Fourier variant homogenization of the heat transfer processes in periodic composites

• Autorzy: Wierzbicki E. , Kula D. , Wodzyński Ł.
• Języki publikacji: EN

Abstrakty

EN

The well-known parabolic Heat Transfer Equation is a simplest recognized description of phenomena related to the heat conductivity in solids with microstructure. However, it is a tool difficult to use due to the discontinuity of coefficients appearing here. The purpose of the paper is to reformulate this equation to the form that allows to represent solutions in the form of Fourier’s expansions. This equivalent re-formulation has the form of infinite number of equations with Fourier coefficients in expansion of the temperaturę field as the basic unknowns. The first term in Fourier representation, being an average temperature field, should satisfy the well-known parabolic heat conduction equation with Fourier coefficients as fields controlling average temperature behavior. The proposed description takes into account changes of the composite periodicity accompanying changes in the variable perpendicular to the surfaces separating components, concerning FGM-type materials and can be treated as the asymptotic version of Heat Transfer Equation obtained as a result of a certain limit passage where the cell size remains unchanged.

Słowa kluczowe

EN

temperature fluctuations; homogenization; tolerance modelling

PL

fluktuacja temperatury; homogenizacja; modelowanie tolerancyjne

• Wydawca: Wydawnictwo Politechniki Łódzkiej
• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 2018
• Tom: Vol. 22, nr 3
• Strony: 719--726
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Wierzbicki E.

• Departments of Civil Engineering, Faculty of Civil and Enviromental Engineering, Warsaw University of Life Sciences, Warsaw, Poland

autor

Kula D.

• Departments of Civil Engineering, Faculty of Civil and Enviromental Engineering, Warsaw University of Life Sciences, Warsaw, Poland

autor

Wodzyński Ł.

• Departments of Civil Engineering, Faculty of Civil and Enviromental Engineering, Warsaw University of Life Sciences, Warsaw, Poland

Bibliografia

• [1] Bensoussan, A., Lions, J.-L. and Papanicolaou, G.: Asymptotic Analysis for Periodic Structures, American Math. Soc., ISBN-10: 0-8218-5324-4, ISBN-13: 978-0-8218-5324-5, 2011.
• [2] Ariault, J.L.: Effective macroscopic description for heat conduction in periodic composites, International Journal of Heat and Mass Transfer, 26, 6, 861-869, DOI: 10.1016/S0017-9310(83)80110-0, 1983.
• [3] Woźniak, Cz. and Wierzbicki, E.: Averaging techniques In thermomechanics of composite solids, Tolerance averaging versus homogenization, Technical University of Częstochowa Press, Częstochowa, 2000.
• [4] Woźniak, C. (Ed.): Thermomechanics of microheterogeneous solids and structures. Tolerance averaging approach, Technical University of Łódź Press, Łódź 2009.
• [5] Woźniak, C. (Ed.): Developments In Mathematical Modeling and Analysis of Microstructured Media, Silesian University Press, Gliwice 2010.
• [6] Jędrysiak, J.: Termomechanics of laminates, plates and shells with functionally graded properties /in Polish/, Technical University of Łódź Press, Łódź 2010.
• [7] Michalak, B.: Termomechanics of solids with a certain nonhonmogeneous microstructure: tolerance approximation technique /in Polish/, Technical University of Łódź, Łódź, 2010.
• [8] Kula, D.: Assessment of the impact of the geometric structure of periodic composites on the intensity of damping the fluctuation of boundary loads /PhD dissertation in Polish/, Faculty of Civil Engineering, Architecture and Environmental Engineering, Łódź University of Technology, 2016.
• [9] Kula, D. and Wierzbicki, E.: On the Fourier series implementation issue tolerance modeling thermal conductivity of periodic composites, Engineering Transaction, 63, 1, 77-92, 2015.
• [10] Kula, D.: 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, 2015.
• [11] Woźniak, M., Wierzbicki, E. and Woźniak, C.: A macroscopic model of the diffusion and heat transfer processes in a periodically micro-stratified solid layer, Acta Mechanica, 157, 175-185, 2002.
• [12] Kula, D., Wierzbicki, E., Witkowska-Dobrev, J. and Wodzyński, Ł.: Fourier variant homogenization treatment of one impulse Boundary effect behaviour, this issue, 2018.
• [13] Wodzyński, Ł., Kula, D. and Wierzbicki, E.: Transport of even and odd temperature fluctuations across the chess-board type periodic composite, this issue, 2018.

Uwagi

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