CONSTITUTIVE MODEL THEORIES AND ISSUES AND PLAUSIBLE PROPOSITIONS/CHALLENGES TO HEAT TRANSPORT CHARACTERIZATION

摘要

The present exposition describes the fundamental issues encompassing some prominent constitutive model theories governing macroscale/microscale heat conduction phenomenon with generalizations drawn concerning the physical relevance and the role of relaxation/retardation times including plausible propositions and challenges to heat transport characterization. Emanating from the Jeffreys type heat-flux constitutive model with physical interpretation provided as comprised of a linear combination of the Fourier and Cattaneo processes respectively, the consequences leading to the Cattaneo heat-flux model and subsequently the Fourier heat-flux model for both macroscale/microscale heat transport are addressed. For macroscale and microscale heat transport, the relevance to the notion of the so-called macroscale and microscale heat conduction model number is then drawn. As such, a generalized one-step [GOS] macroscale heat conduction formulation of the Jeffreys' type with consequences to the hyperbolic one-step [HOS] and the parabolic one-step [POS] formulations are particularly addressed. In addition, for microscale heat transport employing a two-temperature theory, the role of a microscale heat conduction model number is described via a generalized two-step [GTS] relaxation/retardation time-based heating model for use in specialized applications with consequences to the hyperbolic and parabolic two-step HTS/PTS and the HOS/POS formulations respectively. Efforts to provide plausible characterization of the microscale heat conduction model number are undertaken for microscale heat conduction applications by comparisons to available experiments as related to sudden short laser pulse heating of thin films including identifying potential challenges. We define the macroscale/microscale heat conduction model number, F{sub}T and F{sub}(T{sub}e), respectively as: F{sub}T ≌ (Fourier Conductivity(k{sub}F))/(Fourier Conductivity(k{sub}F)+Cattaneo Conductivity(k{sub}C)) F{sub}(T{sub}e) ≌ (Electron Fourier Conductivity(k{sub}(e{sub}F)))/(Electron Fourier Conductivity(k{sub}(e{sub}F))+Electron Cattaneo Conductivity(k{sub}(e{sub}C))) Several noteworthy issues on heat conduction constitutive models are also highlighted. The pros/cons and limitations and a variety of deficiencies existing to date are also described and some of the conceptual pitfalls and issues encompass: (i) Pitfalls in attempting to explain microscale heat transport effects via macroscale heat conduction formulations. (ii) The issues of bounds for macroscale and microscale heat conduction. (iii) On pseudo time dimensional quantities. (iv) The pitfalls of dropping higher-order time derivative terms in the microscale heat transport equations under order-of-magnitude arguments. (v) On a conditional alias of the Jeffreys' type heat flux model provided underlying physics is not being violated.