在塑膠管擠製過程中，對高分子熔膠固化，我們在圓柱座標系使其能量平衡，以達成溫度和固化速率之精確解。我們使用絕熱的內壁與不同的外壁邊界條件：等溫和對流。我們著重在外部水冷卻系統，此為最常見的冷卻方法。在固-液界面中，固化溫度是向內遞減。我們使能量平衡無因次化，並求解完全固化所需之無因次時間。我們達成固化厚度演變之精確解。對於外壁條件：恆溫和對流，我們皆繪製了無因次固化厚度的演變圖。我們還包括兩個實作案例，展示工程師如何使用我們的結果，來設計管件的冷卻室，特別包含冷負荷的方程式。

For polymer melt solidification in plastic pipe extrusion, we perform an energy balance on the pipe extrudate in cylindrical coordinates to arrive at exact solutions for the temperature, and for the solidification rate. We use an adiabatic inner wall, and differing outer wall boundary conditions: isothermal and convection. We focus on the external water-cooling system, the most common cooling method. The solid-liquid interface, at the solidification temperature, moves inward with deceleration. We nondimensionalize the energy balance, and solve for the dimensionless time required for complete solidification. We arrive at exact solutions for the evolving solidified thickness. For both outer wall conditions, isothermal and convection, we plot the dimensionless solidification thickness evolution. We further include two worked examples to show engineers how to use our results for pipe cooling chamber design, including especially, an equation for the cooling load.