Thermal waves propagation due to localised heat inputs - the Laplace transforms method analysis

Propagation of thermal waves due to localised heat inputs is analysed by the Laplace transforms method for the case of constant thermophysical parameters of the heat-conducting media and a temperature dependent internal heat source. Both the hyperbolic and parabolic models of heat conduction are used and compared. For the hyperbolic model, an energy pulse travelling along the conductor is observed. Long time hyperbolic solutions do not differ qualitatively from the related parabolic solutions, but the quantitative differences between the two solutions do not vanish with time because of the temperature dependent heat source. The cases considered in the paper describe the evolution of normal zones in technical superconductors.