本文應用Laplace Adomian分解法解決螺旋鰭片之暫態熱傳遞問題。Laplace Adomian分解法結合Laplace轉換與Adomian分解法，用於求解非線性偏微分方程，其結果為一截斷級數解，而Laplace Adomian分解法相較傳統數值方法，能快速達到收斂並保有高度準確性。
考慮一螺旋鰭片透過傳導傳遞熱量，並在對流及輻射環境下，與外界環境進行熱交換，而螺旋鰭片基部有一週期性溫度邊界，求解螺旋鰭片之溫度分布曲線，並進一步計算熱傳量以及鰭片效率。文中探討各熱傳遞係數與螺紋截距，對溫度分布、熱傳量與鰭片效率的影響，並計算鰭片效率與熱傳遞係數間的關係。
研究結果得知，溫度分布隨著熱對流參數N、熱輻射參數β以及螺紋截距Pi的增加而降低，卻隨著環境溫度的降低而增加。熱傳量則隨著熱對流參數N、熱輻射參數β以及螺紋截距Pi的增加而增加，卻隨著環境溫度的增加而降低。而鰭片效率主要隨著熱對流參數N、熱輻射參數β的增加而降低。
比較所有結果，熱輻射係數β對溫度分布、熱傳量以及鰭片效率的影響皆大於其他係數，而結果也得知，螺旋鰭片的熱傳量與鰭片效率皆比環形鰭片較佳，而當螺紋截距Pi越大時，熱傳量越大且鰭片效率越好。

In this article, the Laplace Adomian decomposition method (LADM) is used to solve the non-linear transient heat transfer analyses in a spiral fin with periodic base temperature. The transient heat transfer problem associates with heat conduction, convection and radiation. The base temperature is periodic and fluctuated around a mean value and its end insulated. Solve the fin temperature distribution in a spiral fin, and calculate the heat flux from the base and the fin efficiency. Investigate the effect of fin temperature distribution and heat flux by heat transfer coefficients, 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 lower surrounding temperature, the higher convection coefficient, radiation coefficient and pitch. The heat flux gets higher by the lower surrounding temperature, the higher convection coefficient, radiation coefficient and pitch. And the fin efficiency gets lower by the higher convection coefficient, radiation coefficient. In the high temperature heat transfer process, the effect caused by radiation coefficient is the largest and the pitch only affect slightly. Increase the radiation coefficient can dissipate heat quickly, make the fin cooled down faster.

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