Edge effects for heat flux in fibrous composites

The temperature fields in deterministic and random composites near the boundary are theoretically investigated in the stationary two-dimensional statement. The temperature distribution and the heat flux are expressed in terms of a series in the radius of ideally conducting fibers. Truncation of the series yields approximate analytical formulas including locations of fibers in symbolic form. It is achieved by extension of Mityushev’s analytical formulas for unbounded composites to boundary value problems. Simple structure of these formulas allows to compute the heat flux practically for arbitrary number of inclusions. It is established that a large number of randomly packed inclusions drastically complicate structure of the local temperature fields which becomes irregular at the mesoscopic scale by comparison with regular composites.