<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

Surface Localized Heat Transfer in Periodic Composites

Faculty of Civil Engineering and Environmental Sciences, Department of Civil Engineering

Acta Mechanica et Automatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"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...

Surface Localized Heat Transfer in Periodic Composites

Published Online: Jul 25, 2019

Page range: 124 - 129

Received: Apr 18, 2019

Accepted: Jun 26, 2019

DOI: https://doi.org/10.2478/ama-2019-0017

Keywords
Heat transfer, periodic composites, homogenized model

© 2019 Dorota Kula et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Surface Localized Heat Transfer in Periodic Composites

Published Online: Jul 25, 2019

Page range: 124 - 129

Received: Apr 18, 2019

Accepted: Jun 26, 2019

DOI: https://doi.org/10.2478/ama-2019-0017

KeywordsHeat transfer, periodic composites, homogenized model

© 2019 Dorota Kula et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Heat transfer, periodic composites, homogenized model