Computation of demagnetizing fields and particle distribution in magnetic fluid with inhomogeneous density

A new algorithm for calculating magnetic fields in a concentrated magnetic fluid with inhomogeneous density is proposed. Inhomogeneity of the fluid is caused by magnetophoresis. In this case, the diffusion and magnetostatic parts of the problem are tightly linked together and are solved jointly. The dynamic diffusion equation is solved by the finite volume method and, to calculate the magnetic field inside the fluid, an iterative process is performed in parallel. The solution to the problem is sought in Cartesian coordinates, and the computational domain is decomposed into rectangular elements. This technique eliminates the need to solve the related boundary-value problem for magnetic fields, accelerates computations and eliminates the error caused by the finite sizes of the outer region. Formulas describing the contribution of the rectangular element to the field intensity in the case of a plane problem are given. Magnetic and concentration fields inside the magnetic fluid filling a rectangular cavity generated under the action of the uniform external filed are calculated.