## Details

Original language | English |
---|---|

Pages (from-to) | 41-61 |

Number of pages | 21 |

Journal | Computers and Mathematics with Applications |

Volume | 148 |

Early online date | 18 Aug 2023 |

Publication status | Published - 15 Oct 2023 |

## Abstract

In the present work, we developed the Neural Networks (NNs) for identifying unknown surface shape of inner wall in the two-dimensional pipeline based on the temperature at uniformly distributed measuring points. The steady-state governing equation is transformed into the anisotropic heat conduction equations, and the irregularly shaped inner boundary is identified by the estimation of circumferential distribution of the effective thermal conductivity of the furnace. After the unhomogenized technique for the effective thermal conductivity model, the meshless generalized finite difference method on a radial is derived to effectively solve the direct problem for training data. The NNs are introduced to calculate the effective thermal conductivity for further detection of unknown internal boundary. Several numerical examples are provided to demonstrate the efficiency and accuracy of the proposed solver.

## Keywords

- Effective thermal conductivity, Internal boundary detection, Inverse heat conduction problem, Neural network, Polar coordinate based generalized finite difference method

## ASJC Scopus subject areas

- Mathematics(all)
**Modelling and Simulation**- Computer Science(all)
**Computational Theory and Mathematics**- Mathematics(all)
**Computational Mathematics**

## Cite this

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**A machine learning approach coupled with polar coordinate based localized collocation method for inner surface identification in heat conduction problem.**/ Chu, Wen Hui; Fu, Zhuo Jia; Tang, Zhuo Chao et al.

In: Computers and Mathematics with Applications, Vol. 148, 15.10.2023, p. 41-61.

Research output: Contribution to journal › Article › Research › peer review

*Computers and Mathematics with Applications*, vol. 148, pp. 41-61. https://doi.org/10.1016/j.camwa.2023.07.031

*Computers and Mathematics with Applications*,

*148*, 41-61. https://doi.org/10.1016/j.camwa.2023.07.031

}

TY - JOUR

T1 - A machine learning approach coupled with polar coordinate based localized collocation method for inner surface identification in heat conduction problem

AU - Chu, Wen Hui

AU - Fu, Zhuo Jia

AU - Tang, Zhuo Chao

AU - Xu, Wen Zhi

AU - Zhuang, Xiao Ying

N1 - Funding Information: The work described in this paper was supported by the National Science Fund of China (Grant No. 12122205 ) and the Six Talent Peaks Project in Jiangsu Province of China (Grant No. 2019-KTHY-009 ).

PY - 2023/10/15

Y1 - 2023/10/15

N2 - In the present work, we developed the Neural Networks (NNs) for identifying unknown surface shape of inner wall in the two-dimensional pipeline based on the temperature at uniformly distributed measuring points. The steady-state governing equation is transformed into the anisotropic heat conduction equations, and the irregularly shaped inner boundary is identified by the estimation of circumferential distribution of the effective thermal conductivity of the furnace. After the unhomogenized technique for the effective thermal conductivity model, the meshless generalized finite difference method on a radial is derived to effectively solve the direct problem for training data. The NNs are introduced to calculate the effective thermal conductivity for further detection of unknown internal boundary. Several numerical examples are provided to demonstrate the efficiency and accuracy of the proposed solver.

AB - In the present work, we developed the Neural Networks (NNs) for identifying unknown surface shape of inner wall in the two-dimensional pipeline based on the temperature at uniformly distributed measuring points. The steady-state governing equation is transformed into the anisotropic heat conduction equations, and the irregularly shaped inner boundary is identified by the estimation of circumferential distribution of the effective thermal conductivity of the furnace. After the unhomogenized technique for the effective thermal conductivity model, the meshless generalized finite difference method on a radial is derived to effectively solve the direct problem for training data. The NNs are introduced to calculate the effective thermal conductivity for further detection of unknown internal boundary. Several numerical examples are provided to demonstrate the efficiency and accuracy of the proposed solver.

KW - Effective thermal conductivity

KW - Internal boundary detection

KW - Inverse heat conduction problem

KW - Neural network

KW - Polar coordinate based generalized finite difference method

UR - http://www.scopus.com/inward/record.url?scp=85168091698&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2023.07.031

DO - 10.1016/j.camwa.2023.07.031

M3 - Article

AN - SCOPUS:85168091698

VL - 148

SP - 41

EP - 61

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

ER -