To read this content please select one of the options below:

An efficient method for transient heat conduction problems with local nonlinearities based on the quasi-superposition principle

Chuanbao Nie (Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, China)
Bowen Fu (Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, China)
Qiang Gao (Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, China)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 14 July 2022

Issue publication date: 3 January 2023

61

Abstract

Purpose

This paper aims to develop an efficient numerical method for nonlinear transient heat conduction problems with local radiation boundary conditions and nonlinear heat sources.

Design/methodology/approach

Based on the physical characteristic of the transient heat conduction and the distribution characteristic of the Green’s function, a quasi-superposition principle is presented for the transient heat conduction problems with local nonlinearities. Then, an efficient method is developed, which indicates that the solution of the original nonlinear problem can be derived by solving some nonlinear problems with small structures and a linear problem with the original structure. These problems are independent of each other and can be solved simultaneously by the parallel computing technique.

Findings

Within a small time step, the nonlinear thermal loads can only induce significant temperature responses of the regions near the positions of the nonlinear thermal loads, whereas the temperature responses of the remaining regions are very close to zero. According to the above physical characteristic, the original nonlinear problem can be transformed into some nonlinear problems with small structures and a linear problem with the original structure.

Originality/value

An efficient and accurate numerical method is presented for transient heat conduction problems with local nonlinearities, and some numerical examples demonstrate the high efficiency and accuracy of the proposed method.

Keywords

Acknowledgements

The authors are grateful for the financial support of the Natural Science Foundation of China (No. 11972107, 91748203) and the Fundamental Research Funds for the Central Universities (DUT2019TD37).

Citation

Nie, C., Fu, B. and Gao, Q. (2023), "An efficient method for transient heat conduction problems with local nonlinearities based on the quasi-superposition principle", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 33 No. 1, pp. 385-410. https://doi.org/10.1108/HFF-02-2022-0087

Publisher

:

Emerald Publishing Limited

Copyright © 2022, Emerald Publishing Limited

Related articles