Simulation of ferrofluids by BEM

In this paper the Boundary element method (BEM) was applied to simulate viscous flow of ferrofluids under the influence of a homogenous external magnetic field. We present a derivation of the boundary integral form of the vorticity transport equation, which includes magnetic body force terms. Furthermore, discretization and numerical solution of the coupled flow and heat transfer problems are presented. The derived numerical model has been used to study the effect of a homogenous external magnetic field on the natural convection of ferrofluids in a differentially heated enclosure. We established that the effects are negligible for magnetic Rayleigh numbers less or equal to the flow Rayleigh number. On the other hand, the magnetic body force changes the flow field significantly and contributes to the instability of the flow