Heat Transfer in Incompressible Magnetic Fluid

In this paper we study the equations describing the dynamics of heat transfer in an incompressible magnetic fluid under the action of an applied magnetic field. The system is a combination of the Navier-Stokes equations, the magnetostatic equations and the temperature equation. We prove global-in-time existence of weak solutions with finite energy to the system posed in a bounded domain of and equipped with initial and boundary conditions. The main difficulty comes from the singularity of the terms representing the Kelvin force due to the magnetization and the thermal power due to the magnetocaloric effect.