Hyperbolic heat conduction and thermal resonances in a cylindrical solid carrying a steady-periodic electric field

Hyperbolic heat conduction in an infinitely long cylindrical solid with internal heat generation produced by Joule effect is considered. The power generated per unit volume is non-uniform and steady periodic. The surface of the cylinder is assumed to exchange heat by convection with an external fluid. The temperature field within the cylinder is determined analytically in a steady-periodic regime. For a fixed material and for a fixed radius of the cylinder, the dependence of the amplitude of thermal waves on the frequency of the electric current is studied and it is proved that thermal resonances occur.