The non-Fourier heat conduction in a finite medium subjected to a periodic heat flux is modelled using the finite integral transform technique and an analytic solution is obtained. An analogy between thermal oscillation and oscillation of mechanical and electrical systems is drawn. A transition criterion from the non-Fourier heat conduction formulation to the Fourier formulation is obtained and a simple analytical expression of the phase and amplitude of thermal oscillation is derived.
Abdel-Hamid, B. (1999). Modelling non-Fourier heat conduction with periodic thermal oscillation using the finite integral transform. Applied Mathematical Modelling, 23(12), 899–914. https://doi.org/10.1016/S0307-904X(99)00017-7