Determination of Constitutive Equations for Magnetic Fluids Using the Theory of Integrity Bases and the Principle of Maximal Dissipation Rate

Abstract

Constitutive equations for magnetic fluids have been investigated by some researchers, however, these equations cannot describe the phenomena of magnetic fluids perfectly for lack of some elements which the constitutive equations should satisfy, for example, some do not consider viscoelastic effects, some do not satisfy the principle of material frame indifference, some are not formulated by using the thermodynamic method. We introduce a new way of determining constitutive equations for magnetic fluids. It is a method which is a combination of the theory of integrity bases and the principle of maximal dissipation rate based on the thermodynamic discussion. Compared with previous methods, it has such merits as the following: all equations satisfy the principle of material frame indifference and only include the terms which are permitted by thermodynamics; non-Nowtonian effects except magnetic effects can be described because nonlinear terms are considered; we can obtain the constitutive equations not only in the case of the compound processes but in that of the complex processes as well.