Thermomagnetic convection in a square enclosure using a line dipole

Abstract

We have simulated thermomagnetic convection in a differentially heated square cavity with an infinitely long third dimension. The cavity is under the influence of an imposed two-dimensional magnetic field that conforms to the Maxwell’s equations. Our objective is to characterize the thermomagnetic convection in terms of the geometric length scales, magnetic fluid properties, temperature differences, and strengths of the imposed magnetic fields. Fluid motion occurs due to both the gradients of the magnetic field and the temperature. Colder fluid that has a larger magnetic susceptibility is attracted toward regions with larger field strength during thermomagnetic convection, which displaces warmer fluid of lower susceptibility. The height-averaged Nusselt number Nuav increases with increasing magnetic dipole strength and temperature but decreases with increasing fluid viscosity. Thermomagnetic heat transfer increases when the length scale decreases if the dipole strength of the source magnet is constant. This makes thermomagnetic convection a potentially viable option for microscale heat transfer applications. Thermomagnetic convection can be correlated with a dimensionless magnetic Rayleigh number Ram=(μ0ρ0βρχm,0m2 ΔT Pr/η2h2) and heat transfer due to this form of convection in the range Ram=2×104–2×107 is as effective as buoyancy-induced convection in the range Ra=1000–106.