Differential Equations and Nonlinear Mechanics
Volume 2009 (2009), Article ID 748794, 11 pages
doi:10.1155/2009/748794
Effects of magnetic field and nonlinear temperature profile on Marangoni convection in micropolar fluid
M.N. Mahmud1
, R. Idris2
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
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.