本文以座標轉換系統分析在波形板上不同熱傳模式之熵增。流場形式包含層流與紊流。紊流強制對流控制方程從完整Navier-Stokes 方程式推導而得，Prandtl’s 轉換理論將原座標朝某方向拉開，波形面可被轉換至可計算的平面座標。轉換的控制方程式其不規則平面會被拉伸為可計算之規則平面，然後再利用三次樣線配置法求解。
當紊流控制方程式簡化層流形式時，所得結果與之前研究比較十分吻合，說明本文所使用之座標轉換技巧及數值方法有利於分析複雜的幾何邊界，且所得的結果亦相當合理。同時，修正形式之無因次熵增也被導出，此式子包含了幾何(平面，波形面)、熱傳(對流與輻射)、流體摩擦力等效應。

In this study, the Prandtl’s transformation method is used to analyze various entropy generation of heat transfer modes on wavy plate.The types of fluid flow include laminar and turbulent flow.The governing equations of turbulent forced convection along wavy surface are derived from complete Navier-Stokes equations. Prandtl’s transposition theorem is used to stretch the ordinary coordinate system in certain direction. The wavy surface can be transferred into a calculable plane surface coordinate system. The transformed governing equations can expand the irregular boundary into a calculable regular plane, and then solve it by using the cubic spline collocation method. When the governing equations of turbulent forced convection are simplified to a case of laminar flow on wavy plate, the results have good agreement with previous works. This indicates that the coordinate transformation and numerical methods used in this study are favorable to solve the complex geometry boundary and give reasonable results. Meanwhile, a modified form for the entropy generation equation is derived. The effect of geometry (e.g. flat surface, wavy surface), fluid friction and heat transfer (e.g. convection and radiation effects) are all included in the modified entropy generation form.

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