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
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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.

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

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