A note on Onsager’s relations
Author:
M. Šilhavý
Journal:
Quart. Appl. Math. 52 (1994), 469-479
MSC:
Primary 73F10; Secondary 73B30, 73F99
DOI:
https://doi.org/10.1090/qam/1292198
MathSciNet review:
MR1292198
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Abstract: A nonlinear viscoelastic material with the heat flux obeying a generalization of Cattaneo’s law is considered. It is shown that for slow processes with small gradients of temperature the exact constitutive equations can be approximated by those of a linear viscous material with Fourier heat conduction. As a consequence of the thermodynamic restrictions on the original constitutive equations, the approximate constitutive equations are shown to satisfy the principle of local equilibrium for energy and entropy, and the kinetic coefficients giving the viscous stress and heat flux vector satisfy Onsager’s relations.
D. Brandon and W. J. Hrusa, Construction of a class of integral models for heat flow in materials with memory, J. Integral Equations Appl. 1, 175–201 (1988)
C. Cattaneo, Sulla conduzione del calore, Atti Sem. Mat. Fis. Univ. Modena 3, 83–101 (1948)
B. D. Coleman, Thermodynamics of materials with memory, Arch. Rational Mech. Anal. 17, 1–46 (1964)
B. D. Coleman and W. Noll, An approximation theorem for functionals, with applications in continuum mechanics, Arch. Rational Mech. Anal. 6, 355–370 (1960)
B. D. Coleman, M. Fabrizio, and D. R. Owen, Thermodynamics and the constitutive relations for second sound in crystals, New Perspectives in Thermodynamics (J. Serrin, ed.), Springer, pp. 171–185, 1986
S. R. de Groot and J. Mazur, Non Equilibrium Thermodynamics, North-Holland, Amsterdam, 1962
M. E. Gurtin and W. J. Hrusa, On energies of nonlinear viscoelastic materials of single-integral type, Quart. Appl. Math. 46, 381–392 (1988)
M. E. Gurtin and W. J. Hrusa, On the thermodynamics of viscoelastic materials of single-integral type, Quart. Appl. Math. 49, 67–85 (1991)
M. E. Gurtin and A. C. Pipkin, A general theory of heat conduction with finite wave speeds, Arch. Rational Mech. Anal. 31, 113–126 (1968)
D. Brandon and W. J. Hrusa, Construction of a class of integral models for heat flow in materials with memory, J. Integral Equations Appl. 1, 175–201 (1988)
C. Cattaneo, Sulla conduzione del calore, Atti Sem. Mat. Fis. Univ. Modena 3, 83–101 (1948)
B. D. Coleman, Thermodynamics of materials with memory, Arch. Rational Mech. Anal. 17, 1–46 (1964)
B. D. Coleman and W. Noll, An approximation theorem for functionals, with applications in continuum mechanics, Arch. Rational Mech. Anal. 6, 355–370 (1960)
B. D. Coleman, M. Fabrizio, and D. R. Owen, Thermodynamics and the constitutive relations for second sound in crystals, New Perspectives in Thermodynamics (J. Serrin, ed.), Springer, pp. 171–185, 1986
S. R. de Groot and J. Mazur, Non Equilibrium Thermodynamics, North-Holland, Amsterdam, 1962
M. E. Gurtin and W. J. Hrusa, On energies of nonlinear viscoelastic materials of single-integral type, Quart. Appl. Math. 46, 381–392 (1988)
M. E. Gurtin and W. J. Hrusa, On the thermodynamics of viscoelastic materials of single-integral type, Quart. Appl. Math. 49, 67–85 (1991)
M. E. Gurtin and A. C. Pipkin, A general theory of heat conduction with finite wave speeds, Arch. Rational Mech. Anal. 31, 113–126 (1968)
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Article copyright:
© Copyright 1994
American Mathematical Society
