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Lagrangian thermodynamics as a particular case of Governing Principle of Dissipative Processes

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Acta Physica Academiae Scientiarum Hungaricae

Abstract

This note deals with the relation between the Governing Principle of Dissipative Processes and the Lagrangian thermodynamics ofBiot. The governing principle is introduced in its universal form and then the flux representation is deduced as a partial form of it for the heat conduction phenomenon. Finally, the Lagrangian thermodynamics ofBiot is introduced in its original form and it is compared with the flux representation for heat conduction in solids. It is shown that for heat conduction phenomena for which the Lagrangian thermodynamics was proposed and applied byBiot, it is equivalent to the flux representation of GPDP.

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References

  1. L. Onsager, Reciprocal relations in irreversible processes. I. Phys. Rev.,37, 405, 1931.

    Article  MATH  ADS  Google Scholar 

  2. L. Onsager, Reciprocal relations in irreversible processes. II. Phys. Rev.,38, 2265, 1931.

    Article  MATH  ADS  Google Scholar 

  3. I. Gyarmati, On the Governing Principle of Dissipative Processes and its Extension to Non-linear Problems. Ann. Phys.,23, 353, 1969.

    Article  Google Scholar 

  4. I. Gyarmati, Non-equilibrium Thermodynamics, Field Theory and Variational Principles. Springer Verlag, Berlin, 1970.

    Google Scholar 

  5. I. Gyarmati, Generalization of the Governing Principle of Dissipative Processes to Complex Scalar Fields. Ann. Phys.,31, 18, 1974.

    Article  MathSciNet  Google Scholar 

  6. M. A. Biot, Variational principles in irreversible thermodynamics with application to viscoelasticity. Phys. Rev.,97, 1463, 1955.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  7. M. A. Biot, New methods in heat flow analysis with application to flight structures. J. Aeronaut, Sci.,24, 857, 1957.

    MATH  MathSciNet  Google Scholar 

  8. M. A. Biot, Further developments of new methods in heat flow analysis. J. Aerospace Sci.,26, 367, 1959.

    MATH  MathSciNet  Google Scholar 

  9. M. A. Biot, variational principles in heat transfer. Oxford University-Press, 1970.

  10. B. A. Finlaysen andL. E. Scriven, On the search for variational principles. Int. J. Heat Mass Transfer,10, 799, 1967.

    Article  Google Scholar 

  11. C. Truesdell, Rational Thermodynamics. McGraw-Hill, New York, 1969.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Kharagpur, India

    P. Singh

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  1. P. Singh
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Singh, P. Lagrangian thermodynamics as a particular case of Governing Principle of Dissipative Processes. Acta Physica 43, 133–140 (1977). https://doi.org/10.1007/BF03158282

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  • DOI: https://doi.org/10.1007/BF03158282

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