本文主要探討在微尺度空間及時間下，熱遲滯現象相關的時間延遲效應，在不同模式中熱傳效應的影響，物理模式分別為Diffusion model、CV wave model、dual-phase-lag model，前者為傳統傅立葉熱傳導方程式，後兩者為雙曲線之微觀熱傳導方程式。CV wave model比Diffusion model多一項溫度對時間的兩次微分項，dual-phase-lag model又比CV wave model多一項溫度對空間兩次微分，對時間一次微分的混合項，此兩項在數值計算時，容易產生震盪和發散。
模擬分析時，以兩個物理模型來分析熱遲滯現象，第ㄧ個是給定高低溫邊界，同時將其無因次化；另ㄧ個則是給定絕熱邊界，並加入ㄧ雷射熱源。以數種不同數值方法，來模擬這兩個模型，並將計算結果和解析解作比較，探討這些數值方法的優缺點，並比較其準確度。從計算結果，可得知在探討第一個物理模型時，隱性法（空間項中央差分、時間項中央差分）為最佳的數值方法，無須考慮穩定度條件且累加誤差最小。在分析第二個物理模型時，顯性法則為最佳之數值方法，但須注意其穩定度的條件。

Under the micro-scale condition of space and time, this paper is to study the time-lagging effect caused by the thermal lagging behavior and its heat transfer effects in three mathematical models, which are the diffusion, CV wave and dual-phase-lag models. The first one is the Fourier’s heat conduction equation and the others are the hyperbolic equations. The CV wave model is more than the diffusion one by one term of second order time derivative and the dual-phase-lag model is more than the CV one by one term of second order time-and-space mixed derivative. These two extra terms make the numerical calculation oscillate and diverge easily.
In the one-dimensional simulation analysis, two physical models are applied. In the first one, the high and low temperature boundaries are used and the model is expressed in the dimensionless form. In the second one, the heat-insulated boundaries and laser heat source are utilized. Several numerical methods are used to simulate these two physical models and the computing results are compared with the exact ones. From the analysis results, it can be found that the implicit method (centered difference for the derivatives of space and time) is the best one for the first physical model without any stability problems. For the second model, the explicit method is the best one, but it needs to take the stability criterion into account.

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