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

## TL;DR

This paper investigates the hyperbolic heat transfer equation in an ablation context, providing an analytic solution, experimental measurements of thermal relaxation time, and emphasizing the importance of hyperbolic modeling over parabolic equations in electrocardiology ablation.

## Contribution

It offers a new analytic solution for the hyperbolic heat equation in ablation, with experimental validation and implications for medical applications.

## Key findings

- Thermal relaxation time τ is about 7 minutes for 0.5% NaCl in water.
- Hyperbolic heat equation is necessary over parabolic models in ablation.
- Analytic solution shows approach to steady state in ablation process.

## 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.