本文探討非牛頓冪次律流體流經曲面之邊界層流流場、熱傳遞與應用熱力學第二定律分析熱流場內的熵產生率問題，並分析在具有輻射、黏滯耗散之下熱流場的速度與溫度分布。利用非牛頓冪次律模型描述流體性質，以此研究因為表面曲率(?)及非牛頓冪次律流體之流動特性指數(n)而產生曲面上之流體流動、熱傳遞及熵產生率隨位置之變化的物理現象。透過相似轉換(Similarity Transformation)將統御方程式由非線性偏微分方程組轉換為非線性常微分方程組，並以流動特性指數n、表面曲率?及與溫度有關之參數(普朗特數Pr,埃克特數Ec,輻射參數Rd )分析曲面系統的熱流場。
應用Laplace Adomain分解法解決曲面熱流場的統御方程式。Laplace Adomain分解法為結合Laplace轉換與Adomain分解法的數值方法，適合用於分析非線性系統的微分方程組，其數值結果為一截斷級數解，搭配Pade 近似能更快速地達到收斂，能夠有效率地處理複雜物理系統的問題。
研究結果可知，對擬塑性流體而言，當流動特性指數(n)越大，速度邊界層厚度越大(速度擴散越慢)，且表面摩擦係數越小(流動阻力越小)。而對於膨脹性流體而言，當流動特性指數(n)越大，速度邊界層厚度越小(速度擴散越快)，且表面摩擦係數越小(流動阻力越小)。但流動特性指數(n)的增加，無論對於任一種流體而言，溫度邊界層厚度皆會增加。藉由探討曲率?對曲面流動系統的影響可知: 曲率?越大，速度邊界層厚度變小，溫度邊界層厚度亦隨之變小。但對於溫度邊界層之影響不大，由此結果可進一步推斷，熱對流基本定律(牛頓冷卻定律)適用於任意外型之物體，並能確定其結果的準確性。除此之外，本文更進一步探討曲面邊界層內部的不可逆性變化。

In this study, we discuss the Non-Newtonian Power-Law Fluid boundary layer flow and heat transfer phenomenon over curved surface, the application of the second-law of thermodynamics to the problems about the rate of entropy generation, and analyze the velocity and temperature distribution under the effect of radiation and viscous dissipation. Using the model of Non-Newtonian Power-Law Fluid to describe the local variation of fluid flow, heat transfer, and rate of entropy generation. The governing equations are transformed from nonlinear partial differential equations to nonlinear ordinary equations by similarity transformation. Analyze the thermo-fluids field by Flow Behavior Index (n), curvature (?), and the parameters related to temperature(Prantl number, Eckert number, and radiation parameter).
The governing equations are solved numerically by Laplace Adomain Decomposition Method (LADM), which is combined with Laplace Transform and Adomain Decomposition Method (ADM). This method is prefer to use to analyze the differential equations of nonlinear systems because the numerical result is a truncated series solution. Combine LADM with Pade Approximation, the series solution will converge faster. LADM have the ability to deal with the problems of complex systems.
For Pseudoplastic fluid, the increase of Flow Behavior Index (n) will cause the increase of the velocity boundary layer thickness, but the decrease of Skin-Friction coefficient. The effect of Skin-Friction coefficient will still be the same for Dilatant fluid, but the effect of velocity boundary layer thickness is opposite. By discussing the effect of curvature, we can know that velocity and temperature boundary layer thickness will both decrease. But the increase of temperature boundary layer thickness is slight. By this result, we can further ensure that the fundamental law of heat convection (Newton's cooling law) is suitable for the object with any shape. Additionally, we further discuss the variation of irreversibilities in the interior of curved boundary layer.

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