How to Modify Dowel’s Equation for Eddy Losses with Cooling Ducts Between Layers?

Dowel's equation for calculating eddy losses in conductors has two parts. First accounts for thickness of the strip and the other for proximity effect. However, motst of the times there are cooling ducts between the layers which will definitely reduce proximity losses, depending upon thickness of the duct. So how to modify the second term when cooling ducts are inserted between the layers?

Dowell's equation for calculating eddy losses in conductors takes into account the thickness of the strip and the proximity effect. However, when cooling ducts are inserted between the layers, it is necessary to modify the second term of the equation to account for the effect of the ducts on the proximity losses. The proximity losses will be reduced depending on the thickness of the ducts. One possible way to modify the second term of the equation would be to incorporate a factor that accounts for the reduction in proximity losses due to the presence of the ducts. This factor could be determined through experimental measurements or numerical simulations.

Thank you. Is there any example or article that we can go through to understand this correction more?

I was also searching for similar article but there is none. We have to speculate. If we consider maximum effect, that is, application of the formula as it is, at 1 mm distance (maximum insulation thickness) then we can go on reducing it linearly (we assume infinite length that is very long conductor). In short, losses due to second term will have to be multiplied by 1x1/d or f=1/d, where d is the radial thickness of the duct in mm. Let there be S sections made by cooling ducts. Then apply second term only to one section. If these losses are W then actual loss will be W(1+f); for all cases when f is less than or equal to 1. Total eddy loss due to proximity will be S*W(1+f). This loss should then be added to first term loss to get total eddy current loss. I think this will work with sufficient accuracy.
Normally number of radial strips are low in layer winding but high in disc winding. It would be interesting to find out effect on losses due to introduction of duct of large thickness (10 mm).

Is it applicable for calculating the eddy current loss in transformers? Thanks in advance.