Surface Localized Heat Transfer in Periodic Composites

A characteristic feature of the description of physical phenomena formulated by an appropriate boundary or initial-boundary value problem and occurring in microstructured materials is the investigation of the unknown field in the form of decomposition referred to as micro-macro hypothesis. The first term of this decomposition is usually the integral average of the unknown physical field. The second term is a certain disturbance imposed on the first term and is represented in the form of a finite or infinite number of singleton fluctuations. Mentioned expansion is usually referred to as a two-scale expansion of the unknown physical field. In the paper, we purpose to apply two-scale expansion in the form of a certain Fourier series as a result of an applying Surface Localization of the unknown field. The considerations are illustrated by two examples, which results in analytical approximated solutions to the Effective Heat Conduction Problem for periodic composites, including the full dependence on the microstructure length parameter.