A scaling analysis to characterize thermomagnetic convection

Thermomagnetic convection is characterized using scaling arguments. We consider a square enclosure filled with a ferrofluid that is under the influence of an external magnetic field created by a line dipole. The height-averaged Nusselt number scales with the magnetic Rayleigh number as image. This result is in excellent agreement with predictions obtained from detailed numerical simulations. Use of the Langevin equation of ferrofluid magnetization identifies an optimum enclosure height for which the Nusselt number reaches a maximum value for a given line dipole strength.