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Exploitation of the
dissipation inequality, if some balances are missing
Wolfgang Muschik, Vita Triani and Christina Papenfuss |
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Vol. 3 (2008), No. 6, 1125–1133
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Abstract |
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The balance equations of continuum thermodynamics need constitutive equations in order to solve them under the constraint that the entropy production appearing in the entropy balance equation must be not negative. This dissipation inequality represents the second law of thermodynamics. There are two procedures which exploit the dissipation inequality to obtain constitutive equations which are in agreement with the second law: the Coleman–Noll and the Liu techniques. Here we use the Liu technique in the special case in which not all balance equations are taken into account when exploiting the dissipation inequality. This case is of interest because often not all balances are known, or only the energy balance is considered. It is also proved that in this abridged exploitation of the dissipation inequality, thermodynamic restrictions for the constitutive equations are obtained, so that these satisfy the second law. These restrictions represent a smaller class of materials than that obtained when all balances are taken into account. |
Keywords
dissipation inequality, reduced set of balances, abridged
exploitation of the dissipation inequality, second law
exploitation, Coleman–Noll procedure, Liu procedure
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Milestones
Received: 7 February 2008
Revised: 26 March 2008
Accepted: 2 April 2008
Published: 1 August 2008
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Authors |
| Wolfgang Muschik | |
| Institut für Theoretische
Physik EW 7-1 Technische Universität Berlin Hardenbergstraße 36 10623 Berlin Germany |
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| Vita Triani | |
| Dipartimento di Matematica ed
Informatica Universitá degli Studi della Basilicata Campus Macchia Romana Potenza, 85100 Italy |
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| Christina Papenfuss | |
| Institut für Mechanik Technische Universität Berlin Strasse des 17. Juni 10623 Berlin Germany |
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