  In this paper, a multiple-relaxation-time lattice Boltzmann model with an
off-diagonal collision matrix was adopted to predict the effective thermal
conductivities of the anisotropic heterogeneous materials whose components are
also anisotropic. The half lattice division scheme was adopted to deal with the
internal boundaries to guarantee the heat flux continuity at the interfaces.
Accuracy of the model was confirmed by comparisons with benchmark results and
existing simulation data. The present method was then adopted to numerically
predict the transverse and longitudinal effective thermal conductivities of
three-dimensional (3D) four-directional braided composites. Some corresponding
experiments based on the Hot Disk method were conducted to measure their
transverse and longitudinal effective thermal conductivities. The predicted
data fit the experiment data well. Influences of fiber volume fractions and
interior braiding angles on the effective thermal conductivities of 3D
four-directional braided composites were then studied. The results show that a
larger fiber volume fraction leads to a larger effective thermal conductivity
along the transverse and longitudinal directions; a larger interior braiding
angle brings a larger transverse thermal conductivity but a smaller one along
the longitudinal direction. It is also shown that for anisotropic materials the
periodic boundary condition is different from the adiabatic boundary condition
and for periodic microstructure unit cell the periodic boundary condition
should be used. Key words: effective thermal conductivities, anisotropic,
multi-relaxation-time, lattice Boltzmann method, three-dimensional
four-directional braided composites
