The nonlinear inverse heat transfer problem is important in numerous scientific research and engineering applications. Considering the erosion-corrosion phenomenon of refractory brick walls in the melting furnace is a necessary research process for safe operation of the furnace. In this paper we present a nonlinear inverse heat transfer analysis approach for predicting wall erosion and time-varying thickness of the bank layer covering the inner surface of refractory brick walls of a melting furnace. The direct problem is a nonlinear one-dimensional mathematical model for the phase change process using the enthalpy method, which describes the concentrate melting process in the melting furnace. The numerical solution of this mathematical model uses finite difference method. In the nonlinear inverse heat transfer problem considered here, the time-varying heat flux and the thickness of the bank layer are unknown. We aim to determine these unknown parameters using temperature measurements obtained from the sensor. The inverse approach is based on the high-order modified Levenberg-Marquardt method (HMLMM) combined with the Broyden method. HMLMM combined with Broyden method can save a lot of Jacobian calculations and reduce the computational cost. Numerical results show that the proposed method is computationally more efficient than the inverse method in which the conventional Levenberg-Marquardt method (LMM) is used.
| Published in | Research and Innovation (Volume 2, Issue 2) |
| DOI | 10.11648/j.ri.20260202.18 |
| Page(s) | 183-195 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2026. Published by Science Publishing Group |
Inverse Heat Transfer, Inverse Problem, High-order Modified Levenberg-Marquardt Method
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APA Style
Yun, G., Ji, G., Choe, S., Ri, C. (2026). Nonlinear Inverse Heat Transfer Analysis in a Melting Furnace Using a High-order Modified Levenberg-Marquardt Method. Research and Innovation, 2(2), 183-195. https://doi.org/10.11648/j.ri.20260202.18
ACS Style
Yun, G.; Ji, G.; Choe, S.; Ri, C. Nonlinear Inverse Heat Transfer Analysis in a Melting Furnace Using a High-order Modified Levenberg-Marquardt Method. Res. Innovation 2026, 2(2), 183-195. doi: 10.11648/j.ri.20260202.18
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Download@article{10.11648/j.ri.20260202.18,
author = {Gwang-Ryong Yun and Guan-Gyu Ji and Song-Chol Choe and Chol Ri},
title = {Nonlinear Inverse Heat Transfer Analysis in a Melting Furnace Using a High-order Modified Levenberg-Marquardt Method},
journal = {Research and Innovation},
volume = {2},
number = {2},
pages = {183-195},
doi = {10.11648/j.ri.20260202.18},
url = {https://doi.org/10.11648/j.ri.20260202.18},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ri.20260202.18},
abstract = {The nonlinear inverse heat transfer problem is important in numerous scientific research and engineering applications. Considering the erosion-corrosion phenomenon of refractory brick walls in the melting furnace is a necessary research process for safe operation of the furnace. In this paper we present a nonlinear inverse heat transfer analysis approach for predicting wall erosion and time-varying thickness of the bank layer covering the inner surface of refractory brick walls of a melting furnace. The direct problem is a nonlinear one-dimensional mathematical model for the phase change process using the enthalpy method, which describes the concentrate melting process in the melting furnace. The numerical solution of this mathematical model uses finite difference method. In the nonlinear inverse heat transfer problem considered here, the time-varying heat flux and the thickness of the bank layer are unknown. We aim to determine these unknown parameters using temperature measurements obtained from the sensor. The inverse approach is based on the high-order modified Levenberg-Marquardt method (HMLMM) combined with the Broyden method. HMLMM combined with Broyden method can save a lot of Jacobian calculations and reduce the computational cost. Numerical results show that the proposed method is computationally more efficient than the inverse method in which the conventional Levenberg-Marquardt method (LMM) is used.},
year = {2026}
}
TY - JOUR T1 - Nonlinear Inverse Heat Transfer Analysis in a Melting Furnace Using a High-order Modified Levenberg-Marquardt Method AU - Gwang-Ryong Yun AU - Guan-Gyu Ji AU - Song-Chol Choe AU - Chol Ri Y1 - 2026/01/31 PY - 2026 N1 - https://doi.org/10.11648/j.ri.20260202.18 DO - 10.11648/j.ri.20260202.18 T2 - Research and Innovation JF - Research and Innovation JO - Research and Innovation SP - 183 EP - 195 PB - Science Publishing Group UR - https://doi.org/10.11648/j.ri.20260202.18 AB - The nonlinear inverse heat transfer problem is important in numerous scientific research and engineering applications. Considering the erosion-corrosion phenomenon of refractory brick walls in the melting furnace is a necessary research process for safe operation of the furnace. In this paper we present a nonlinear inverse heat transfer analysis approach for predicting wall erosion and time-varying thickness of the bank layer covering the inner surface of refractory brick walls of a melting furnace. The direct problem is a nonlinear one-dimensional mathematical model for the phase change process using the enthalpy method, which describes the concentrate melting process in the melting furnace. The numerical solution of this mathematical model uses finite difference method. In the nonlinear inverse heat transfer problem considered here, the time-varying heat flux and the thickness of the bank layer are unknown. We aim to determine these unknown parameters using temperature measurements obtained from the sensor. The inverse approach is based on the high-order modified Levenberg-Marquardt method (HMLMM) combined with the Broyden method. HMLMM combined with Broyden method can save a lot of Jacobian calculations and reduce the computational cost. Numerical results show that the proposed method is computationally more efficient than the inverse method in which the conventional Levenberg-Marquardt method (LMM) is used. VL - 2 IS - 2 ER -
Institute of Mathematics, State Academy of Sciences, Pyongyang, Democratic People’s Republic of Korea
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