The width and placement of the duct is important for cooling as well as for the minimum length of copper per turn. A wider duct gives better cooling but also increases the length of subsequent turn, thereby increasing I2r loss also.
Cooling, over loading and capacity addition of transformers/reactors are inter related. I developed some formula for life consumption, and life consuming cost for trans formers. When it would needed and would it be economical to add the capacity, instead of overloading on the basis of cooper loss cost, with increased life consuming cost. Designed cooling ducts are O.K, till temperature rise which gives life consuming cost unity, with designed numbers, shape, spacing and size of cooling ducts, at rated load (considering 20 years of life). For detailed study can refer my papers on, 'Microprocessor based hot spot temperature measurement for over load time limit computation and control............of power transformers'. etc.
could you please extend the information you provided to the intended power range and frequency range of the transformer? I think that it makes a huge difference whether to talk about 50 Hz or 1 MHz. The fact that you are writing about ducts makes it more likely that you look for solutions for bulky 50 Hz transformers in the kW-MW range. This is because it is not aware to me that power electronics transformers are known which use special ducts for heat removal. Actually, it could be worth trying to establish some small ducts that could increase surface and thereby heat transfer ... .
Yes, I am referring to power frequency transformers and inductors, used with 50Hz power electronic systems. Transformers are used for input isolation for rectifiers and output isolation of inverters while the inductors are used in the ac lines of IGBT PWM converters and PWM inverter output filters. Transformers can be of medium power capacity, say around 100kVA. Line inductors and filter inductors will be of smaller kVA but have quite an amount of core loss due to the higher frequency current components apart from copper loss, hence need proper duct design. While Amorphous cores gives better results, lack of availability of appropriate cores often force the designer to use CRGO (silicon steel) cores for the larger ratings.
High grade CRGO can be run at higher fluxdensities that amorphous cores which enables you to use less copper and thus reduced I2R losses. In aircooled transformers heat dissipation is the main issue. Besides I2R you also need to consider eddy current losses. Winding construction is another factor to consider. LV windings could be made using copper foil which gives a good spacefactor and efficient cooling. Also consider the temperature class. At higher temperatures you will get higher heat dissipation and may be able to get by with just a single duct. The temperature rise depends on total losses, surface area, temperature, and airflow.
With so many variables, the best approach will be to determine the info you need emperically. Just wind a simple 2 layer coil with a 6-10mm duct between the layers. Make ID and length similar to what you expect for the 100kVA transformer. Put thermal insulation on the inside (to simulate the heat generated by the core or other winding). Then monitor the temperature while you increase the current. Repeat with thermal insulation on the outside (so you get just the cooling effect of the duct) Then repeat the experiment with a different size duct between the layers. You will then have W/cm2 for different size ducts and can also deduce W/cm2 for the outside layer. Plug that information in your design formulae and you should be able to optimise your design for different kVA ratings and fluxdensities in minimal time.