New analytic solutions to 2D transient heat conduction problems with/without heat sources in the symplectic space

doi:10.1007/s10483-022-2891-6

Applied Mathematics and Mechanics (English Edition) ›› 2022, Vol. 43 ›› Issue (8): 1233-1248.doi: https://doi.org/10.1007/s10483-022-2891-6

New analytic solutions to 2D transient heat conduction problems with/without heat sources in the symplectic space

Dian XU, Xinran ZHENG, Dongqi AN, Chao ZHOU, Xiuwen HUANG, Rui LI

State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, and International Research Center for Computational Mechanics, Dalian University of Technology, Dalian 116024, Liaoning Province, China

收稿日期:2022-02-12 修回日期:2022-06-06 发布日期:2022-07-27
通讯作者: Rui LI, E-mail: ruili@dlut.edu.cn
基金资助:
the National Natural Science Foundation of China (Nos. 12022209, 11972103, and U21A20429) and the Fundamental Research Funds for the Central Universities of China (No. DUT21LAB124)

New analytic solutions to 2D transient heat conduction problems with/without heat sources in the symplectic space

Dian XU, Xinran ZHENG, Dongqi AN, Chao ZHOU, Xiuwen HUANG, Rui LI

State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, and International Research Center for Computational Mechanics, Dalian University of Technology, Dalian 116024, Liaoning Province, China

Received:2022-02-12 Revised:2022-06-06 Published:2022-07-27
Contact: Rui LI, E-mail: ruili@dlut.edu.cn
Supported by:
the National Natural Science Foundation of China (Nos. 12022209, 11972103, and U21A20429) and the Fundamental Research Funds for the Central Universities of China (No. DUT21LAB124)

摘要/Abstract

摘要： The two-dimensional (2D) transient heat conduction problems with/without heat sources in a rectangular domain under different combinations of temperature and heat flux boundary conditions are studied by a novel symplectic superposition method (SSM). The solution process is within the Hamiltonian system framework such that the mathematical procedures in the symplectic space can be implemented, which provides an exceptional direct rigorous derivation without any assumptions or predetermination of the solution forms compared with the conventional inverse/semi-inverse methods. The distinctive advantage of the SSM offers an access to new analytic heat conduction solutions. The results obtained by the SSM agree well with those obtained from the finite element method (FEM), which confirms the accuracy of the SSM.

关键词: heat conduction, heat source, symplectic superposition method (SSM)

Abstract: The two-dimensional (2D) transient heat conduction problems with/without heat sources in a rectangular domain under different combinations of temperature and heat flux boundary conditions are studied by a novel symplectic superposition method (SSM). The solution process is within the Hamiltonian system framework such that the mathematical procedures in the symplectic space can be implemented, which provides an exceptional direct rigorous derivation without any assumptions or predetermination of the solution forms compared with the conventional inverse/semi-inverse methods. The distinctive advantage of the SSM offers an access to new analytic heat conduction solutions. The results obtained by the SSM agree well with those obtained from the finite element method (FEM), which confirms the accuracy of the SSM.

Key words: heat conduction, heat source, symplectic superposition method (SSM)

中图分类号:

Dian XU, Xinran ZHENG, Dongqi AN, Chao ZHOU, Xiuwen HUANG, Rui LI. New analytic solutions to 2D transient heat conduction problems with/without heat sources in the symplectic space[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(8): 1233-1248.

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New analytic solutions to 2D transient heat conduction problems with/without heat sources in the symplectic space

New analytic solutions to 2D transient heat conduction problems with/without heat sources in the symplectic space

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