On a new C- and F-processes heat conduction constitutive model and the associated generalized theory of dynamic thermoelasticity

Emanating from the Boltzmann transport equation, a new C- and F-processes h eat conduction constitutive model is derived. The model acknowledges the no tion of the simultaneous coexistence of both the slow Cattaneo-type C-proce sses and fast Fourier-type F-processes in the mechanisms of heat conduction . The C- and F-processes heat conduction constitutive model and the corresp onding temperature equation that results from coupling the constitutive mod el with the energy equation naturally lead to a generalization of the macro scale in space one-temperature theory for heat conduction in solids of the Jeffreys'-type model, Cattaneo model, and the Fourier model for heat conduc tion in solids. This is unlike the Jeffreys'-type phenomenological model, w hich cannot reduce to the classical Fourier model (but only to a Fourier-li ke representation with relaxation) and it cannot explain the underlying phy sics associated wit the C- and F-processes model. Additionally, the microsc ale in space two-temperature theory for pulse heating of metals is also hig h-lighted via the C- and F- processes hat conduction constitutive model. Em phasis is placed on the development of a new C- and F-processes heat conduc tion model based on generalized thermoelastic theory to study the dynamic t hermoelastic behavior of solids with special features that can lead to and explain the classical and nonclassical dynamic thermoelastic theories. Fina lly some conceptual pitfalls that appear in the literature are addressed.