非稳态导热问题分析解特征函数正交性的讨论

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

非稳态导热问题分析解是传热学中十分重要的内容之一,多数传热学教材对特征函数正交性的论述较为简略,影响了对求解过程的理解.本文以大平板非稳态导热问题分析解求解过程为例,重点讨论了特征函数正交性的含义、特征函数正交性的证明以及特征函数正交性的应用,给出了保持求解过程连贯、帮助学生理解的教学建议,为非稳态导热问题分析解及其数学解析过程的教学提供了参考.

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.