Differential Equations and Nonlinear Mechanics
Volume 2009 (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. Hashim3

1Malaysian Institute of Chemical & Bioengineering Technology, Universiti Kuala Lumpur, 78000 Alor Gajah Melaka, Malaysia
2Department of Mathematics, Faculty of Science & Technology, Universiti Malaysia Terengganu, 21030 Kuala Terengganu, Malaysia
3Centre for Modelling & Data Analysis, School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor, Malaysia

Received 20 May 2009; Accepted 8 December 2009

Academic Editor: Tasawar K. Hayat

Copyright © 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.

Abstract

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.