热流边界下无限大平板的瞬态热传导分析

Analysis of Transient Heat Conduction of Infinite Flat Plate Subjected to Heat Flow Boundary

摘要: 实时了解和掌握飞行器周围的温度状况，对飞行器的安全运行至关重要。本文将受热流作用的飞行器视为一个受随时间变化热流边界条件的一维无限大平板，利用分离变量法对该问题进行了解析求解。由于该问题为求解边界条件为非齐次的定解问题，我们通过引入辅助函数将问题描述为齐次问题，并给出了具体的求解模式。最后，将理论分析结果与有限元模拟结果进行了比较，结果表明两种方法获得的计算结果基本一致。

Abstract: Understanding and grasping the temperature condition around aircraft in real time is critical for its safe operation. In this paper, the problem of an aircraft subjected to heat flow is regarded as a one-dimensional infinite plate with a time-varying heat flow boundary condition, and is solved analytically by the method of separation of variables. Since this is an inhomogeneous boundary-value problem, we describe the problem as homogeneous by introducing auxiliary functions, and give a specific solving method. Finally, the theoretical analysis results are compared with the finite element simulation results, and the results show that the calculation results obtained by the two methods are basically consistent.