A. Barletta et E. Zanchini, THE TEMPERATURE-FIELD IN A CYLINDRICAL ELECTRIC CONDUCTOR WITH ANNULAR SECTION, International journal of heat and mass transfer, 38(15), 1995, pp. 2821-2832
The heat conduction in a hollow cylindrical electric resistor which ca
rries an alternating current is analysed. The hole within the cylinder
is either empty or filled with a dielectric solid. The non-uniform po
wer generated per unit volume in the resistor by the Joule effect is e
valuated, and the steady periodic Fourier equation is written in a dim
ensionless form both in the domain occupied by the resistor and in tha
t occupied by the dielectric, if present. A boundary condition of the
third kind is assigned at the external surface of the cylinder. The di
mensionless temperature field is determined analytically as a function
of position, time and a proper set of dimensionless parameters.