A new complete set of the basic equations for magnetic fluids with internal rotation are determined by the thermodynamical method in which free energy and dissipation function are used on basis of the coservation laws. Then a simple way to find a form of the dissipation function is given. As a result, the quasi-conservative part in the constitutive equation of stress and the constitutive equation of couple stress are derived in a physically suitable form in comparison with the other theories. Exact representation for the pressure part of stress is obtained, and Maxwellian stress tensor is introduced into the constitutive equation of stress. An equation of energy for magnetic fluids possessing an internal angular momentum which has never been presented is formulated in this paper.
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