Plastic Pipe Solidification: Exact Solutions in Cylindrical Coordinates
Giacomin, A. Jeffrey
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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 adimensionalize the energy balance, and solve for 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 plastics engineers how to use our results for pipe cooling chamber design.