非稳态导热问题分析解特征函数正交性的讨论

doi:10.16854/j.cnki.1000-0712.230085

College Physics ›› 2024, Vol. 43 ›› Issue (02): 8-.doi: 10.16854/j.cnki.1000-0712.230085

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Discussion on eigenfunction orthogonality for analytical solution of unsteady heat conduction problem

JIN Wan-long1, SHI Wan-yuan2, CHE De-fu1

1. School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China;
2. School of Energy and Power Engineering, Chongqing University, Chongqing 400044, China

Received:2023-03-19 Revised:2023-05-08 Online:2024-03-14 Published:2024-03-22

Abstract

Abstract: The analytical solution of the unsteady heat conduction problem is one of the critical contents of heat transfer. However, the explanations of eigenfunction orthogonality in most heat transfer textbooks are relatively simple, which hinders the understanding of solving process. Taking the analytical solution procedure of the large plane wall unsteady heat conduction problem for example, the meaning of eigenfunction orthogonality, the proof of eigenfunction orthogonality and the application of eigenfunction orthogonality were discussed emphatically. Several teaching suggestions for keeping the solution process coherent and helping students understand were given. It provides a reference for the teaching of the analytical solution and mathematical analysis of the unsteady heat conduction problem.

Key words: unsteady heat conduction, analytical solution, eigenfunction, orthogonality

JIN Wan-long1, SHI Wan-yuan2, CHE De-fu1. Discussion on eigenfunction orthogonality for analytical solution of unsteady heat conduction problem[J].College Physics, 2024, 43(02): 8-.

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Discussion on eigenfunction orthogonality for analytical solution of unsteady heat conduction problem

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