擠出製程中為了讓剛擠製出環形鋼模的塑膠管件從高溫高黏度之熔融態固化至一般成品。一般而言，其冷卻方法可為將高溫成品擠製進入冷卻水中或者噴灑冷卻水至產品表面，稱之為淬火。此方式為控制管件外壁溫度等於冷卻水的溫度。本文首先針對此階段等溫管件外壁的條件下，提出一精確的塑膠管淬火相變化解析解，再進行固化時間對溫度及半徑的方程式之無因次化。同時檢驗其冷卻未完全之情況。最後藉由比對有限元素解來提升此解析解之正確性，同時搭配案例驗證以幫助工程師設計淬火冷卻槽。

When plastic pipe is extruded, it emerges from an annular die as hot molten plastic. This highly viscous liquid must then be solidified. This is normally accomplished by either plunging it under cold water, or by spraying cold water onto its outer surface. Called "quenching", this unit operation then solidifies the plastic by maintaining its outer wall temperature at the cold-water temperature. We first provide an exact analytical solution for the quenching of plastic pipe with phase change, subject to this cold, wet isothermal outer wall. We give the dimensionless solidification time as a function of the dimensionless solidification temperature and dimensionless radius. We then examine the case where the cooling is imperfect. Finally, we evaluate these analytical solutions by comparing them with their corresponding finite element solutions, and we then use these finite element solutions to delimit the accuracy of our analytical solutions. We include worked examples to help plastics engineers design the quench tank.