Some noteworthy and historical perspectives and an overview of macroscale and microscale heat transport behavior in materials and structures are presented. The topic of heat waves is also discussed. The significance 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 Jeffreys type heat flux constitutive model, with consequences to the Cattaneo heat flux model and subsequently to the Fourier heat flux model. Both macroscopic model formulations for applications to macroscopic heat conduction problems and two-step models for use in specialized applications to account for microscale heat transport mechanisms are overviewed with emphasis on the proposition of a Generalized Two-Step 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.
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The first author is pleased to acknowledge the contributions of several former graduate research students and colleagues. In particular, the contributions of Drs. S. B. Railkar and R. R. Namburu and D. E. Glass are duly acknowledged. Special acknowledgment is due to Professors D. D. Joseph and E. M. Sparrow for various relevant technical discussions. Support in part, from the U.S. Army Research Office (ARO) and Battelle, Research Triangle Park, North Carolina, under grants DAAH04-96-0172 and DAAH05-96-C-0086 are gratefully acknowledged. Special thanks are also due to Dr. Andrew Mark, Mr. Bill Mermagen Sr., and Mr. C. Nietubicz of the U.S. Army Research Laboratory, the IMT, and the ARL/MSRC technical activities and facilities. Additional support in the form of computer grants from the Minnesota Supercomputer Institute (MSI), University of Minnesota are also acknowledged.