Fundamental equations for magnetic fluids by micropolar theory. 2nd report: Constitutive equations.

Abstract

Most of the previous theories for fundamental equations of magnetic fluids have not been able to describe both viscoelastic effect and internal rotation simultaneously. They cannot give the behaviour of magnetic fluids completely. In the plesent paper, to derive the complete set of equations for magnetic fluids, we unify the micropolar theory and the thermodynamical method. First, thermodynamical equations for magnetic fluids, for example, Gibbs' equation and dissipative function, are obtained by using the strain tensors for micropolar theory, the balance equations and electromagnetic equations which were derived in the previous paper. And next, the constitutive equations including nonlinear terms are obtained by using the principle of material frame indifference and the principle of maximal dissipation rate. These constitutive equations can represent the behaviour sufficiently when we must consider viscoelastic effect, internal rotation and nonlinear effect.