The hyperbolic heat transfer equation and the ablation problem: Theory and experiment

Abstract

We study the ablation problem for the hyperbolic heat equation in an axisymmetrical geometry which can be conveniently realized in the lab. We determine an analytic solution which shows the approach to steady state. The thermal relaxation time $\tau$ is best obtained from the small time behavior. The measurements give a surprisingly large $\tau$ of about 7 minutes for 0.5 % NaCl in water. This shows that the hyperbolic equation must certainly be used instead of the parabolic heat equation in the ablation problem of electrocardiology.