Application of MFS for determination of effective thermal conductivity of unidirectional composites with linearly temperature dependent conductivity of constituents

In this paper the problem of the effective conductivity in composite material is considered. It is assumed that the thermal conductivity coefficients of both the matrix and fibres materials are temperature-dependent. It yields the temperature-dependency of the effective thermal conductivity. To determine the effective thermal conductivity a unit-cell approach is used, i.e. heat flow in repeated element, which consists of one fibre in the matrix, is considered. It leads to 2-D nonlinear boundary value problems in matrix and fibre regions. In the paper, it is proposed to solve the given nonlinear boundary value problem by Picard iteration. For every iteration step, the linear boundary value problem with two uncoupled linear partially differential equations and coupled boundary conditions is solved. The method of fundamental solution, supported by radial basis functions approximation, is implemented to obtain the required solutions. The numerical experiment has been performed. The results of the experiment and some conclusions are included as well.