Unsteady Boundary Layer Flow and Heat Transfer over a Stretching Surface in a Micropolar Fluid ROSLINDA NAZAR, ANUAR ISHAK, MASLINA DARUS School of Mathematical Sciences Universiti Kebangsaan Malaysia 43600 UKM Bangi, Selangor MALAYSIA IOAN POP Faculty of Mathematics University of Cluj CP 253, R-3400 Cluj ROMANIA Abstract: - The present study deals with the analysis of unsteady boundary layer flow and heat transfer of an incompressible micropolar fluid over a stretching sheet when the sheet is stretched in its own plane. The velocity and temperature are assumed to vary linearly with the distance along the sheet. Two equal and opposite forces are impulsively applied along the x-axis so that the sheet is stretched, keeping the origin fixed in a micropolar fluid. The transformed unsteady boundary layer equations are solved numerically using the Keller-box method for the whole transient from the initial state flow to the final steady-state flow. Numerical results are obtained for the velocity, microrotation and temperature distributions as well as the skin friction coefficient and local Nusselt number for various values of the material parameter K and Prandtl number Pr, when n= ½ (weak concentration particles at the plate). Key-Words: - Boundary layer, Heat transfer, Micropolar fluid, Stretching surface, Unsteady flow 1 Introduction The fluid dynamics due to a stretching sheet is important in extrusion processes. The production of sheeting material arises in a number of industrial manufacturing processes and includes both metal and polymer sheets. The quality of the final product depends on the rate of heat transfer at the stretching surface. Since the pioneering study by Crane [1] who presented an exact analytical solution for the steady two-dimensional stretching of a surface in a quiescent fluid, many authors have considered various aspects of this problem and obtained similarity solutions. Many authors presented some mathematical results, and a good amount of references can be found in the papers by Magyari and Keller [2,3], Liao and Pop [4], Nazar et al. [5] and Ishak et al. [6,7]. The studies carried out in these papers deal only with steady-state flow, but the flow and thermal fields may be unsteady due to either impulsive stretching of the surface or external stream and sudden change in the surface temperature. Kumari et al. [8] studied the unsteady free convection flow over a continuous moving vertical surface in an ambient fluid, and Ishak et al. [9] investigated theoretically the unsteady mixed convection boundary layer flow and heat transfer due to a stretching vertical surface in a quiescent viscous and incompressible fluid. Further, Pop and Na [10] and Wang et al. [11] deal with the unsteady boundary layer flow due to impulsive starting from rest of a stretching sheet in a viscous fluid and Nazar et al. [12] studied the problem of unsteady boundary layer flow due to a stretching surface in a rotating fluid. Further, Liao [13] and Xu et al. [14] obtained series solutions of the unsteady boundary layer flows and unsteady three-dimensional MHD flow and heat transfer in the boundary layer over an impulsively stretching plate, respectively. On the other hand, it is well known that the theory of micropolar fluids has generated a lot of interests and many flow problems have been studied. The theory of micropolar fluids, which display the effects of local rotary inertia and couple stresses, can explain the flow behavior in which the classical Newtonian fluids theory is inadequate. This theory takes into account the microscopic effects arising from the local structure and micromotions of the fluid elements. The theory is expected to provide a mathematical model, which can be used to describe the behavior of non- Newtonian fluids in many practical applications. Since introduced by Eringen [15,16], several researchers have considered various stretching problems in micropolar fluids including the present authors (see Ishak et al. [6,7]). Extensive reviews of the theory and its applications can be found in the review articles by Ariman et al. [17,18] and the recent books by Lukaszewicz [19] and Eringen [20]. Proceedings of the 13th WSEAS International Conference on APPLIED MATHEMATICS (MATH'08) ISSN: 1790-2769 273 ISBN: 978-960-474-034-5