This article explains how Fourier’s law, Newton’s cooling law, and the heat conduction equation are applied to real mold temperature control systems, with practical data and design considerations for mold makers.

In mold temperature control, three fundamental heat transfer formulas govern nearly every design decision we make. The first is Fourier’s law of conduction, which states that heat flux is proportional to the temperature gradient and thermal conductivity of the material. For a typical P20 steel mold cavity, with a thermal conductivity of about 29 W/m·K, a 10°C temperature difference across a 20 mm wall thickness yields a heat flux of roughly 14.5 kW/m². This directly influences how we space cooling channels—if we place them too far from the cavity surface, the temperature gradient becomes too steep, causing uneven shrinkage and warpage. In practice, we keep cooling lines within 1.5 to 2 times the channel diameter from the mold face, and we calculate the required flow rate using the heat load from the part’s cycle time and material specific heat.

The second formula is Newton’s law of cooling for convective heat transfer between the coolant and the channel wall. Here, the heat transfer coefficient (h) depends on flow regime, coolant viscosity, and channel geometry. For water at 20°C flowing at 1.5 m/s in a 10 mm diameter channel, the Reynolds number is around 15,000, indicating turbulent flow, which gives an h value of approximately 4,000–6,000 W/m²·K. This is why we always specify turbulent flow in cooling circuits—laminar flow (Re < 2,300) can cut heat extraction by more than half. When designing for high-cavity-count molds, we use the total heat dissipation requirement (in kW) and divide by the available surface area of the cooling channels to verify that the convective coefficient is sufficient. If not, we increase flow rate or reduce channel diameter, but we also watch pressure drop, which rises with the square of velocity.

The third formula is the transient heat conduction equation, often simplified to the lumped capacitance model for thin mold sections. For a 5 mm thick core insert, the Biot number is typically below 0.1, so we can treat it as a uniform temperature body. This lets us calculate the cooling time using the part’s thermal diffusivity and the desired ejection temperature. For ABS with a diffusivity of 0.1 mm²/s, cooling from 220°C to 60°C in a 2 mm wall takes about 12 seconds—this matches many real cycle time studies. However, for thicker sections or beryllium-copper inserts (which have a diffusivity three times higher than steel), the lumped model fails, and we must use finite element analysis to predict hot spots. In daily quoting, we use these formulas to estimate cooling time, water flow, and chiller capacity—getting these numbers wrong leads to rejected parts and missed delivery dates. For more detailed mold sourcing and thermal design calculations, visit MoldWorld (www.moldw.com) for technical articles and supplier listings.