Macroscale and Microscale Thermal Transport and Thermo-mechanical Interactions: Some Noteworthy Perspectives

Some noteworthy and historical perspectives and overview of macroscale and microscale heat transport behavior in materials and structures are presented. The topic of heat waves is also discussed. The signiicance of constitutive models for both macroscale and microscale heat conduction are described in conjunction with generalizations drawn concerning the physical relevance and the role of relaxation and retardation times emanating from the Jeereys type heat ux constitutive model, with consequences to the Cattaneo heat ux model and subsequently to the Fourier heat ux model. Both macroscopic model formulations for applications to macroscopic heat conduction problems and two-step models for use in specialized applications in order to account for microscale heat transport mechanisms are overviewed with emphasis on the proposition of a Generalized Two-Step (GTS) relaxation/retardation time based heating model. So as to bring forth a variety of issues in a single forum, illustrative numerical applications are overviewed including some relevance to thermo-mechanical interactions. Overview For most engineering applications, the heat conduction phenomenon is described by Fourier's law which is based on phenomenological models. Originally observed experimentally by Biot and derived and named after Fourier 1], it is based on the continuum assumption of the material and from a macroscopic continuum sense. The mechanisms of conduction, from a sense of microscopic scales, however consider the heat transfer by molecular motion to include transport by heat carriers free electrons and vibration of lattices (phonons)] with diiusion in the medium from a high temperature region to a low temperature region. Since the mechanisms of transport by heat conduction deals with random movement of a large number of such heat carriers, during a nite time period t== O(1)], the statistical movement of the individual heat carriers has been mostly considered to not signii-cantly eeect the heat conduction phenomenon at temperatures higher than the Debye temperature. Traditionally, for the purpose of most practical engineering applications, from a macroscopic sense, a continuum assumption was made to rule out the heat carriers' movement from the conduction equation. This assumption neglects the micro-structure and scales of the media and assumes the media to be a continuous continuum thus restricting the theory to deal with only macroscopic information. The Fourier's law was derived under this so-called phenomenological approach. As such, it is quite reasonable to consider its validity for the regimes: L O(1) (1) t O(1) (2)