Meaning
Dimensionless ratios evaluating the balance between mechanically generated viscous dissipation and conductive heat removal establish thermal stability criteria for flowing viscous fluids. The brinkman number expresses the ratio of heat generated by viscous shear to the heat transferred by conduction through the polymer melt to cold boundary walls. Melt flow channels in processing machinery sustain steep velocity gradients that transform motor work directly into thermal energy.
The value approaches zero during slow flow of low-viscosity polymers in wide tooling conduits, indicating conduction manages the thermal profile, but surpasses unity when high-viscosity resins travel through narrow channels at high shear rates.
Governing Mechanism
Viscous heat generation scales with the square of the shear rate multiplied by the dynamic viscosity of the polymer. Heat removal operates as a linear function of the melt thermal conductivity divided by the characteristic gap dimension, while relying on the temperature differential maintained between channel walls and bulk melt. Because polymer melts exhibit poor thermal conductivity, typically between 0.15 and 0.30 Watts per metre-Kelvin, heat cannot escape rapidly across thick sections.
The brinkman number consequently climbs whenever screw speeds increase or runner diameters contract.
Operational Penalty
High values denote runaway internal temperature spikes that barrel and mould cooling circuits cannot extract. When processing shear-sensitive engineering resins like polyoxymethylene or unplasticised polyvinyl chloride, excessive viscous heating triggers autocatalytic polymer chain scission and gas liberation. Tooling designers who undersize hot runner gates push the local brinkman number well past critical thresholds, generating burn marks on cosmetic surfaces and thermal degradation within the core.
Virgin resins transition into lower-viscosity fluids as internal heat builds, which masks filling pressure issues while generating unexpected shrinkage gradients across the moulding.
Tooling Verification
Calculating this quantity during tooling design establishes safe shear limits for runners, gates, and extrusion dies before cutting steel. Simulation packages verify the brinkman number by tracking non-isothermal temperature rises along flow lengths, confirming whether chill lines can arrest the heat rise. Thin-wall mouldings routinely operate in regimes where the value exceeds ten, necessitating deliberate gate land enlargements to avoid thermal degradation.
Regrind compounds containing varying melt flow rates create sudden shifts in local dissipation rates, shifting part dimensions over time. The metric serves as a design limit where increasing mechanical cooling capacity yields diminishing returns against poor channel geometry.
