Discrete cooling ducts define complete packet-and-oil-channel layouts. Compare constructible positions and connections together with magnetic area, heat paths and coil fit to select the useful core arrangement. [1]
Enumerate the buildable duct arrangements first: permitted counts, positions, spacer constructions and packet schedules. Continuous dimensions can then be optimized within each arrangement.
Rebuild magnetic area for every arrangement
At a fixed outer envelope, a new void generally removes steel from the available section. Calculate the effective magnetic area from the actual steel packets; do not include the duct in gross area and then apply a stacking factor intended for steel plus coating.
If steel area is held constant instead, adding ducts can enlarge the limb envelope and consume coil clearance. Those are two different comparisons. State which is being made before attributing a loss or temperature change to “better cooling.”
| Duct candidate | Magnetic rebuild | Cooling rebuild | Feasibility check |
|---|---|---|---|
| No internal duct | Baseline packet section | External cooling and through-pack conduction | Interior temperature at required duty |
| One specified duct arrangement | Net steel area and local flux redistribution | Entry, channel and exit restrictions | Spacer support, fit and hottest packet |
| Multiple specified ducts | Every packet and changed envelope | Flow division between connected channels | Flow-starved region and additional interfaces |
The rows describe candidate families, not a recommendation to progress toward more ducts. Actual positions and dimensions should accompany each row.
Check whether the proposed duct carries oil
Trace the entry and exit to the surrounding circuit. A narrow channel with restricted ends may carry less flow than its open area suggests. More parallel passages also do not guarantee equal flow: their resistances and driving pressure differ.
Evaluate relevant fluid properties at the duty temperatures and use the actual cooling mode. Reusing the same heat-transfer coefficient on every new channel can award a thermal benefit before the flow calculation has established it.
Thermal conduction across the laminated packet is directional and includes interface effects. A new duct may shorten a conduction path while reducing magnetic area and increasing loss. Compare the recalculated heat source and heat removal together, keeping the hottest location rather than only the average temperature.
Keep discrete transitions outside smooth interpolation
A half-duct or a fractional spacer count is not a buildable solution. Recalculate the complete geometry when duct count changes, including support, coating contact and any required electrical insulation. A surrogate fitted to one arrangement should not silently interpolate to another topology.
Use the catalogue density, 7,650 kg/m³, to account for steel displaced by a duct. [2] Assume a new continuous duct removes 0.0040 m³ from an unchanged gross envelope: steel mass falls by 30.6 kg. If effective magnetic area falls from an assumed 0.0200 m² to 0.0192 m² at unchanged flux, a baseline 1.60 T rises to 1.667 T. The mass reduction is therefore accompanied by a 4.17% average flux increase. Recalculate the magnetic source and winding fit as well as the cooling benefit; carrying the original watts into the ducted layout would hide the electrical cost of the opening.
Duct continuity, spacer thickness, packet compression and joint schedule determine how much steel is actually displaced. Issue a complete buildable layout before assigning a thermal advantage to another duct count.
Compare magnetic, thermal and fit margins for every surviving layout. Price any larger outer section needed to recover steel area and release the complete packet-and-channel construction.
References
- Z. Chen, Z. He and S. Wang, Transformer Iron Core Temperature Field Calculation Based on Finite Element Analysis, Energies 18, 6537, 2025. DOI: 10.3390/en18246537.
- Nippon Steel Corporation, Grain-Oriented Electrical Steel Sheets, catalogue D004je, April 2020, specification and typical-property tables.