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.

References [Enhancements On Off] (What's this?)

  • [1] M. A. Biot, A virtual dissipation principle and Lagrangian equations in nonlinear irreversible thermodynamics, Bull. Roy. Acad. Belgium 5th Ser., 61, 5-30 (1975) MR 0371269
  • [2] M. A. Biot, Variational-Lagrangian irreversible thermodynamics of nonlinear thermorheology, Quart. Appl. Math, (in press) MR 0462245
  • [3] M. A. Biot, Thermoelasticity and irreversible thermodynamics, J. Appl. Phys. 27, 240-253 (1956) MR 0077441
  • [4] M. A. Biot, Lagrangian thermodynamics of heat transfer in systems including fluid motion, J. Aerospace Sci. 29, 568-577 (1962) MR 0162492
  • [5] M. A. Biot, Generalized variational principles for convective heat transfer and irreversible thermodynamics, J. Math. Mech. 15, 177-186 (1966) MR 0187587
  • [6] M. A. Biot, Variational principles in heat transfer, Oxford Univ. Press, 1970

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

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