  I present theoretical calculations of the thermal conductivity of Fermi
liquid 3He confined to a slab of thickness of order 100nm. The effect of the
roughness of the confining surfaces is included directly in terms of the
surface roughness power spectrum which may be determined experimentally.
Transport at low temperatures is limited by scattering off rough surfaces and
evolves into the known high-temperature limit in bulk through an anomalous
regime in which both inelastic quasiparticle scattering and elastic scattering
off the rough surface coexist. I show preliminary calculations for the
coefficients of thermal conductivity. These studies are applicable in the
context of electrical transport in metal nanowires as well as experiments that
probe the superfluid phase diagram of liquid 3He in a slab geometry.
