Khalid et al. / Malaysian Journal of Fundamental and Applied Sciences Vol. 13, No. 4 (2017) 654-658 654 Heat transfer in free convection flow of micropolar fluids over an oscillating vertical plate Asma Khalid a , Ilyas Khan b , Sharidan Shafie c,* a Department of Mathematics, SBK Women's University, Quetta 87300, Pakistan b College of Engineering Majmaah University, Majmaah 11952, Saudi Arabia c Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Mayalsia Johor, Malaysia * Corresponding author: sharidan@utm.my Article history Received 29 August 2017 Accepted 30 November 2017 Graphical abstract Abstract An analytical investigation is carried out to study the unsteady free convection stream of micropolar fluids over an oscillating vertical plate. Wall couple stress is promised at the bounding plate with isothermal temperature. Problem is displayed in terms of combined partial differential equations together with certain physical conditions and then written in non-dimensional form. Exact solutions are achieved using the Laplace transform technique. Analytical results of velocity, microrotation and temperature are plotted in graphs and debated for different inserted parameters. Excellent validation of present results is acquired with existing results in literature. It is observed that, the velocity is smaller for micropolar fluids than for Newtonian fluids. Keywords: Micropolar fluids, microrotaions, free convection, exact solutions © 2017 Penerbit UTM Press. All rights reserved INTRODUCTION Rheological characteristics of non-Newtonian fluids are termed by their constitutive equations. Because of complex nature of non- Newtonian fluids, several models or constitutive equations have been suggested based on their empirical observations. Amongst them, one model was proposed by (Eringen, 1966) using micromorphic fluid theory, known as micropolar fluids. Micropolar fluids pose microrotation and microinertia effect and constitute a significant branch of fluids. In literature micropolar fluids are used to describe flow characteristics of colloidal suspensions, geomor-phological sediments, liquid crystals, polymeric additives, haematological suspensions, lubricants and many other biological fluids (Ariman et al., 1973). Eringen and Lukaszewicz discussed fascinating characteristics of theory and applications of micropolor fluids (Erigen, 2001; Lukaszewicz 1999). (Nazar et al., 2002) examined boundary layer flow of micropolar fluid past an isothermal sphere by taking the free convection. (Cheng, 2008) discussed natural convection for micropolar fluids in combined transfer of heat and mass over a sphere accepting constant wall temperature together with constant wall concentration. (Sherief et al., 2011) used Laplace transform method and studied unsteady flow of a micropolar fluid from with rapidly stimulated plate. Analysis of heat transfer from moving surfaces with internal heat generation in a micropolar fluid is carried out by (El-Hakiem, 2014 ). (Hassanien et al., 1997) investigated the natural convection boundary layer flow of a micropolar fluid. (Ishak et al., 2008) discussed the micropolar fluids with heat transfer over a stretching surface with variable heat flux. (Lok et et al., 2005) reported the steady mixed convection flow near the stagnation point on a vertical surface of a micropolar fluid. Boundary layer stagnation point flow past a moving wall of a micropolar fluid has been studied by (Gorla, 1983). (Damesh et al., 2007) illustrated the micropolar fluid with unsteady natural convection heat transfer over a vertical surface with constant heat flux using numerical technique, whereas conjugate transfer of heat and mass in unsteady flow of a micropolar fluids with wall couple stress studied by (Khalid et al., 2015). (Abo-Dahab et al., 2013) investigated the unsteady flow of rotating and chemically reacting slip-flow regime with heat generation MHD micropolar fluid. The aim of the present work is to provide exact solutions for the unsteady free convection flow of an incompressible micropolar fluid over an infinite vertical plate oscillating in its own plan. More exactly, heat transfer when the bounding plate takes wall couple stress with isothermal temperature is studied. PROBLEM FORMULATION Assume, unsteady boundary layer stream of an incompressible micropolar fluid in the region 0 y  determine by a plane surface positioned at 0 y  with a fixed end at 0  x . It is expected that at the initial moment 0, t  both the plate and the fluid are at rest at the constant temperature T  . At time 0 t   the plate begins to oscillate in its plane ( 0 y  ) according to RESEARCH ARTICLE