Estimaci\'on y An\'alisis de Sensibilidad para el Coeficiente de Difusividad en un Problema de Conducci\'on de Calor

TL;DR

This paper focuses on estimating the thermal diffusivity coefficient of a homogeneous metal rod using temperature measurements over time, employing inverse problem techniques and analyzing sensitivity to improve accuracy.

Contribution

It introduces a method for estimating diffusivity in heat conduction problems and analyzes the sensitivity of temperature to this coefficient using numerical and analytical approaches.

Findings

Numerical experiments achieved high accuracy in diffusivity estimates.

Sensitivity analysis provided insights into the influence of diffusivity on temperature.

Finite difference scheme effectively discretized the heat conduction problem.

Abstract

The aim of this article is to discuss the estimation of the diffusivity coefficient of a homogeneous metal rod from temperature values at a fixed point in the bar for different time instants. The time-dependent problem of heat conduction is analyzed in an insulated conductor wire of length l considering constant boundary conditions. The problem is modeled by a parabolic partial differential equation, imposing Dirichlet boundary conditions. We consider simulated temperature values at a point of the bar for different time instants and estimate the coefficient of diffusivity using usual techniques for solving inverse problems. For the discretization of the equation we consider a finite difference centered scheme. We include an analytical and numerical study of the sensitivity of the temperature function with respect to the coefficient of diffusivity. Numerical experiments show very good accuracy in the estimates.