Local Non-Equilibrium Heat Transfer in an Anisotropic Half-Space Affected by a Non-Steady State Point Heat Source

The study applies a new analytical solution to investigating a local thermal non-equilibrium occurring when wave heat transfer takes place in the vicinity of spacetime boundaries of an anisotropic half-space affected by a time-dependent point heat source. The time delay between the heat flow and the temperature gradient, which is equal to the relaxation time, causes the local non-equilibrium. It may be clearly observed in the vicinity of the boundaries when the time is short and thus comparable to the relaxation time. We show how the non-steady-state temperature field initially forms; considerably differing from that in the cases when there is no relaxation time, both quantitatively and qualitatively. Specifically, at the boundaries of moving fronts the temperature field undergoes discontinuities of the first kind, characteristic of the wave heat transfer. These discontinuity magnitudes tend towards zero over time; however, the second derivatives of the temperature profile with respect to spacelike variables are not continuous anyway. We analyse new numerical results. The paper is pertinent in the field of fast processes of relativistic mechanics

The study was supported by a Russian Science Foundation (grant no. 16-19-10340)

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