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Relativistic heat conduction refers to the modelling of heat conduction in a way compatible with special relativity. This article discusses models using a wave equation with a dissipative term.
Heat conduction in a Newtonian context is modelled by the Fourier equation:
where θ is temperature, t is time, α = k/ is thermal diffusivity, k is thermal conductivity, ρ is density, and c is specific heat capacity. The Laplace operator, ∇ 2 {\displaystyle \scriptstyle \nabla ^{2}} , is defined in Cartesian coordinates as
This Fourier equation can be derived by substituting Fourier’s linear approximation of the heat flux vector, q, as a function of temperature gradient,
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