ON A NEW C- AND F-PROCESSES HEAT CONDUCTION CONSTITUTIVE MODEL AND THE ASSOCIATED GENERALIZED THEORY OF DYNAMIC THERMOELASTICITY

Abstract

Emanating from the Boltzmann transport equation, a new C- and F-processes heat conduction constitutive model is derived. The model acknowledges the notion of the simultaneous coexistence of both the slow Cattaneo-type C-processes and fast Fourier-type F-processes in the mechanisms of heat conduction. The C- and F-processes heat conduction constitutive model and the corresponding temperature equation that results from coupling the constitutive model with the energy equation naturally lead to a generalization of the macroscale in space one-temperature theory for heat conduction in solids of the Jeffreys'-type model, Cattaneo model, and the Fourier model for heat conduction in solids. This is unlike the Jeffreys'-type phenomenological model, which cannot reduce to the classical Fourier model (but only to a Fourier-like representation with relaxation) and it cannot explain the underlying physics associated with the C- and F-processes model. Additionally, the microscale in space two-temperature theory for pulse heating of metals is also highlighted via the C- and F-processes heat conduction constitutive model. Emphasis is placed on the development of a new C- and F-processes heat conduction model based on generalized thermoelastic theory to study the dynamic thermoelastic behavior of solids with special features that can lead to and explain the classical and nonclassical dynamic thermoelastic theories. Finally some conceptual pitfalls that appear in the literature are addressed.