Mathematical Modeling of Flow Control Using Magnetic Fluid and Field

In this paper some previous studies related to those for flow control aspects of the hydrodynamics of magnetic fluid and field are reviewed first and recent mathematical approaches for the corresponding systems of partial differential equations are discussed. Next, mathematical modeling of a two-fluid system, with one fluid being a non-conducting ferrofluid and another fluid being a regular non-ferrofluid is considered. A numerical method is used to solve the mathematical system for the problem, which, in particular, captures the flow structure in the two-fluid system. The convective flow velocities and the heat fluxes were determined for various values of the parameters of the problem. Certain aspects of the magnetic fluids and fields were found to be useful for convective flow control, which is important in many application areas including microgravity space applications. In particular, under some conditions, the surface force that can exist at the interface between the two fluid zones was found to reduce the magnitude of the flow velocity and instabilities that may occur in the two-fluid system.