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
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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.
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M. E. Gurtin and W. O. Williams, On the Clausius-Duhem inequality, Z. Angew. Math. Phys. 17, 626–633 (1966)
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C. Truesdell and R. Toupin, The classical field theories, Handbuch der Physik, Band III1, Springer-Verlag, Berlin and New York, 1960
B. D. Coleman and W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal. 13, 167–178 (1963)
B. D. Coleman and V. J. Mizel, Existence of caloric equations of state in thermodynamics, J. Chem. Phys. 40, 1116–1125 (1964)
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
M. E. Gurtin, Thermodynamics and the possibility of spatial interaction in rigid heat conductors, Arch. Rational Mech. Anal. 18, 335–342 (1965)
M. E. Gurtin and W. O. Williams, On the Clausius-Duhem inequality, Z. Angew. Math. Phys. 17, 626–633 (1966)
B. D. Coleman and M. E. Gurtin, Equipresence and constitutive equations for rigid heat conductors, Z. Angew. Math. Phys. 18, 199–208 (1967)
M. E. Gurtin and W. O. Williams, An axiomatic foundation for continuum thermodynamics, Arch. Rational Mech. Anal. 26, 83–117 (1967)
G. M. C. Fisher and M. J. Leitman, On continuum thermodynamics with surfaces, Arch. Rational Mech. Anal. 30, 225–262 (1968)
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Article copyright:
© Copyright 1970
American Mathematical Society
