Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Variational irreversible thermodynamics of heat and mass transfer in porous solids: new concepts and methods

Author: M. A. Biot
Journal: Quart. Appl. Math. 36 (1978), 19-38
MSC: Primary 80.49
DOI: https://doi.org/10.1090/qam/475341
MathSciNet review: 475341
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A recently developed variational principle of virtual dissipation along with a new approach to the thermodynamics of open systems is applied to coupled mass and heat transfer in a porous solid containing a fluid. General differential field equations are derived directly from the variational principle. A general energy flux theorem is formulated. Vapor-liquid phase transition and capillary condensation are discussed. Field equations for nonequilibrium adsorption are also obtained. Lagrangian equations with generalized coordinates are derived directly from the variational principle without use of the field equations. They provide the foundation of finite-element methods as well as of many other techniques particularly suitable in geothermal systems analysis.

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 (Classes des Sciences) 61, 6-30 (1975) MR 0371269
  • [2] M. A. Biot, Variational principles in irreversible thermodynamics with application to viscoelasticity, Phys. Rev. 97, 1463-1469 (1955) MR 0070514
  • [3] M. A. Biot, Variational-Lagrangian irreversible thermodynamics of nonlinear thermorheology. Quart. Appl. Math. 24, 213-248 (1976) MR 0462245
  • [4] M. A. Biot, New chemical thermodynamics of open systems. Thermobaric potential, a new concept, Bull. Roy. Acad. Belgium (Classe des Sciences) 62, 239-258 (and Erratum p. 678) (1976) MR 0426639
  • [5] M. A. Biot, New fundamental concepts and results in thermodynamics with chemical applications, Chemical Physics 22, 183-198 (1977) MR 0503006
  • [6] M. A. Biot, Variational thermodynamics of viscous compressible heat-conducting fluids, Quart. Appl. Math. 34, 323-329 (1977) MR 0462246
  • [7] M. A. Biot, Variational-Lagrangian thermodynamics of nonisothermal finite strain mechanics of porous solids and thermomolecular diffusion, Int. J. Solids Structures 13, 579-597 (1977) MR 0449201
  • [8] J. Willard Gibbs, Scientific papers, Vol. 1. Thermodynamics, Longmans Green and Co., London, 1906
  • [9] M. A. Biot, Variational principles in heat transfer. A unified Lagrangian analysis of dissipative phenomena, Oxford Press, London, 1970
  • [10] J. Meixner, Zur Thermodynamik der Thermodiffusion, Ann. Physik 39, 333-356 (1941)
  • [11] L. Onsager, Reciprocal relations in irreversible processes I, Phys. Rev. 37, 405-426 (1930)
  • [12] L. Onsager, Reciprocal relations in irreversible thermodynamics II, Phys. Rev. 37, 2265-2279 (1931)
  • [13] S. R. De Groot, Thermodynamics of irreversible processes, North Holland Publishing Co., Amsterdam, 1952
  • [14] M. King Hubbert, The theory of ground-water motion, J. Geology, 48, 785-944 (1940)
  • [15] A. E. Scheidegger, The physics of flow through porous media, Macmillan, New York, 1960 MR 0127717

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 80.49

Retrieve articles in all journals with MSC: 80.49

Additional Information

DOI: https://doi.org/10.1090/qam/475341
Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society