  The effect of sample size and surface roughness on the phonon thermal
conductivity $\kappa_p$ of Nd$_2$CuO$_4$ single crystals was studied down to 50
mK. At 0.5 K, $\kappa_p$ is proportional to $\sqrt{A}$, where $A$ is the
cross-sectional area of the sample. This demonstrates that $\kappa_p$ is
dominated by boundary scattering below 0.5 K or so. However, the expected $T^3$
dependence of $\kappa_p$ is not observed down to 50 mK. Upon roughing the
surfaces, the $T^3$ dependence is restored, showing that departures from $T^3$
are due to specular reflection of phonons off the mirror-like sample surfaces.
We propose an empirical power law fit, to $\kappa_p \sim T^{\alpha}$ (where
$\alpha < 3$) in cuprate single crystals. Using this method, we show that
recent thermal conductivity studies of Zn doping in YBa$_2$Cu$_3$O$_y$
re-affirm the universal heat conductivity of d-wave quasiparticles at $T \to
0$.
