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
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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.
- M. A. Biot, A virtual dissipation principle and Lagrangian equations in non-linear irreversible thermodynamics, Acad. Roy. Belg. Bull. Cl. Sci. (5) 61 (1975), 6–30. MR 371269
- M. A. Biot, Variational principles in irreversible thermodynamics with application to viscoelasticity, Phys. Rev. (2) 97 (1955), 1463–1469. MR 70514
- M. A. Biot, Variational-Lagrangian irreversible thermodynamics of nonlinear thermorheology, Quart. Appl. Math. 34 (1976/77), no. 3, 213–248. MR 462245, DOI https://doi.org/10.1090/S0033-569X-1976-0462245-2
- M. A. Biot, New chemical thermodynamics of open systems. Thermobaric potential, a new concept, Acad. Roy. Belg. Bull. Cl. Sci. (5) 62 (1976), no. 4, 239–258. MR 426639
- M. A. Biot, New fundamental concepts and results in thermodynamics with chemical applications, Chem. Phys. 22 (1977), no. 2, 183–198. MR 503006, DOI https://doi.org/10.1016/0301-0104%2877%2987002-X
- M. A. Biot, Variational thermodynamics of viscous compressible heat-conducting fluids, Quart. Appl. Math. 34 (1976/77), no. 4, 323–329. MR 462246, DOI https://doi.org/10.1090/S0033-569X-1977-0462246-1
- M. A. Biot, Variational Lagrangian-thermodynamics of nonisothermal finite strain mechanics of porous solids and thermomolecular diffusion, Internat. J. Solids Structures 13 (1977), no. 6, 579–597. MR 449201, DOI https://doi.org/10.1016/0020-7683%2877%2990031-2
J. Willard Gibbs, Scientific papers, Vol. 1. Thermodynamics, Longmans Green and Co., London, 1906
M. A. Biot, Variational principles in heat transfer. A unified Lagrangian analysis of dissipative phenomena, Oxford Press, London, 1970
J. Meixner, Zur Thermodynamik der Thermodiffusion, Ann. Physik 39, 333–356 (1941)
L. Onsager, Reciprocal relations in irreversible processes I, Phys. Rev. 37, 405–426 (1930)
L. Onsager, Reciprocal relations in irreversible thermodynamics II, Phys. Rev. 37, 2265–2279 (1931)
S. R. De Groot, Thermodynamics of irreversible processes, North Holland Publishing Co., Amsterdam, 1952
M. King Hubbert, The theory of ground-water motion, J. Geology, 48, 785–944 (1940)
- Adrian E. Scheidegger, The physics of flow through porous media, Revised edition, The Macmillan Co., New York, 1960. MR 0127717
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)
M. A. Biot, Variational principles in irreversible thermodynamics with application to viscoelasticity, Phys. Rev. 97, 1463–1469 (1955)
M. A. Biot, Variational-Lagrangian irreversible thermodynamics of nonlinear thermorheology. Quart. Appl. Math. 24, 213–248 (1976)
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)
M. A. Biot, New fundamental concepts and results in thermodynamics with chemical applications, Chemical Physics 22, 183–198 (1977)
M. A. Biot, Variational thermodynamics of viscous compressible heat-conducting fluids, Quart. Appl. Math. 34, 323–329 (1977)
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)
J. Willard Gibbs, Scientific papers, Vol. 1. Thermodynamics, Longmans Green and Co., London, 1906
M. A. Biot, Variational principles in heat transfer. A unified Lagrangian analysis of dissipative phenomena, Oxford Press, London, 1970
J. Meixner, Zur Thermodynamik der Thermodiffusion, Ann. Physik 39, 333–356 (1941)
L. Onsager, Reciprocal relations in irreversible processes I, Phys. Rev. 37, 405–426 (1930)
L. Onsager, Reciprocal relations in irreversible thermodynamics II, Phys. Rev. 37, 2265–2279 (1931)
S. R. De Groot, Thermodynamics of irreversible processes, North Holland Publishing Co., Amsterdam, 1952
M. King Hubbert, The theory of ground-water motion, J. Geology, 48, 785–944 (1940)
A. E. Scheidegger, The physics of flow through porous media, Macmillan, New York, 1960
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© Copyright 1978
American Mathematical Society
