A New Complete Set of Basic Equations for Conducting Magnetic Fluids with Internal Rotation (Thermodynamical Discussions)

A new complete set of basic equations for magnetic fluids having good conductivity of heat and electricity with internal rotation has not been derived before. In this paper, governing equations for such conducting magnetic fluids are formulated by the thermodynamical method, in which free energy and the dissipation function are used on the basic of kinematical balance equations in the polar theory. A simple method for determining a constitutive equation of magnetization is proposed, so that the relaxation equation of magnetization becomes unnecessary. It is shown that the equations obtained in this paper involve almost all equations concerned with magnetic fluids. The new system of equations for nonconducting magnetic fluids derived here is more general and strict in comparison with those previously presented. Hence, it will be possible to treat rapid changes of magnetic fields by the present theory.