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

Hyperbolic heal 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.