# Numerical identification of temperature dependent thermal conductivity using least squares method

Anna Ivanova (Institute of Applied Mathematics and Mechanics, Donetsk, Ukraine)
Stanislaw Migorski (Faculty of Mathematics and Computer Science, Jagiellonian University, Krakow, Poland)
Rafal Wyczolkowski (Institute of Production Management, Czestochowa University of Technology, Czestochowa, Poland)
Dmitry Ivanov (Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Sloviansk, Ukraine)

ISSN: 0961-5539

Article publication date: 19 July 2019

Issue publication date: 22 May 2020

## Abstract

### Purpose

This paper aims to considered the problem of identification of temperature-dependent thermal conductivity in the nonstationary, nonlinear heat equation. To describe the heat transfer in the furnace charge occupied by a homogeneous porous material, the heat equation is formulated. The inverse problem consists in finding the heat conductivity parameter, which depends on the temperature, from the measurements of the temperature in fixed points of the material.

### Design/methodology/approach

A numerical method based on the finite-difference scheme and the least squares approach for numerical solution of the direct and inverse problems has been recently developed.

### Findings

The influence of different numerical scheme parameters on the accuracy of the identified conductivity coefficient is studied. The results of the experiment carried out on real measurements are presented. Their results confirm the ones obtained earlier by using other methods.

### Originality/value

Novelty is in a new, easy way to identify thermal conductivity by known temperature measurements. This method is based on special finite-difference scheme, which gives a resolvable system of algebraic equations. The results sensitivity on changes in the method parameters was studies. The algorithms of identification in the case of a purely mathematical experiment and in the case of real measurements, their differences and the practical details are presented.

## Citation

Ivanova, A., Migorski, S., Wyczolkowski, R. and Ivanov, D. (2020), "Numerical identification of temperature dependent thermal conductivity using least squares method", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 30 No. 6, pp. 3083-3099. https://doi.org/10.1108/HFF-10-2018-0589

## Publisher

:

Emerald Publishing Limited