Surface localized heat transfer in periodic composites

• Autorzy: Kula Dorota , Wierzbicki Ewaryst

Identyfikatory

DOI

10.2478/ama-2019-0017

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

heat transfer; periodic composites; homogenized model

• Wydawca: Oficyna Wydawnicza Politechniki Białostockiej
• Czasopismo: Acta Mechanica et Automatica
• Rocznik: 2019
• Tom: Vol. 13, no. 2
• Strony: 124--129
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Kula Dorota

• Faculty of Civil Engineering and Environmental Sciences, Department of Civil Engineering, Warsaw University of Life Sciences, ul. Nowoursynowska 166, 02-787 Warszawa, Poland

autor

Wierzbicki Ewaryst

• Faculty of Civil Engineering and Environmental Sciences, Department of Civil Engineering, Warsaw University of Life Sciences, ul. Nowoursynowska 166, 02-787 Warszawa, Poland

Bibliografia

• 1. Ariault J.L. (1983), Effective macroscopic description for heat conduction in periodic composites, International Journal of Heat and Mass Transfer, 26(6), 861–869.
• 2. Bensoussan A., Lions J.-L., Papanicolaou G. (2011), Asymptotic Analysis for Periodic Structures, American Math. Soc., ISBN-10: 0- 8218-5324-4 ISBN-13: 978-0-8218-5324-5.3
• 3. Jędrysiak J. (2010), Thermomechanics of laminates, plates and shells with functionally graded properties (in Polish), Technical University of Łódź Press.
• 4. Kula D. (2015), On the existence of the sinusoidal–type temperature fluctuations independently suppressed by the periodic two – phased conducting layer, Acta Scientarum Polonorum, Ser, Arch., 63(1), 77–92.
• 5. Kula D., Wierzbicki E. (2015), On the Fourier series implementation issue tolerance modelling thermal conductivity of periodic composites, Engineering Transaction, 63(1), 77–92.
• 6. Michalak B. (2010), Thermomechanics of solids with a certain nonhomogeneous microstructure: tolerance approximation technique (in Polish), Technical University of Łódź Press.
• 7. Ostrowski P.: (2017), Tolerance modelling of Thermomechanics in microstructured media, Technical University of Łódź Press.
• 8. Wodzyński Ł., Kula D., Wierzbicki E. (2018). Effective macroscopic description for heat conduction in periodic composites, Proceedings of the 22nd International Conference on Computer Methods in Mechanics: Lublin, Poland, 13–16 September 2017, eds. Jerzy Podgórski, Ewa Blazik Borowa, Jarosław Bęc, Tadeusz Burczyński, Mieczysław Kuczma, Jarosław Latalski, Jerzy Warmiński. - AIP Publishing, 1–8.
• 9. Woźniak Cz., Wierzbicki E.: (2000), Averaging techniques In thermomechanics of composite solids, Tolerance averaging versus homogenization, Technical University of Częstochowa Press.
• 10. Woźniak M., Wierzbicki E., Woźniak Cz. (2002), A macroscopic model of the diffusion and heat transfer processes in a periodically micro-stratified solid layer, Acta Mechanica, 157, 175–185.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).