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 high-lighted 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.
Bibliographical noteFunding Information:
Received 15 Decembr 2000e; accepted 28 Decemr 2b0.00e The authors are very pleased to acknowledge support in part by Battelle/U.S. Army Reseach rOf¢ce (ARO) Reseach rTriangle Park, North Carolina, under gantrnumber DAAH04-96-C-0086, and by the Army High Performance Computing Research Center (AHPCRC) under the auspices of the Department of the Army, Army Research Laboratory (ARL) cooperative agreement number DAAH04-95-2-0003/contract number DAAH04-95-C-0008. Te chnonttdesontnoecessarily re£ect the position or the policy of the government, and no of¢cial endorsement should be inferred. Support in part by Dr. Andrew Mark of the Integrated Modeling and Testing (IMT) Computational Technical Activity and the ARL/MSRC facilities is also gratefully acknowledged. Special thanks are due to the CIC Directorate at the U.S. Army Research Laboratory (ARL), Aberdeen Proving Ground, Maryland. Other related support in form of computer grants from the Minnesota Supercomputer Institute (MSI), Minneapolis, Minnesota is also gratefully acknowledged.