关键词: 非稳态导热, 分析解, 特征函数, 正交性

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