Conservation laws for the Cattaneo heat propagation

Abstract

In this work we determine for the Cattaneo heat propagation system all the supplementary balance laws (conservation laws) of the same order (zero) as the system itself and extract the constitutive relations (expression for the internal energy) dictated by the Entropy Principle. The space of all supplementary balance laws (having the functional dimension 8) contains four original balance laws and their deformations depending on 4 functions of temperature $\theta$ - $\lambda(\theta),K^{A}(\theta),A=1,2,3$. The requirements of the II law of thermodynamics leads to the exclusion of three of these functions ($K^A$) and to further restriction to the form of internal energy. In its final formulation, entropy balance represent the deformation of the energy balance law by the functional parameter $\lambda (\theta)$.