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从声子散射模型出发,用拉普拉斯变换法得到三层一维非金属薄膜在简谐温度边界条件下温度响应的解。通过算例分析,讨论了在微尺度条件下非金属薄膜的热响应特征。计算表明,热响应温度和热传播速度随特征参数E的变化而变化。在薄膜中不同位置处,当E<0.1时,波动特性明显,最高响应温度在波的传播方向上先减小后增大;当E>0.1时,最高响应温度持续减小。当E取较大值时,热传播速度也较大,达到最大响应温度的热响应时间几乎相同。而在薄膜后表面,热传播速度随E的增大而增大。另外,当E<0.25,最大热扰动响应温度随E的增大而减小;当E>0.25时,最大热扰动响应温度随E的增大而增大。
Based on the phonon scattering model, the temperature response of the three-layer one-dimensional non-metallic thin film at the harmonic temperature boundary condition was obtained by the Laplace transform method. Through the example analysis, the thermal response characteristics of the non-metallic thin film under micro-scale conditions are discussed. The calculation shows that the thermal response temperature and the heat propagation velocity change with the change of the characteristic parameter E. At different positions in the film, when E <0.1, the wave characteristic is obvious. The maximum response temperature decreases first and then increases in the wave propagation direction. When E> 0.1, the maximum response temperature decreases continuously. When E takes a larger value, the heat propagation speed is also larger, and the thermal response time to reach the maximum response temperature is almost the same. On the back surface of the film, the heat propagation velocity increases with the increase of E. In addition, when E <0.25, the maximum heat disturbance response temperature decreases with the increase of E; when E> 0.25, the maximum heat disturbance response temperature increases with E increasing.