On the thermodynamics of some generalized second-grade fluids
The generalized second-grade fluids, which have been used for modeling the creep of ice and the flow of coal-water and coal-oil slurries, are among the simplest non-Newtonian fluid models that can describe shear-thinning/thickening and exhibit normal stress effects. In this article, we conduct thermodynamic analysis on a class of generalized second-grade fluids, one distinguishing feature of which is the existence of a constitutive function that describes frictional heating. We work within the framework of Serrin’s original formulation of neoclassical thermodynamics, where internal energy and entropy functions, if they exist for a continuous body at all, are to be derived from the classical First Law and (quantitatively reformulated) Second Law of thermodynamics for cycles. For the class of generalized second-grade fluids in question, we show from the First Law that an internal energy density u exists, and we derive the equation of energy balance; from the Second Law, we demonstrate the existence of an entropy density s and derive the Clausius–Duhem inequality that it satisfies.We obtain explicit expressions for u, s and the frictional heating , and derive thermodynamic restrictions on thematerial functions of temperature μ, α1, and α2 that appear in the constitutive relation for the Cauchy stress. For the special case of second-grade fluids, our expressions for u and s agree with those which Dunn and Fosdick [6] derived under the theoretical framework of the rational thermodynamics of Coleman and Noll.
- Research Organization:
- National Energy Technology Laboratory - In-house Research; National Energy Technology Laboratory (NETL), Pittsburgh, PA, and Morgantown, WV (United States)
- Sponsoring Organization:
- USDOE Assistant Secretary for Fossil Energy (FE)
- OSTI ID:
- 1012919
- Report Number(s):
- netltpr-2914
- Journal Information:
- CONTINUUM MECHANICS AND THERMODYNAMICS, Journal Name: CONTINUUM MECHANICS AND THERMODYNAMICS Journal Issue: 1 Vol. 22
- Country of Publication:
- United States
- Language:
- English
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