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An efficient and accurate method for transient heat conduction in a periodic structure with moving heat sources

Haichao Cui (Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, International Center for Computational Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian, China)
Qiang Gao (Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, International Center for Computational Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian, China)
Xiaolan Li (Department of Engineering Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, International Center for Computational Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian, China)
Huajiang Ouyang (School of Engineering, University of Liverpool, Liverpool, UK)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 13 February 2020

Issue publication date: 24 February 2020

Abstract

Purpose

This paper aims to propose an efficient and accurate method to analyse the transient heat conduction in a periodic structure with moving heat sources.

Design/methodology/approach

The moving heat source is modelled as a localised Gaussian distribution in space. Based on the spatial distribution, the physical feature of transient heat conduction and the periodic property of structure, a special feature of temperature responses caused by the moving heat source is illustrated. Then, combined with the superposition principle of linear system, within a small time-step, computation of results corresponding to the whole structure excited by the Gaussian heat source is transformed into that of some small-scale structures. Lastly, the precise integration method (PIM) is used to solve the temperature responses of each small-scale structure efficiently and accurately.

Findings

Within a reasonable time-step, the heat source applied on a unit cell can only cause the temperature responses of a limited number of adjacent unit cells. According to the above feature and the periodic property of a structure, the contributions caused by the moving heat source for the most of time-steps are repeatable, and the temperature responses of the entire periodic structure can be obtained by some small-scale structures.

Originality/value

A novel numerical method is proposed for analysing moving heat source problems, and the numerical examples demonstrate that the proposed method is much more efficient than the traditional methods, even for larger-scale problems and multiple moving heat source problems.

Keywords

Acknowledgements

The authors would like to thank the editor and three anonymous reviewers for their valuable comments and suggestions, which have helped improve the overall quality of the paper. The authors are grateful for the financial support of the Natural Science Foundation of China (No. 11572076). The first author would like to acknowledge the support from the China Scholarship Council (CSC) that sponsors his visit to the University of Liverpool where much of the work in this paper is conducted.

Citation

Cui, H., Gao, Q., Li, X. and Ouyang, H. (2020), "An efficient and accurate method for transient heat conduction in a periodic structure with moving heat sources", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 30 No. 3, pp. 1318-1344. https://doi.org/10.1108/HFF-06-2019-0495

Publisher

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Emerald Publishing Limited

Copyright © 2019, Emerald Publishing Limited