A transient ballistic–diffusive heat conduction model for heat pulse propagation in nonmetallic crystals

Abstract

A hybrid phonon gas model was developed to describe heat pulse propagation in dielectric crystals. In this model, heat energy is described as a mixture of longitudinal and transverse phonon gases. The novel aspects of this model include: (1) the distinction between longitudinal and transverse phonon excitations is taken into account; (2) transitions between ballistic and second sound transport, ballistic and diffusive transport, and second sound and diffusive transport are successfully captured. For the first time, benchmark cases of heat-pulse experiments in NaF at low temperatures in ballistic, ballistic–diffusive, and diffusive regions have been completely reconstructed in numerical simulations, which demonstrate the validity of the new model. It was elucidated how heat pulses are transmitted by longitudinal, ballistic transverse and dispersive transverse phonons at low temperatures. The numerical results not only yield new insight in physics of transient ballistic–diffusive heat conduction with effects from different phonon scattering processes, but also provide numerical tools to study similar transient ballistic–diffusive heat conduction in nanoelectronics and modern optoelectronics.