Analytical Solutions of Enhanced Gray Boltzmann Transport Equation on Transient Thermal Grating and Time-Domain Thermoreflectance Experiments

As reported by many studies, Fourier’s law breaks down in micro/nanoscale due to the nondiffusive heat transport. To account for the nondiffusive heat transport, high-fidelity nondiffusive models with good efficiency for the experimental data analysis in nanothermometry are necessary but unfortunately missing. In this paper, based on a validated enhance Gray Boltzmann transport equation, we offer the analytical solutions for two important nanothermometry techniques, namely the transient thermal gratings (TTG) and time-domain thermoreflectance (TDTR) experiments. The analytical solutions obtained by inverse Fourier transform are compared to the experimental signals in both TTG and TDTR cases. The excellent agreements between the analytical solutions and the experiments demonstrate the applicability of the EG-BTE in experimental data analysis as an efficient replacement of Fourier’s law.