Conduction in a two-component composite film, subject to a magnetic fi
eld, is treated numerically with an interface integral equation method
. The composite is chosen to be a square array of starfish-shaped incl
usions in an anisotropic matrix. Highly accurate calculations are perf
ormed and used to investigate microstructure-independent relations bet
ween the effective conductivity tensor elements. Asymptotic studies of
closely spaced superconducting and insulating disks in an anisotropic
matrix verify theoretical results. All the results in this paper are
valid for the analog to the Hall effect in heat conduction, the Righi-
Leduc effect.