The governing equations for magnetic fluids with good conductivity of heat and electricity have not been sufficiently discussed thermodynamically. In this paper a new strict simplified method of deriving the basic equations for such conducting magnetic fluids is presented using the thermodynamical method in which free energy and dissipation function are used on the assumption of the nonrelativistic and nonpolar theory. As the result, a physically desirable expression of the pressure part and Maxwellian stress in the constitutive equation of stress is derived in a general theory that polarized and magnetized media exist. Then the followng results are obtained from this theory: the surface forces acting on the material control surface include not only stress but also electromagnetic momentum flux density and the pointing vectors in the material volume are obtained in the relativistic electromagnetic fields which move against the fixed system.
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