Estimation Technique for a Contact Point Between two Materials in a Stationary Heat Transfer Problem

TL;DR

This paper introduces a novel method to estimate the unknown contact point between two materials in a stationary heat transfer problem using boundary measurements, with analysis of accuracy and error influence.

Contribution

A new technique for estimating the interface location between two materials in a heat transfer problem from boundary data is proposed and validated.

Findings

The method accurately estimates the interface point from noisy boundary measurements.

Necessary and sufficient conditions for the estimation are derived.

Error analysis shows robustness of the approach under data noise.

Abstract

An inverse problem for a stationary heat transfer process is studied for a totally isolated bar on its lateral surface, of negligible diameter, made up of two consecutive sections of different, isotropic and homogeneous materials. At the left boundary, a Dirichlet type condition is imposed that represents a constant temperature source while a Robin type condition that models the heat dissipation by convection is considered at the right one. Many articles in the literature focus on thermal and stress analysis at the interface but no one is dedicated to the estimation of the contact point location between the two materials. In this work, it is assumed that the interface position is unknown. A technique to determine it from a unique noisy flow measurement at the right boundary is introduced. Necessary and sufficient conditions are derived in order to obtain the estimation of the interface point from a heat flux measured at the right boundary. Numerical solutions are obtained together with an expression for the estimation error. Moreover, an elasticity analysis is included to study the influence of data errors. The results show that our approach is useful for determining the location of the materials interface.