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A study on magnetic convection in a narrow rectangular cavity

H. L. G. Couto - N. B. Marcelino - F. R. Cunha

Universidade de Bras\'ilia, Faculdade de Tecnologia, Depto. de Engenharia Mec\^anica Grupo de Mec\^anica dos Fluidos de Escoamentos Complexos - VORTEX Campus Universitário Darcy Ribeiro, 70910-900, Bras\'ilia, DF, Brazil

Abstract
The thermoconvective motion of a ferrofluid under an applied magnetic field is investigated theoretically by a dimensional analysis for different conditions of gravitational and magnetic Rayleigh numbers. Vertical walls are heated and the horizontal ones are insulated. A constant heat flux boundary condition on the heated wall is considered. The scaling analysis is based on the momentum and energy equations of a non-isothermal ferrofluid. The key dimensionless parameter are identified, which provide a measure of the thermal efficacy of the investigated heating system in terms of gravitational and magnetic Rayleigh numbers, \Rag and \Ram, respectively. When a magnetic force balances viscous forces in the convective flow, we find the magnetic Nusselt number \Num scaling like \Ram1/3. The scaling analysis is then complemented when the predictions are quantified by numerical values of typical thermodynamic and magnetic fluid properties. A potential application of the problem treated in this work is related to the possibility to use the ferrofluid as a more efficient refrigerator fluid of electrical transforms by adding to a carrier mineral oil a low volume fraction of nanomagnetic particles. The present analysis indicates that for a \Ram=104 based on the carrier fluid properties and a magnetic particle volume fraction of just 1% the refrigerating heat flux increases by about 20%. Figs 2, Refs 21.

Magnetohydrodynamics 43, No. 4, 421-428, 2007 [PDF, 0.15 Mb]

Copyright: Institute of Physics, University of Latvia
Electronic edition ISSN 1574-0579
Printed edition ISSN 0024-998X
DOI: http://doi.org/10.22364/mhd