An analysis of the dynamic behavior of a magnetorheological (MR) fluid is given in terms of a vectorial internal variable describing the change of the macroscopic average of the relative position vector of suspensions. Under the restriction of the second law, the constitutive equations of the MR fluid for stress, heat flux, magnetization and internal variable can be derived. The related issue of dissipative and energy transfer mechanisms is treated at some length. Studies on the steady shear flow indicate the direction of the internal variable is independent of shear rate. The Bingham-type constitutive equation for shear stress is obtained and endowed with a new meaning. The pressure-driven flow, another significant flow type for the design of MR devices, is also analyzed to study the plug flow region and the relationship between yield stress and flow rate. In addition, a criterion of flow initiated by the applied shear force is proposed based on the saturation of the internal variable and the condition of the equilibrium of forces in the fluid and solid regions.
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Received April 08, 1997
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Yeh, C., Chen, K. A thermodynamic model for magnetorheological fluids. Continuum Mech Thermodyn 9, 273–291 (1997). https://doi.org/10.1007/s001610050071
- Shear Stress
- Heat Flux
- Shear Rate
- Constitutive Equation
- Internal Variable