  Thin-film-based nanoporous membrane technologies exploit evaporation to
efficiently cool microscale and nanoscale electronic devices. At these scales,
when domain sizes become comparable to the mean free path in the vapour,
traditional macroscopic approaches such as the Navier-Stokes-Fourier (NSF)
equations become less accurate, and the use of higher-order moment methods is
called for. Two higher-order moment equations are considered; the linearised
versions of the Grad 13 and Regularised 13 equations. These are applied to the
problem of nanoporous evaporation, and results are compared to the NSF method
and the method of direct simulation Monte Carlo (i.e. solutions to the
Boltzmann equations). Linear and non-linear versions of the boundary conditions
are examined, with the latter providing improved results, at little additional
computational expense, compared to the linear form. The outcome is a
simultaneously accurate and computationally efficient method, which can provide
simulation-for-design capabilities at the nanoscale.
