  Presented here is a nanowire model, consisting of coupled elastic membranes
with the purpose of investigating thermal transport in quasi-one-dimensional
quantum systems. The vibrations of each elastic membrane are quantized and the
flow of the vibrational energy between adjacent membranes is allowed. The ends
of the nanowire are attached to thermal baths held at different temperatures.
We derived quantum master equation for energy flow across the nanowire and
obtained thermal currents and other key observables. We study the effects of a
disordered boundary on the thermal current by randomizing the membrane radii.
We evaluate the model as a nanowire analogue as well as study the effects of a
disordered boundary on thermal conductivity. The calculations show that the
membrane lattice model demonstrates diameter phonon confinement and a severe
reduction in thermal conductivity due to surface roughness which is
characteristic of semiconductor nanowires. The surface roughness also produces
a length dependence of the thermal conductivity of the form $\kappa=\alpha
L^{\beta}$, with $\beta$ dependent on disorder characteristics, in the
otherwise ballistic regime. Finally, the parameters of the model are fitted to
available experimental data for silicon nanowires and the results of the
calculations are assessed against the experimental data.
