University of Oulu

Ilpo Mäkelä, Ville-Valtteri Visuri & Timo Fabritius (2023) A mathematical model for the thermal state of a steel ladle, Ironmaking & Steelmaking, 50:7, 867-877, DOI: 10.1080/03019233.2023.2201544

A mathematical model for the thermal state of a steel ladle

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Author: Mäkelä, Ilpo1; Visuri, Ville-Valtteri1; Fabritius, Timo1
Organizations: 1Process Metallurgy Research Unit, University of Oulu, Oulu, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 2.4 MB)
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Language: English
Published: Informa, 2023
Publish Date: 2023-09-07


A dynamic one-dimensional mathematical model was developed for predicting the thermal state of a steelmaking ladle. The model is intended to be used in process control applications, in which fast computational times are desirable alongside model accuracy. The calculation domain was discretized using the finite difference method, and time integration was performed using both the implicit Euler and Crank–Nicolson methods, the performances of which were compared. The model was implemented in Python programming language and validated using data from our own measurements and other studies available in the literature. The results indicate that the model can reproduce the measured temperature evolution of the ladles within 5°C at best. The worst performance was observed during cooling, where the model underestimates the temperature at the innermost measurement point by up to 200°C. With computation times of around 16–23 s for one hour of simulation, the model is computationally sufficiently fast for online applications.

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Series: Ironmaking & steelmaking
ISSN: 0301-9233
ISSN-E: 1743-2812
ISSN-L: 0301-9233
Volume: 50
Issue: 7
Pages: 867 - 877
DOI: 10.1080/03019233.2023.2201544
Type of Publication: A1 Journal article – refereed
Field of Science: 213 Electronic, automation and communications engineering, electronics
222 Other engineering and technologies
Funding: This work was supported by Business Finland under grant number [41700/31/2020].
Copyright information: © 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use,distribution, and reproduction in any medium, provided the original work is properly cited. The terms on which this article has been published allow the posting of the Accepted Manuscript in a repository by the author(s) or with their consent.