本文提出一種混合拉氏轉換法（Laplace transform technique）和有限差分法（Finite difference method）的數值方法，並配合最小平方法和溫度量測值來預測CPU之散熱鰭片(Heatsink)的散熱量。首先利用拉氏轉換法處理統制微分方程式及邊界條件之時間域而後再以有限差分法處理轉換後之統制微分方程式及邊界條件，最後再以數值逆拉氏轉換法求取標準試件之溫度值。本文在進行逆算過程時，估算值(Estimates)的函數型態先前是未知的。為了欲求得較精確的估算值，整個時間域被分割成數個小時間區間(Sub-time interval)，而後再利用本文之混合逆算法求出每一小時間區間的估算值。本文數值方法的優點是可以求得在某一特定時間的溫度值，而不需要由初始時間慢慢地求解。最小平方法的應用在於使數值結果能較快速地收斂。預測結果顯示本文之數值方法能夠有效地預測出較精確的估算值且所求得於量測點之溫度值也頗吻合實驗值。因此，本文之逆向熱傳導方法配合溫度量測值，可用來預測CPU與散熱鰭片間之溫度值並減少接觸熱阻的影響。文中也將探討量測誤差對預測值的影響。

　　The present study introduces a hybrid numerical method to predict the heat dissipation on CPU heatsink. This algorithm combines the Laplace transform technique and the finite-difference method in conjunction with the least-squares scheme and temperature measurements. Time-dependent terms in the governing differential equation and the boundary conditions are removed by using the Laplace transform technique, and then the resulting differential governing equation and boundary conditions are solved by using the finite-difference method. The temperature distribution in the standard material is obtained by using the numerical inversion of Laplace transform. The functional form of the unknow estimates is not given a prior before performing the inverse calculation. To obtain more accurate estimates, the whole time domain is divided into several sub-time domains. The hybrid inverse scheme is applied to obtain the present estimates for each sub-time domain. The advantage of the present numerical scheme is that, the temperature can be calculated at a specific time without step-by-step computation from the initial time. Due to the application of the least-squares scheme, the convergence of the present estimates can become fast. The results show that the present numerical method can accurately and efficiently obtain the present estimates. Thus, it can be concluded that the present numerical method with experimental data can be applied to estimate temperature distribution between CPU and heatsink. It also shows that the contact resistance will be decreased between CPU and heatsink. The effect of measurement error will also be investigated in this thesis.

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