On the thermodynamics of some generalized second-grade fluids

Man, Chi-Sing; Massoudi, Mehrdad
January 2010
Continuum Mechanics & Thermodynamics;Jan2010, Vol. 22 Issue 1, p27
Academic Journal
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 F 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 F, and derive thermodynamic restrictions on the material functions of temperature �, a1, and a2 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.


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