  We analyze the effect of restricted geometries on the contribution of
Nambu-Goldstone bosons (phonons) to the shear viscosity, $\eta$, of a
superfluid. For illustrative purpose we examine a simplified system consisting
of a circular boundary of radius $R$, confining a two-dimensional rarefied gas
of phonons. Considering the Maxwell-type conditions, we show that phonons that
are not in equilibrium with the boundary and that are not specularly reflected
exert a shear stress on the boundary. In this case it is possible to define an
effective (ballistic) shear viscosity coefficient $\eta \propto \rho_{\rm ph}
\chi R$, where $\rho_{\rm ph}$ is the density of phonons and $\chi$ is a
parameter which characterizes the type of scattering at the boundary. For an
optically trapped superfluid our results corroborate the findings of Refs.
\cite{Mannarelli:2012su, Mannarelli:2012eg}, which imply that at very low
temperature the shear viscosity correlates with the size of the optical trap
and decreases with decreasing temperature.
