Symmetric forms of the equations of heat transport in a rigid conductor of heat with internal state variables I. analysis of the model and thermodynamic restrictions via the 'main dependency relation'

摘要

the objective of this series of two papers is twofold: to analyse the phenomeno- logical model of a rigid conductor of heat with (vector) internal state variable, and to promote the application of the "main dependency relation" (MDR) as a tool for derivation of the restrictions on constitutive functions implied by the entropy in- equality as well as a tool for direct derivation of alternative symmetric systems of field equations. In this paper (Part I), the analysis of the model of a rigid conductor of heat with (vector) internal state variable is focused on two aspects, namely, in the form of the respective field equations and on the relation to other phenomenological models proposed in the literature, with the emphasis put on those models which have been successfully adjusted to experimental data on heat transport at finite speeds.