Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 
 

 

Continuum thermodynamics with surfaces: Restrictions on constitutive equations


Authors: George M. C. Fisher and Marshall J. Leitman
Journal: Quart. Appl. Math. 28 (1970), 303-311
DOI: https://doi.org/10.1090/qam/99789
MathSciNet review: QAM99789
Full-text PDF Free Access

Abstract | References | Additional Information

Abstract: In an earlier paper we deduced, using measure theoretic concepts, forms for the first and second laws of thermodynamics on surfaces which are distinguished by area-continuous and time-dependent energy and entropy. In that paper we avoided making constitutive assumptions since we sought expressions for the physical laws which were, indeed, independent of particular material assumptions.


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

  • [1] C. Truesdell and R. Toupin, The classical field theories, Handbuch der Physik, Band III1, Springer-Verlag, Berlin and New York, 1960 MR 0118005
  • [2] B. D. Coleman and W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal. 13, 167-178 (1963) MR 0153153
  • [3] B. D. Coleman and V. J. Mizel, Existence of caloric equations of state in thermodynamics, J. Chem. Phys. 40, 1116-1125 (1964) MR 0161576
  • [4] C. Truesdell and W. Noll, The nonlinear field theories of mechanics, Handbuch der Physik, Band III3, Springer-Verlag, Berlin and New York, 1965, pp. 1-602 MR 1215940
  • [5] M. E. Gurtin, Thermodynamics and the possibility of spatial interaction in rigid heat conductors, Arch. Rational Mech. Anal. 18, 335-342 (1965) MR 0174282
  • [6] M. E. Gurtin and W. O. Williams, On the Clausius-Duhem inequality, Z. Angew. Math. Phys. 17, 626-633 (1966)
  • [7] B. D. Coleman and M. E. Gurtin, Equipresence and constitutive equations for rigid heat conductors, Z. Angew. Math. Phys. 18, 199-208 (1967) MR 0214334
  • [8] M. E. Gurtin and W. O. Williams, An axiomatic foundation for continuum thermodynamics, Arch. Rational Mech. Anal. 26, 83-117 (1967) MR 0214335
  • [9] G. M. C. Fisher and M. J. Leitman, On continuum thermodynamics with surfaces, Arch. Rational Mech. Anal. 30, 225-262 (1968) MR 0229428


Additional Information

DOI: https://doi.org/10.1090/qam/99789
Article copyright: © Copyright 1970 American Mathematical Society

American Mathematical Society