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, \Ra_g and \Ra_m, respectively. When a magnetic force balances viscous forces in the convective flow, we find the magnetic Nusselt number \Nu_m scaling like \Ra_m^1/3. 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 \Ra_m=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.