  Recently, a pump beam size dependence of thermal conductivity was observed in
Si at cryogenic temperatures using time-domain thermal reflectance (TDTR).
These observations were attributed to quasiballistic phonon transport, but the
interpretation of the measurements has been semi-empirical. Here we present a
numerical study of the heat conduction that occurs in the full 3D geometry of a
TDTR experiment, including an interface, using the Boltzmann Transport
Equation. We identify the radial suppression function that describes the
suppression in heat flux, compared to Fourier's law, that occurs due to
quasiballistic transport and demonstrate good agreement with experimental data.
We also discuss unresolved discrepancies that are important topics for future
study.
