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Journal of Applied Mathematics
Volume 2011, Article ID 538637, 14 pages
Research Article

Simulation of Thermomagnetic Convection in a Cavity Using the Lattice Boltzmann Model

1Department of Mechanical Engineering, University of New Brunswick, Fredericton, NB, Canada E3B 5A3
2Department of Mechanical Engineering, University of Aveiro, Aveiro 3810-193, Portugal

Received 15 January 2011; Accepted 14 March 2011

Academic Editor: Shuyu Sun

Copyright © 2011 Mahshid Hadavand and Antonio C. M. Sousa. 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.


Thermomagnetic convection in a differentially heated square cavity with an infinitely long third dimension is numerically simulated using the single relaxation time lattice Boltzmann method (LBM). This problem is of considerable interest when dealing with cooling of microelectronic devices, in situations where natural convection does not meet the cooling requirements, and forced convection is not viable due to the difficulties associated with pumping a ferrofluid. Therefore, circulation is achieved by imposing a magnetic field, which is created and controlled by placing a dipole at the bottom of the enclosure. The magnitude of the magnetic force is controlled by changing the electrical current through the dipole. In this study, the effects of combined natural convection and magnetic convection, which is commonly known as “thermomagnetic convection,” are analysed in terms of the flow modes and heat transfer characteristics of a magnetic fluid.