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在柱坐标系下,以热传导方程及边界条件为基础,通过Hankel变换及逆变换,得到多层热单介质膜中的温度场.以特殊参数为例,对膜层为三层时的特殊情况进行讨论,得知对于高热扩散率的薄膜材料,纵向和横向的热导率比值越大,相位的变化也越大.低热扩散率薄膜材料,不同的纵向和横向的热导率比对光热信号的影响很小.同时,光吸收系数越小,频率变化对相位影响越明显.
Based on the heat conduction equation and the boundary conditions, the temperature field in the multi-layer thermal single medium is obtained by Hankel transform and inverse transform in the cylindrical coordinate system. Taking the special parameters as an example, The results show that for the high thermal diffusivity film materials, the larger the ratio of thermal conductivity in the longitudinal and transverse directions, the greater the change in phase. Low thermal diffusivity Thin film materials, with different longitudinal and transverse thermal conductivities, The influence of the signal is small.At the same time, the smaller the light absorption coefficient, the more obvious the influence of the frequency change on the phase.