Rapid solidification and a finite velocity for the propagation of heat

The Fourier thermal conduction model is subject to a pathological anomaly in that it predicts an infinite velocity of propagation for heat. A finite propagation velocity can be introduced by adding a hyperbolic relaxation term to the conventional model. We show that in high-speed pulsed laser melting experiments, ignoring the hyperbolic nature of thermal conduction may lead to the surface temperature being seriously underestimated. We also develop a model of dendritic growth within a hyperbolic conduction framework. It is found that stable dendritic growth is only possible if the growth velocity is less than half the thermal wave velocity, C.