  A mathematical model is presented for thermal transport in nanowires with
rectangular cross sections. Expressions for the effective thermal conductivity
of the nanowire across a range of temperatures and cross-sectional aspect
ratios are obtained by solving the Guyer--Krumhansl hydrodynamic equation for
the thermal flux with a slip boundary condition. Our results show that square
nanowires transport thermal energy more efficiently than rectangular nanowires
due to optimal separation between the boundaries. However, circular nanowires
are found to be even more efficient than square nanowires due to the lack of
corners in the cross section, which locally reduce the thermal flux and inhibit
the conduction of heat. By using a temperature-dependent slip coefficient, we
show that the model is able to accurately capture experimental data of the
effective thermal conductivity obtained from Si nanowires, demonstrating that
phonon hydrodynamics is a powerful framework that can be applied to nanosystems
even at room temperature.
