本文應用Laplace Adomian分解法求解套裝式螺旋鰭片的暫態熱傳遞問題。Laplace Adomian分解法結合Laplace轉換與Adomian分解法，用於解決非線性的偏微分方程，其結果為一截斷級數解，而使用Laplace Adomian分解法的優點為快速達到收斂並且能有高度精準度。
考慮一套裝式螺旋鰭片透過傳導傳遞熱量，並且外在環境存在對流和輻射的情況下，與外界進行熱交換，而鰭片的基部有一週期性溫度邊界，求解螺旋鰭片的溫度分布，並進一步求得熱傳量且計算鰭片熱效率。文章最後會探討各熱傳遞係數、畢奧數、環境溫度還有螺紋截距對於溫度分布、熱傳量和鰭片效率的影響，並分析各系數間與熱效率的關係。
計算結果得知，溫度分布隨著熱對流參數β、熱輻射係數γ以及螺紋截距P_i的增加而下降，卻隨著畢奧數Bi與環境溫度的增加而增加。熱傳量則隨著熱對流參數β、熱輻射係數γ以及螺紋截距P_i的增加而增加，卻隨著環境溫度的增加而下降。而鰭片熱效率主要隨著熱對流參數β和熱輻射係數γ的增加而降低，卻隨著畢奧數Bi的增加而增加。
最後，比較所有結果，可以得知熱輻射係數γ對於溫度分布、熱傳量和鰭片效率的影響皆大於其他係數，也可以得知，螺旋鰭片的熱傳量與鰭片效率皆較環型鰭片佳，而當螺紋截距P_i越大時，熱傳量越大且鰭片效率越好。

In this paper, the Laplace Adomian decomposition method (LADM) is used to solve the non-linear transient heat transfer analysis in a nesting type spiral fin with periodic base temperature. This transient heat transfer problem associates with heat conduction, convection and radiation. Because of nesting type structure, it also associates with contact resistance. It’s boundary condition conclude periodic base temperature and at fin end insulated. Solving the fin temperature distribution in a nesting type spiral fin, then calculate the heat flux from the fin base, and calculate the fin efficiency. Investigating the effect of fin temperature distribution and heat flux by heat transfer coefficients, Biot number, surrounding temperature and the pitch. Also, show the relation between fin efficiency and heat transfer coefficients.

The results show that fin temperature distribution gets lower by the higher convection coefficient and radiation coefficient, the lower surrounding temperature and Biot number. The heat flux gets higher by the higher convection coefficient, radiation coefficient, Biot number, and pitch, the lower surrounding temperature. And the fin efficiency gets lower by the higher convection coefficient and radiation coefficient. In this process, the effect caused by radiation coefficient is the largest and pitch effect insignificant. Increase the radiation coefficient can dissipate heat faster, make the fin cool down quickly.

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