Abstract: In this paper, by using the two-space method, homogenized equations for steady heat conduction in the composite material cylinders with dilutely-distributed elliptic cylinders of impurities are derived, and the explicit expressions for the corresponding effective heat conductivity of those which are concerned are obtained. It is also shown that the macroscopic heat conduction is anisotropic when the cross-sections of the impurity cylinders are unidliec-tionally oriented and isotropic when the angular distribution of the cross-sections is uniform.

Key words: nonlinear system, numerical solution, uniqueness and existence, algorithm