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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 236901, 15 pages
http://dx.doi.org/10.1155/2013/236901
Research Article

A Linear Stability Analysis of Thermal Convection in a Fluid Layer with Simultaneous Rotation and Magnetic Field Acting in Different Directions

Departamento de Termofluidos, Facultad de Ingeniería, Universidad Nacional Autónoma de México, 04510 México, DF, Mexico

Received 11 February 2013; Accepted 22 May 2013

Academic Editor: Zhijun Zhang

Copyright © 2013 Ruben Avila and Ares Cabello. 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 onset of thermal convection of a Boussinesq fluid located in an unbounded layer heated from below and subject simultaneously to rotation and magnetic field, whose vectors act in different directions, is presented. To the knowledge of the authors, the convective thermal instability analysis for this complex problem has not been previously reported. In this paper, we use the Tau Chebyshev spectral method to calculate the value of the critical parameters (wave number and Rayleigh number at the onset of convection) as a function of (i) different kinds of boundaries, (ii) angle between the three vectors, and (iii) different values of the Taylor number (rate of rotation) and magnetic parameter (strength of the magnetic force). For the classical problems previously reported in the literature, we compare our calculations with Chandrasekhar’s variational method results and show that the present method is applicable.