Abstract
Manipulating thermal conductivities are fundamentally important for controlling the conduction of heat at will. Thermal cloaks and concentrators, which have been extensively studied recently, are actually graded materials designed according to coordinate transformation approaches, and their effective thermal conductivity can be seen to equal that of the host medium outside the cloak or concentrator. Here we attempt to investigate a more general problem: what is the effective thermal conductivity of graded materials? In particular, we perform a first-principles approach to the analytic exact results of effective thermal conductivities of materials possessing either power-law or linear gradation profiles. On the other hand, by solving Laplace’s equation, we derive a differential equation for calculating the effective thermal conductivity of a material whose thermal conductivity varies along the radius with arbitrary gradation profiles. The two methods agree well with each other for both external and internal heat sources, as confirmed by simulations and experiments. This chapter provides different methods for designing new thermal metamaterials (including thermal cloaks and concentrators), in order to control or manipulate the transfer of heat
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Huang, JP. (2020). Heat Conduction Equation. In: Theoretical Thermotics. Springer, Singapore. https://doi.org/10.1007/978-981-15-2301-4_7
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DOI: https://doi.org/10.1007/978-981-15-2301-4_7
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