  In this paper we determine, in dimension three, the effective conductivities
of non periodic high-contrast two-phase cylindrical composites, placed in a
constant magnetic field, without any assumption on the geometry of their cross
sections. Our method, in the spirit of the H-convergence of Murat-Tartar, is
based on a compactness result and the cylindrical nature of the microstructure.
The homogenized laws we obtain extend those of the periodic fibre-reinforcing
case of [M. Briane and L. Pater. Homogenization of high-contrast two-phase
conductivities perturbed by a magnetic field. Comparison between dimension two
and dimension three. J. Math. Anal. Appl., 393 (2) (2012), 563 -589] to the
case of periodic and non periodic composites with more general transversal
geometries.
