摘要
本文探討有限溫度脈衝及週期性溫度脈衝在三種不同熱傳導觀點下的一維傳播特色，三種模式分別是Diffusion model、 CV model 及 DPL model，後二者為雙曲線型之微觀熱傳導模式，前者則為傳統傅立葉熱傳導定律。所用的數值方法為Laplace transform及Riemann-sum approximation。由數值結果探討單一溫度脈衝及週期溫度脈衝在不同時間時於各模式作用下的傳播特徵，並指出三種模式於微觀情形下合而為一的區域。文中並討論在較大無因次時間β時，CV model產生的特殊能量分佈現象，即為兩相等強度的波峰，稱之為double-peaks的雙峰現象。另外正弦波、三角波及不同寬度脈衝波的影響也將在文中一並探討。最後以兩波對撞可能違反熱力學第二定律的特性及行為作一探討。研究結果顯示CV model之適用區域以無因次空間尺度來表示為2.8<δ<8 。

Abstract

In this study, the characteristics of three conduction models with finite pulse and periodic-pulses temperature sources are investigated. The three models are Diffusion model, CV model and DPL model. The latter two models possess hyperbolic features of micro-scale heat conduction and the former behaves as the conventional Fourier conduction.
Numerical experiments via Laplace transform and Riemann-sum approximation are used to show the propagation features of these three models. The regions that these three models merged together are explored. The results indicate a special double-peaks phenomenon of CV model at larger non-dimensional time. The sine pulse, triangle pulse and wider finite pulse are also used to investigate their effects on the heat transfer modes.
In addition, the two-waves collision phenomenon and the possibility of violation of the 2nd law of the thermodynamics are also examined. From the results obtained, the region of 2.8<δ<8 is proposed as the applicable region of CV model in the micro-scale heat transfer area.

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