Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Variational thermodynamics of viscous compressible heat-conducting fluids

Author: M. A. Biot
Journal: Quart. Appl. Math. 34 (1977), 323-329
MSC: Primary 80.49
DOI: https://doi.org/10.1090/qam/462246
MathSciNet review: 462246
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Abstract: A new variational principle of virtual dissipation generalizing d'Alembert's principle to nonlinear irreversible thermodynamics is applied to compressible heat-conducting fluids with Newtonian and non-Newtonian viscosity. The principle is applied in the context of Eulerian formalism where the flow is described with reference to a fixed coordinate system. New concepts of entropy displacement and mass displacement are used as well as a new definition of the chemical potential which avoids the usual ambiguities of the classical thermodynamic approach. The variational principle is used to derive a novel form of field differential equations for the coupled fluid dynamics and convective heat transfer.

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DOI: https://doi.org/10.1090/qam/462246
Article copyright: © Copyright 1977 American Mathematical Society

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