Surface Temperature of Helmholtz Coil

[tachyon1123]

I am designing a Helmholtz Coil with radius 0.5m with 20 gauge Copper wire having 1000 turns. The power generated by passing 1A current through the coil is around 130W. One coil weighs 15.4kg and the cylindrical surface area exposed to air is 0.364m^2. I need to calculate the steady state temperature of the coil to see whether the coil would get too hot to operate safely. I am assuming that the coil cools down via conduction through air since the coil would be indoors. What would be the best way to get a rough estimate of the temperature at the surface of the coil?

 

[Future Bruno]

The best way to estimate the temperature of the coil at the surface is to calculate the convective heat transfer coefficient, h. This is done by dividing the total power (130W) by the exposed surface area (0.364m^2) and the overall thermal resistance of the coil which can be calculated by dividing the thermal conductivity of air (0.024 W/mK) by the exposed surface area. Once you have the h value, you can use the formula q = h x (T1 - T2) to calculate the temperature at the surface of the coil. T1 is the ambient temperature and T2 is the temperature of the surface of the coil.