# Detection of time-varying heat sources using an analytic forward model

## TL;DR

This paper introduces an analytic model for detecting static and dynamic heat sources by solving the 3D heat equation, with algorithms tested via simulations, applicable in material testing and medical imaging.

## Contribution

It provides a novel simple analytic point source model for time-varying heat sources and algorithms for source detection and spectral analysis.

## Key findings

- Algorithms successfully detect source location and spectral content.
- Numerical tests demonstrate the model's effectiveness.
- Framework shows promise for practical inverse heat source problems.

## Abstract

We present a simple, analytic point source model for both static and time-varying point-like heat sources and the resulting temperature profile that solves the heat equation in dimension three. Simple algorithms to detect the location and spectral content of these sources are developed and numerically tested using Finite Element Mesh simulations. The resulting framework for heat source reconstruction problems, which are ill-posed inverse problems, seems promising and warrants for future research. Possible fields of application for our work are material testing, to detect manufacturing defects, and medical imaging to detect abnormal health conditions.