Transformation Thermotics and Effective Medium Theory for Thermal Conduction

Abstract

AbstractIn this Chapter, we embark on an exploration of the intricacies of heat conduction, primarily delving into the transformation thermotics and the effective medium theory. Beginning with the foundational Fourier’s law of heat conduction, an intriguing observation is the form invariance of the associated equations under arbitrary coordinate transformations. This symmetry elucidates a novel method for orchestrating the temperature field and heat flux dynamics. To illustrate the practical implications and operationalizability of the thermal transformation, we conceptualized and implemented a thermal cloak. It should be noted, however, that the parameters projected theoretically often manifest as inhomogeneous and anisotropic, posing considerable challenges for tangible synthesis. A viable approach to circumnavigate these challenges is to pivot the focus towards the thermally effective medium theory. In the ensuing sections, we will delve into a systematic exposition of the effective medium theory, subsequently crafting functional structures illuminated by three distinct frameworks: linear theory, wherein the thermal conductivity remains unaffected by temperature variations, nonlinear theory, and the theory of heat sources.