Cooling System Design in Moulds: Heat Transfer Kinetics, Turbulent Channels & Conformal Lines

Cooling accounts for 60% to 80% of the total injection moulding cycle time. Designing efficient mold cooling channels directly dictates plant productivity, part warpage, thermal residual stresses, and dimensional tolerances. Achieving turbulent coolant flow ($Re > 4,000$) through strategically placed drilled channels, baffles, bubblers, or 3D-printed conformal cooling lines maximizes heat extraction efficiency.

By completing this lesson, you will be able to:

• Calculate total thermal energy extraction ($Q_{total}$) per injection cycle.
• Determine theoretical minimum cooling time ($t_c$) based on part thickness and thermal diffusivity.
• Verify coolant turbulent flow using Reynolds Number ($Re > 4,000$).
• Compare drilled straight-line channels vs 3D printed conformal cooling circuits.

graph TD
    A["Hot Polymer Melt Injection (230°C in Mold Cavity)"] --> B["Heat Conduction through Steel Mold Plates (P20 / H13)"]
    B --> C["Turbulent Coolant Heat Extraction (Re > 4000 in Cooling Channels)"]
    C --> D["Coolant Temperature Rise (Delta T <= 2°C - 3°C across Circuit)"]
    D --> E["Part Solidification & Ejection (T <= Tejection)"]

4.1 Theoretical Cooling Time Equation ($t_c$)

For a flat plate component of wall thickness $h$, cooling time $t_c$ assumes 1D thermal conduction across isothermal mold surfaces:

t_c = rac{h^2}{pi^2 alpha} lnleft[ rac{8}{pi^2} left( rac{T_{melt} - T_{mold}}{T_{eject} - T_{mold}} ight) ight]

Explicit Input Parameter Table for Reproduction

Worked Numerical Example:

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Problem: Calculate theoretical cooling time $t_c$ using the explicit parameter table above.

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Solution:

1. Calculate temperature ratio term:

ext{Ratio} = rac{8}{pi^2} left( rac{230 - 40}{90 - 40} ight) = 0.81057 imes left( rac{190}{50} ight) = 0.81057 imes 3.80 = 3.08016

1. Calculate Natural Logarithm:

$$ln(3.08016) = 1.1250$$

1. Calculate $t_c$:

t_c = rac{(0.0030)^2}{pi^2 imes (8.50 imes 10^{-8})} imes 1.1250 = rac{9.0 imes 10^{-6}}{8.389 imes 10^{-7}} imes 1.1250 = 10.728 imes 1.1250 = 12.07 ext{ seconds}

• Conformal Cooling in Automotive Lens Moulds: 3D printed DMLS tool steel inserts reducing cycle time by 32%. (Illustrative Indian industry scenario based on automotive lighting tooling).

• Reynolds Number ($Re$): Dimensionless flow ratio ($Re > 4000$ ensures turbulent heat transfer).
• Conformal Cooling: 3D cooling channels that follow complex cavity contours at uniform distances.

1. ISO 20457:2018 — Plastics moulded parts — Tolerances and acceptance conditions, ISO.
2. Menges, G., & Mohren, P. (2001). How to Make Injection Molds, 3rd Ed., Hanser Publishers.