Thermal Resonance Under Frequency Excitations

The resonance phenomenon of thermal waves is studied in this work. Under the excitation of a body heat source oscillating at a certain frequency, both the temperature and the heat flux waves are found excitable to resonance. The physical conditions necessary for this unusual behavior to occur are obtained in terms of the resonance amplitude and the modal frequency. It has been shown that thermal resonance is a high-mode phenomenon. Only the wave modes with a modal frequency exceeding a critical value of 0.6436f, with f being the critical frequency of the solid medium, may present resonance. This unique behavior is attributed to the partition of the over- and underdamped waves oscillating in time. The critical mode numbers governing (i) the transition from an over- to an underdamped mode, and (ii) the occurrence of thermal resonance phenomenon, are derived analytically. A length parameter, the relaxation distance extended from the concept of relaxation time, is found to dominate these critical mode numbers. Last, the thermal wave speed is related to the resonance frequency, which provides an alternative approach to determining the thermal wave speed in solids.