Frequency response of certain temporal and complex transfer functions for the Interfacial 1D temperature wave - Haidar, Nassar (Comptes Rendus. Mécanique, 2023)
This note is concerned with the dynamics of 1D temperature waves generated by time modulation of a boundary heat flux. It demonstrates how a certain temporal transfer function of both parabolic and low frequency hyperbolic interfacial temperature waves happens to be frequency semi-invariant with a vibrating boundary heat flux. It is proved that only high frequency hyperbolic interfacial temperature waves can have a fully frequency-invariant temporal transfer function relative to such a vibrating boundary. The frequency response of an associated complex transfer function is also studied and demonstrated to behave, at low frequencies, as fixed lag compensator. Only according to hyperbolic theory of heat conduct, this compensator converts, at high frequencies, to a fixed gain amplifier.