Engineering Transactions, 63, 1, pp. 77–92, 2015

The Fourier Series Implementation Issues in the Tolerance Modeling of Thermal Conductivity of Periodic Composites

Dorota KULA
Warsaw University of Life Sciences 02-787 Warsaw Nowoursynowska 166 PhD student in Technical University of Łódź
Poland

Ewaryst WIERZBICKI
Warsaw University of Life Sciences 02-787 Warsaw Nowoursynowska 166
Poland

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.
Keywords: tolerance averaging, heat conduction, periodic conductors, boundary effect, Fourier series.
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References

Woźniak Cz., Wierzbicki E., Averaging techniques In thermomechanics of composite solids, Tolerance averaging versus homogenization, Wydawnictwo Politechniki Częstochowskiej, Częstochowa 2000.

Nagórko W., Wybrane metody modelowania płyt niejednorodnych, Publications of Warsaw University of Life Sciences – SGGW, Warsaw 2008.

Woźniak Cz. (Ed.), Thermomechanics of microheterogeneous solids and structures. Tolerance averaging approach, Wydawnictwo Politechniki Łódzkiej, Łódź 2009

WoźniakCz. (Ed.), Developments In Mathematical Modeling and Analysis of Microstructured Media, Wydawnictwo Politechniki Śląskiej, Gliwice 2010.

Jędrysiak J. , Termomechanika laminatów, płyt i powłok o funkcyjnej gradacji własności, Wydawnictwo Politechniki Łódzkiej, Łódź 2010.

Michalak B., Termomechanika ciał z pewną niejednorodną mikrostrukturą: technika tolerancyjnej aproksymacji, Wydawnictwo Politechniki Łódzkiej, Lódź 2010.

Wierzbicki E., Kula D., Mazewska M., 2014, O fourierowskiej realizacji tolerancyjnego modelowania zagadnień przewodnictwa ciepła prostych kompozytów periodycznych, w: Modelowanie struktur i konstrukcji inżynierskich, red. Grzegorz Jemielita, Monika Wągrowska, Wydawnictwo SGGW, Warszawa, str. 253-265

Nagórko W., Wągrowska M., A contribution to model ling of composite solids, J. Theor. Appl. Mech., 2002, 40, 149-158.

Cielecka I., Jędrysiak J., A non-asymptotic model of dynamics of honeycomb lattice-type plates, J. Sound and Vibration, 2006, 296, 130-149.

Kula D., Mazewska M, Wierzbicki E., Some remarks on the tolerance averaging of heat conduction In chessboard palisade-type periodic composites, Scientific Review, Engineering and Enviromental Sciences Vol. 21 (3), Nr 57, 131-140, Warszawa 2012.

Mazewska M., Tolerance modeling of boundary effect behavior in hexagonal-type composites, doctoral dissertation, Szkoła Główna Gospodarstwa Wiejskiego, Warszawa 2013.

Mazewska M., Kula D., Wierzbicki E., On the boundary effect behavior in the hexagonal- type biperiodic structures with rotational symmetry, Journal of Applied Mathematics and Computational Mechanics, 2 2014, 134-144.

Mazewska M., Wierzbicki E., Modelowanie tolerancyjne przewodnictwa ciepła

w kompozytach o strukturze dwukierunkowo-periodycznej, Acta Scientarum Polonarum, Seria Architectura 12 (1) 2013, 3-17, Warszawa 2013.

Wierzbicki E., Woźniak Cz., On the dynamic behaviour of honeycomb based composite solids, Acta Mechanica, 2000, 141, 161-172.

Matysiak S.J., Jevtushenko A.A., Ivanyk E.G. (2002), Contact temperature and wear of composite elements during braking, Int. J. Heat and Mass Transfer, Vol. 45, 193-199.




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