Unique Reconstruction of the Heat-Reflection Indices at Solid Interfaces

TL;DR

This paper proves that heat-reflection coefficients at solid interfaces can be uniquely determined from surface temperature measurements, advancing the mathematical understanding of phonon-based heat transfer models.

Contribution

It provides a rigorous mathematical proof for the unique reconstruction of heat-reflection indices from experimental surface temperature data.

Findings

Unique reconstruction of heat-reflection coefficients established

Mathematical model applied to multilayer media including metals and silicon

Supports experimental inference of interface heat properties

Abstract

We show the unique reconstruction of the heat-reflection coefficients in a phonon transport equation. This is a mathematical model used to characterize the dynamics of heat-conducting phonons in multiple layers of media, commonly composed of metals and silicon. In experiments, the heat-reflection indices are inferred by measuring the temperature at the surface of the exterior metal after applying heat sources. In this article, we rigorously justify the unique reconstruction of these indices by using such procedures.