Abstract
In this paper we establish the restrictions imposed by the Second law of Thermodynamics on the relaxation functions which arise in the theory of heat conduction with finite wave speeds. We show that (i) the initial values of the energy relaxation function and the heat flux relaxation function are non-negative, (ii) the initial slope of the heat flux relaxation function is non-positive, and (iii) the equilibrium conductivity is non-negative. These results have important implications with regard to the behavior of waves and the uniqueness of solutions.
Zusammenfassung
In dieser Arbeit werden die durch den zweiten Hauptsatz der Thermodynamik gegebenen Beschränkungen der Relaxationsfunktionen aufgezeigt, die in der Theorie der Wärmeleitung mit endlicher Ausbreitungsgeschwindigkeit auftreten. Es wird gezeigt, dass erstens die Anfangswerte der Energie-Relaxationsfunktion und der Wärmefluss-Relaxationsfunktion nicht negativ sind, zweitens die Anfangsableitung der Wärmefluss-Relaxationsfunktion nicht positiv ist, drittens die Gleichgewichts-Wärmeleit fähigkeit nicht negativ ist. Diese Resultate haben wichtige Konsequenzen in Bezug auf das Verhalten der Wellenausbreitung und die Eindeutigkeit der Lösungen.
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Chen, P.J., Nunziato, J.W. Thermodynamic restrictions on the relaxation functions of the theory of heat conduction with finite wave speeds. Journal of Applied Mathematics and Physics (ZAMP) 25, 791–798 (1974). https://doi.org/10.1007/BF01590264
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DOI: https://doi.org/10.1007/BF01590264