao, 2009). The pioneering work on a moving surface was done by Sakiadis (1961); and later Crane (1970) extended to fluid flow over a linearly stretched plate. Thereafter, this prob- lem has been studied extensively in various aspects in Newtonian fluids such as Dutta et al. (1985); Grubka and Bobba (1985); Chen and Char (1988), etc. This kind of problems was extended to non-Newtonian fluids since many of industrial fluids such as polymeric liquids, blood, artificial fibres, paints, and liquid crys- tal exhibit non-Newtonian fluid behaviour. It is worth mentioning that Eringen (1966, 1972) was the first developed the theory of micropolar fluids that can be used to explain those kinds of fluids. An excellent review of the study of micropolar fluid was discussed by Ariman et al. (1973) and the recent book by Lukaszewicz (1999). Guram and Smith (1980) studied the stagnation flow of micropolar fluids with strong and weak interactions using the fourth order Runge–Kutta method. Later, Gorla (1983) used the similar method to investigate the boundary layer flow at a stagna- tion point on a moving wall of a micropolar fluid. Soundalgekar and Takhar (1983) analysed the flow and heat transfer past a con- tinuous moving plate immersed in a micropolar fluid. The similar problem was extended by Gorla and Reddy (1987); Bhargava et al. (2003); and Ishak et al. (2006, 2007) by taking into account the continuously moving plate in a parallel free stream. Recently, Kumar (2009) studied the problem of heat and mass transfer in a hydromagnetic flow of a micropolar fluid past a stretching sheet using a finite element method. ∗ Author to whom correspondence may be addressed. E-mail address: anuarishak@yahoo.com Can. J. Chem. Eng. 90:621–626, 2012 © 2011 Canadian Society for Chemical Engineering DOI 10.1002/cjce.20517 Published online 30 March 2011 in Wiley Online Library (wileyonlinelibrary.com). | VOLUME 90, JUNE 2012 | | THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING | 621 |