Finite element analysis for cooling effect of magnetic fluid with alternating magnetic field

We present a fully coupled finite element method (FEM) for analyzing a cooling effect of magnetic fluid with an alternating magnetic field driven with the power frequency, 60 Hz. There are two different heat sources with an alternating magnetic field such as the Joule's loss in coils excited with electric input and the power dissipation corresponding to Neel and Brownian relaxation. Because the input frequency is relatively low, the Joule's loss in coil is a dominant heat source. The heat, therefore, transfers from the coil to the magnetic fluid and the natural convection phenomena arise on the coil surfaces. To consider the natural convection phenomena, the buoyant force density was considered in a magnetic fluid. Additionally, the forced convection, magnetoconvection, results from the magnetic body force density with the magnetization as a function of magnetic field intensity and temperature. These two convection phenomena play a key role for cooling effect of magnetic fluid with an alternating magnetic field. To derive the magnetic body force density, we, here, numerically employed the continuous approach of Kelvin force density, which has been derived by introducing the virtual air-gap scheme incorporating with the FEM. The Langevin function was employed to consider the nonlinear magnetic susceptibility for evaluating the Kelvin force density and the power dissipations due to the Neel relaxation and Brownian relaxation.