In the hot end of a 3-D printer, polymer feedstock flows through a heated cylinder in order to become pliable. This setup determines a natural upper limit to the speed at which the polymer may be extruded. The case of polymers which undergo the crystalline-melt transition is considered; the resulting mathematical model is a Stefan-like moving boundary-value problem for the polymer temperature. Using the heat balance integral method provides an analytical approximation for the temperature. Several different conditions which use this temperature to establish the maximum velocity are considered; using a pointwise polymer exit temperature in the hot end matches well with experimental data.
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The authors thank the Office of Undergraduate Research and Experiential Learning at the University of Delaware for their support of this project. We also thank the reviewers for their insightful comments which helped improve this manuscript. Many of the calculations herein were performed with the assistance of Maple and Matlab.
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Sitison, J.W., Edwards, D.A. The heat balance integral method for cylindrical extruders. J Eng Math 122, 1–16 (2020). https://doi.org/10.1007/s10665-020-10041-y
- 3-D printing
- Additive manufacturing
- Heat balance integral method
- Stefan problem