Periodic Heat Flux-Temperature Phase Difference for Thin Metal Films

Abstract

Abstract The two-step parabolic model approximately describes microscale heat transfer in metals. Heat transfer in thin films with sinusoidal heat flux input on one surface is described by a Green’s function solution of the two-step parabolic model. The dimensionless phase angle between the sinusoidal energy input and the lattice temperature response at the opposite surface of a thin film is calculated for several dimensionless parameters that include the energy input frequency, electron-phonon coupling factor, thermal conductivity, thickness of the film, and electron and lattice heat capacities. For low dimensionless frequencies, the temperature behavior is essentially Fourier except for very thin metal films and/or for materials with very low electronphonon coupling factors. The departure from Fourier behavior as input frequency increases could allow future experimental determination of electron-phonon coupling factor and electron heat capacity. Comparison with previous calculations for thermal wave and Fourier heat transfer models shows that the dimensionless phase angle for the two-step model is generally less than for the other models.