Meaning
Dimensionless ratio that determines whether the heat transfer across a narrow gap is governed by macroscopic fluid dynamics or by individual molecular collisions. In polymer processing, knudsen number gas conduction describes the heat flow across the air gap that forms as a part shrinks away from the mold wall. The value depends on the mean free path of the gas molecules relative to the size of the gap.
Microscopic Transport
Heat transfer through the air gap becomes less efficient as the gap width approaches the microscopic scale. When the knudsen number gas conduction value is high, the gas no longer behaves as a continuous medium. Molecular collisions with the walls dominate the energy exchange.
This phenomenon is prominent in micro-molding where gap sizes are extremely small.
Simulation Detail
Effective thermal conductivity of the gas trapped in the gap is lower than the bulk value. Standard cooling simulations often miss this detail. Incorporating the knudsen number gas conduction into the thermal model allows for more accurate prediction of the cooling time.
Engineers use this to avoid ejecting parts that are still too soft in the center.
Stress Variation
Shrinkage rates across the part surface are affected by local variations in gas conduction. If the gap width is non-uniform, the part will cool at different rates, leading to internal stresses. The knudsen number gas conduction helps explain why certain regions of a part might show sink marks while others remain flat.
High-performance resins with tight tolerance requirements necessitate this level of physical modeling. Without this correction, the simulation would assume a uniform thermal resistance that does not exist in reality. Such a simplified model fails to predict the subtle warpage seen in thin-walled technical components where the gap size is of the same order as the mean free path of the air molecules.
