Transient Electrical Heating of Toroidal Coils of Rectangular Cross Section

The exact solution is obtained for the transient thermal response of toroidal coils of rectangular cross section with orthotropic constant thermal conductivity, constant density, and specific heat, and linear boundary conditions. The solution is a rapidly converging doubly infinite eigenfunction expansion whose leading term is generally accurate to within 5 percent. No conclusive results were obtained from our evaluation of the applicability of previously obtained solutions for the infinite rod approximation for the toroidal coils. In some cases, the infinite rod approximation is accurate even for large curvatures, but in other cases it is in substantial error for relatively small curvatures. Hence, the solution presented here is generally recommended to predict the temperature distribution in toroidal coils and a number of design curves are provided for prediction purposes.