The fourier series implementation issues in the tolerance modeling of thermal conductivity of periodic composites

The aim of this study is to propose a partially-averaged model of heat conduction in simple micro-periodic composite conductors. In this model, as in many known models of this type, the type of microstructure is represented by the single scalar parameter, which is referred to as microstructure parameter. Unlike other known averaged models of this type, the resulting model allows for the formulation exact solutions to initial-boundary value problems formulated for the parabolic heat conduction equation. If tolerance approximations will be applied to averaged temperature filed this model becomes asymptotically exact model. The term “asymptotically exact model” refers to models in the framework of which solutions coincident with exact solutions to the mentioned problems for the parabolic heat transfer equation when the microstructure parameter tends to zero.