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1
Content available remote The fourier series implementation issues in the tolerance modeling of thermal conductivity of periodic composites
Kula D., Wierzbicki E.
Engineering Transactions
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2015
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Vol. 63, iss. 1
77--92
EN
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.
2
Content available remote On the isotropic properties of a hexagonal - type rigid conductor
Siedlecka U., Wierzbicki E.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2005
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Vol. 4, nr 1
239-245
EN
A new macroscopic model for the non-stationary heat transfer processes in a periodic hexagonal-type anisotropic rigid conductor is formulated. The main aim of this contribution is to show that the macroscopic properties of this conductor are transversally isotropic. The tolerance averaging technique as a tool of macroscopic modelling is taken into account [1].
3
Content available An averaged isotropic model of nonstationary heat transfer in anisotropic hexagonal-type condustors
Wierzbicki E., Siedlecka U.
Journal of Theoretical and Applied Mechanics
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2004
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Vol. 42 nr 4
755-770
EN
A new macroscopic model for non-stationary heat transfer processes in a periodic hexagonal-type anisotropic rigid conductor is formulated. The main aim of this contribution is to show that the macroscopic properties of such a conductor are transversally isotropic. The tolerance averaging technique as a tool of macroscopic modelling is taken into account.
PL
Celem pracy jest sformułowanie makroskopowego modelu niestacjonarnego przepływu ciepła w lokalnie anizotropowych heksagonalnych przewodnikach prostych. Jako narzędzie modelowania zastosowano technikę tolerancyjnego uśredniania. Sformułowano warunki wystarczające na to, by otrzymane równania były izotropowe. Zasadniczym rezultatem pracy jest wykazanie, że własności makroskopowe lokalnie anizotropowech przewodników mogą być transwersalnie izotropowe.
4
Content available remote On a macroscopic modelling of nonstationary heat conduction problems in hexagonal - type rigid conductors
Siedlecka U., Wierzbicki E.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2003
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Vol. 2, nr 1
169--174
EN
The aim of this contribution is to formulate a macroscopic model for the nonstationary heat transfer processes in an arbitrary hexagonal - type rigid conductor with isotropiclocal material. As a tool of modelling the tolerance averaging technique is taken into account [1]. It is shown that under certain conditions the obtained model equations are isotropic.
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