Hindawi Publishing Corporation Differential Equations and Nonlinear Mechanics Volume 2009, Article ID 748794, 11 pages doi:10.1155/2009/748794 Research Article Effects of Magnetic Field and Nonlinear Temperature Profile on Marangoni Convection in Micropolar Fluid M. N. Mahmud, 1 R. Idris, 2 and I. Hashim 3 1 Malaysian Institute of Chemical & Bioengineering Technology, Universiti Kuala Lumpur, 78000 Alor Gajah Melaka, Malaysia 2 Department of Mathematics, Faculty of Science & Technology, Universiti Malaysia Terengganu, 21030 Kuala Terengganu, Malaysia 3 Centre for Modelling & Data Analysis, School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor, Malaysia Correspondence should be addressed to I. Hashim, ishak h@ukm.my Received 20 May 2009; Accepted 8 December 2009 Recommended by Tasawar K. Hayat The combined effects of a uniform vertical magnetic field and a nonuniform basic temperature profile on the onset of steady Marangoni convection in a horizontal layer of micropolar fluid are studied. The closed-form expression for the Marangoni number M for the onset of convection, valid for polynomial-type basic temperature profiles upto a third order, is obtained by the use of the single-term Galerkin technique. The critical conditions for the onset of convection have been presented graphically. Copyright q 2009 M. N. Mahmud et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction Convective flow in a thin layer of fluid, free at the upper surface and heated from below, is of fundamental importance and a prototype to a more complex configuration in experiments and industrial processes. The convective flows in a liquid layer can be driven by buoyancy forces due to temperature gradients and/or thermocapillary Marangoni forces caused by surface tension gradients. Thermal convective problems have long been studied extensively since the pioneering experimental and theoretical works of B´ enard 1, Rayleigh 2, and Pearson 3. The instability problems have been studied in several other directions cf. 4– 18. Most of the previous studies were concerned with convection in Newtonian fluids. However, much less work has been done on convection in non-Newtonian fluids such