MATHEMATICAL THEORY OF THERMAL INERTIA REVISITED 2: APPLICATION OF HYPERBOLIC HEAT DIFFUSION THEORY TO REALIZE RELATIVISTIC THERMAL INERTIA.

English Abstract:

Thermal inertia is an important parameter for inferring thermophysical properties of planetary surfaces from orbit [1,2]. It is defined as the square root of the thermal conductivity, density, and heat capacity. We revisited its derivation to propose analogous periodic diffusive inertia terms for similar mathematical scenarios [3]. Thermal conductivity (k) is analogous to electrical conductivity (σ or inverse resistance 1/R); thermal heat capacity (c) is analogous to electrical capacitance (C). We then wondered what is the thermal equivalent to electrical inductance (L), and what is its significance for planetary science?

We apply hyperbolic heat diffusion theory to derive a new equation for the periodic heat flux through a planetary surface [4-6]. As a hyperbolic heat equation, the heat transfer is treated as a propagating wave with a finite speed rather than an instantaneous effect using Fourier’s Law. In doing this, a relativistic thermal inertia is realized that accounts for the finite propagation speed of heat. Finally, we determine that the relativistic thermal inertia is theoretically insignificant on diurnal timescales for planetary bodies.

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