【摘要】 为解决微尺度下金属薄膜中的热传导问题,利用电子-声子相互作用的抛物型两步热传导模型,考虑金属晶格对热传导的效应,研究了一半无限大金属薄膜在边界上受简谐温度作用的一维热传导问题,应用拉普拉斯变换及数值反变换技术,得到了温度的分布,并考虑了金属晶格相对热扩散率Fl、电子相对热扩散率Fe、热松弛时间比B及外加简谐温度频率ω的效应对金属薄膜中温度分布的影响.研究结果表明:晶格对温度分布有显著的影响;薄膜中的温度及热影响区随着Fe的增大而降低、变小,而随Fl、B及ω的增大而增高、变大;热在薄膜中以有限的速度进行传播.更多还原

【Abstract】 Based on the parabolic twostep heat conduction model, the heat conduction problem of a semiinfinite metal film subject to a harmonic temperature at its boundary is investigated by considering the metal lattice heat conduction contribution to metal film. The Laplace transform and Laplace numerical inversion are applied to obtaining the distribution of temperature. The effects of the relative thermal diffusivity of lattice Fl, the relative thermal diffusivity of electron Fe, the ratio of relaxation times B and the frequency of the applied harmonic temperature ω on the temperature distribution in metal film are considered and displayed graphically. From the distributions of temperature, it can be found that metal lattice heat conduction significantly affects temperature distribution in metal film, and the temperature value as well as heat disturbed region decreases with Fe becoming larger, and increases with Fl, B and ω becoming larger respectively. 更多还原