基于导热传递函数的球壳体动态导热特性研究

为分析球壳体导热系统的动态导热特性，推导了其导热传递函数的表达式.通过建立球壳体导热系统在球面坐标下的一维物理模型，用拉普拉斯变换法求解了描述其非稳态导热过程的微分方程，并推导出了球壳体的导热传递函数.在不同的边界条件下对球壳体导热传递函数的具体表达式进行了讨论.通过导热传递函数求得了一个具体球壳体系统温度输出与温度激励的振幅比和相位差的表达式，并由此分析了该系统振幅比和相位差随半径以及温度激励频率的变化规律.计算结果表明，利用导热传递函数可以全面表征球壳体的动态导热特性，并为此类导热问题及其反问题的分析和求解提供了新的思路

Study on dynamic characters of global shell using heat conduction transfer functions

To study the dynamic heat conduction characters, the heat conduction transfer functions of the global shell heat conduction system were studied. A one-dimensional physical model of the global shell heat conduction system was established in the spherical coordinate system. The differential equation that describes the unsteady heat conduction process in the global shell was solved using Laplace transformation, and the heat conduction transfer function was obtained. The specific expressions of the function were discussed respectively under different boundary conditions. The formulas of amplitude ratio and phase difference between temperature output and temperature input of the global shell heat conduction system were achieved using heat conduction transfer function, and the variance tendencies of amplitude ratio and phase difference versus radius and frequency were analyzed. The result shows that the transfer function can be used to well describe the dynamic heat conduction characters of the global shell system, and to solve the global shell heat conduction problems and their inverse problems.