chemical engineering research and design 89 (2011) 2291–2297 Contents lists available at ScienceDirect Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd MHD flow of a micropolar fluid towards a vertical permeable plate with prescribed surface heat flux Nor Azizah Yacob a , Anuar Ishak b,c,∗ a Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Pahang, 26400 Bandar Tun Razak Jengka, Pahang, Malaysia b Centre for Modelling & Data Analysis, School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia c Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia abstract The problem of a steady mixed convection stagnation point flow towards a permeable vertical plate with prescribed surface heat flux immersed in an incompressible micropolar fluid is studied numerically. The governing partial differential equations are first transformed into a system of ordinary differential equations using a similarity trans- formation, before being solved numerically by a finite-difference scheme known as the Keller-box method and the Runge–Kutta–Fehlberg method with shooting technique. The effects of the material parameter, buoyancy parameter, suction/injection parameter and the Prandtl number on the fluid flow and heat transfer characteristics are discussed. It is found that dual solutions exist for both assisting and opposing flows. The skin friction coefficient and the local Nusselt number increase in the presence of suction and magnetic field. Moreover, suction as well as fluids with larger Prandtl number widens the range of the buoyancy parameter for which the solution exists. © 2011 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Magnetohydrodynamic; Suction/injection; Dual solutions; Micropolar fluid 1. Introduction The study of magnetohydrodynamic (MHD) flow has received a great deal of research interest due to its importance in many engineering applications, such as plasma studies, MHD power generators, petroleum industries, liquid metals system of fusion reactors, cooling of nuclear reactors, the boundary layer control in aerodynamics and crystal growth (Harada and Tsunoda, 1998; Kirillov et al., 1995; Shang, 2001; Abricka et al., 1997). For example, to design self-cooled liquid metal blankets for fusion reactors, one must know about the behavior of MHD flows at high Hartmann numbers (Sterl, 1990). The MHD flow over a permeable vertical surface in a viscous fluid has been discussed by several authors, such as Chamkha (1998), who studied the mixed convection flow at the stagna- tion point of a vertical semi-infinite permeable surface in the presence of a magnetic field. Saha et al. (2007) investigated the effect of Hall current on the magnetohydrodynamic nat- ∗ Corresponding author at: Centre for Modelling & Data Analysis, School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia. Tel.: +60 3 8921 5756; fax: +60 3 8925 4519. E-mail address: anuarishak@yahoo.com (A. Ishak). Received 22 September 2010; Received in revised form 19 January 2011; Accepted 23 March 2011 ural convection flow past a semi-infinite permeable flat plate, while Aydin and Kaya (2009) studied the MHD mixed con- vection flow of a viscous dissipating fluid about a permeable vertical plate. Motivated by the above-mentioned studies, we consider in this paper the effects of suction and injection on the MHD mixed convection boundary layer flow near a stag- nation point on a permeable vertical surface immersed in an incompressible micropolar fluid with prescribed surface heat flux. We consider a small Prandtl number, represented a liquid metal which usually used in nuclear engineering as a coolant (Saha et al., 2007). Ramachandran et al. (1988) considered the similar problem with non-magnetic effect for impermeable surface immersed in a viscous fluid. They found that dual solutions exist for a certain range of the buoyancy param- eter, only for the opposing flow case. Thereafter, Devi et al. (1991) extended this problem to the unsteady case, while Lok et al. (2005) investigated the case where the plate immersed in a micropolar fluid. They also found that dual solutions exist 0263-8762/$ – see front matter © 2011 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.cherd.2011.03.011