Relativistic heat conduction
Relativistic heat conduction refers to the modelling of heat conduction (and similar diffusion processes) in a way compatible with special relativity. This article discusses models using a wave equation with a dissipative term.
Ali and Zhang claim their model of relativistic heat conduction is the only one compatible with the theory of special relativity, the second law of thermodynamics, electrodynamics, and quantum mechanics, simultaneously. The main features of their model are:
These outcomes are achieved by (1) upgrading the Fourier equation of heat conduction to the form of a Telegraph equation of electrodynamics, and (2) introducing a new definition of the heat flux vector. Consequently, their model gives rise to a number of phenomena, such as thermal resonance and thermal shock waves, which are possible during high-frequency pulsed laser heating of thermal insulators.
For most of the last two centuries, heat conduction has been modelled by the well-known Fourier equation:
where θ is temperature,t is time, α = k/(ρ c) is thermal diffusivity, k is thermal conductivity, ρ is density, and c is specific heat capacity. The Laplace operator,, is defined in Cartesian coordinates as
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