Determination of two homogeneous materials in a bar with solid-solid interface

GUILLERMO FEDERICO UMBRICHT; DOMINGO ALBERTO TARZIA; DIANA RUBIO

Mathematical Modelling of Engineering Problems

International Information and Engineering Technology Association

Año: 2022

2369-0739

The objective of the work is to identify two unknown materials that compose a bar withinterface solid-solid. The thermal conductivity of each material is determined based onsimulated noisy data from a stationary heat transfer process along the bar, that isassumed to be fully insulated on its lateral surface. At the left boundary, a Dirichletcondition is imposed that represents a source of constant temperature. At the other endof the bar, a Robin condition that models heat dissipation by convection, is assumed.The thermal conductivity coefficients of both solids are determined under two differentsituations: a) two noisy temperature measurements, one at the interface and the other atthe right boundary; b) a temperature measurement at the interface and a heat flowmeasurement at the right edge of the bar. The bounds for the errors in the identificationof the unknown coefficients are obtained based on the data measurements, the roomtemperature and temperature values at the boundary and interface. Numerical examplesare given to illustrate the ideas used for the parameter identification and elasticityanalysis is carried out to measure the dependence of the data on the estimatedparameters.