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1
Content available remote Sturm-Liouville eigenvalue problems with Mathematica
100%
Siedlecka U.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2011
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tom Vol. 10, nr 2
217-223
EN
In this paper, the power series method is applied to a class of Sturm-Liouville eigenproblems. The procedure of a symbolic solution to the problem in the Mathematica program for Airy's differential equation representing the considered class of S-L equations is presented. An example of numerical results is given.
2
Content available remote A contribution to the macroscopic modelling of hyperbolic heat transfer in a micro-periodic rigid conductor
100%
Siedlecka U.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2004
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tom Vol. 3, nr 1
195--200
EN
The aim of this contribution is to analyze the propagation of initial temperature disturbances on a macroscopic level. The main result of in this contribution is a formulation of an independent system of equations describing the above problem. The derived macroscopic heat transfer equations will be represented by the independent temperature disturbance equations and by the equation for the microscopic (averaged) temperature field. To make this note self-consistent we outline in the subsequent sections the basic preliminary concepts of the tolerance averaging technique. The detailed discussion of this technique can be found in [5].
3
Content available remote A contribution to the macroscopic modelling of hyperbolic heat transfer in a micro-periodic rigid conductor
100%
Siedlecka U.
Vibrations in Physical Systems
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2004
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tom Vol. 21
327--330
4
Content available Heat conduction in a finite medium using the fractional single-phase-lag model
100%
Siedlecka U.
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nr 2
5
Content available Radial heat conduction in a multilayered sphere
100%
Siedlecka U.
Journal of Applied Mathematics and Computational Mechanics
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2014
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tom Vol. 13, nr 4
109--116
EN
In this paper, an exact analytical solution of the radial heat conduction problem in a hollow multilayered sphere is presented. The boundary conditions of the third kind and perfect contact at the interfaces are assumed. The temperatures are obtained by using the Green’s function method. The Green’s functions are expressed in the form of the series of appropriate eigenfunctions.
6
Content available remote On a certain special problem of the quasi-linear heat conduction in a periodically-layered conductor
100%
Siedlecka U.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2009
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tom Vol. 8, nr 1
173-176
EN
The aim of contribution is to investigate a quasi-linear heat conduction in the two-phased periodically-spaced multilayered rigid conductor. The analysis is based on the tolerance averaging technique. Considerations are restricted to the heat conduction in the direction normal to the interfaces.
7
Content available remote Some remarks on the influence of initial temperature fluctuations on the heat transfer process in microperiodic laminated rigid conductors
63%
Wierzbicki E. , Siedlecka U.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2007
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tom Vol. 6, nr 1
269-276
EN
In the note a certain aspects of the interrelation between initial temperature fluctuations and the averaged temperature field in the microperiodic laminated rigid conductors are investigated. The tolerance averaging technique is t into account as a tool of modelling. It was shown that there exist initial values of initial temperature fluctuations that the heat transfer process is independent of them.
8
Content available Heat conduction problem in a two-layered hollow cylinder by using the Green's function method
63%
Kukla S. , Siedlecka U.
Journal of Applied Mathematics and Computational Mechanics
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2013
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tom Vol. 12, nr 2
45--50
EN
In this paper, a solution of the heat conduction problem in a two-layered hollow cylinder by using the Green’s function method is presented. The considerations concern the heat conduction in the radial direction while taking into account time-dependent boundary conditions. The continuity condition of the temperature at the dividing surface of the layers is written in the form of a Volterra integral equation.
9
Content available Laplace transform solution of the problem of time-fractional heat conduction in a two-layered slab
63%
Kukla S. , Siedlecka U.
Journal of Applied Mathematics and Computational Mechanics
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2015
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tom Vol. 14, nr 4
105--113
EN
In this paper the Laplace transformation for solving the problem of fractional heat conduction in a two-layered slab has been applied. The different orders of Caputo derivative in the time-fractional equation governed the heat transfer in the layers are assumed. The inverse Laplace transform by using a numerical method is determined. The numerical results obtained by using of the eigenfunctions method and by numerically inverting the Laplace transform are compared.
10
Content available remote On the isotropic properties of a hexagonal - type rigid conductor
63%
Siedlecka U. , Wierzbicki E.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2005
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tom 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].
11
Content available remote Finite difference method in Fourier equation internal case : direct formulas
63%
Biernat G. , Siedlecka U.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2011
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tom Vol. 10, nr 2
11-16
EN
In the paper we present the method of calculating the matrix block determinant which characterizes internal heat conduction in the (x, y, t) case.
12
Content available An analytical solution to the problem of time-fractional heat conduction in a composite sphere
63%
Kukla S. , Siedlecka U.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2017
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tom Vol. 65, nr 2
179--186
EN
An analytical solution to the problem of time-fractional heat conduction in a sphere consisting of an inner solid sphere and concentric spherical layers is presented. In the heat conduction equation, the Caputo time-derivative of fractional order and the Robin boundary condition at the outer surface of the sphere are assumed. The spherical layers are characterized by different material properties and perfect thermal contact is assumed between the layers. The analytical solution to the problem of heat conduction in the sphere for time-dependent surrounding temperature and for time-space-dependent volumetric heat source is derived. Numerical examples are presented to show the effect of the harmonically varying intensity of the heat source and the harmonically varying surrounding temperature on the temperature in the sphere for different orders of the Caputo time-derivative.
13
Content available An averaged isotropic model of nonstationary heat transfer in anisotropic hexagonal-type condustors
63%
Wierzbicki E. , Siedlecka U.
Journal of Theoretical and Applied Mechanics
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2004
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tom 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.
14
Content available Fractional heat conduction in multilayer spherical bodies
63%
Kukla S. , Siedlecka U.
Journal of Applied Mathematics and Computational Mechanics
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2016
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tom Vol. 15, nr 4
83--92
EN
In this paper an analytical solution of the time-fractional heat conduction problem in a spherical coordinate system is presented. The considerations deal the two-dimensional problem in multilayer spherical bodies including a hollow sphere, hemisphere and spherical wedge. The mathematical Robin conditions are assumed. The solution is a sum of time-dependent function satisfied homogenous boundary conditions and of a solution of the steady-state problem. Numerical example shows the temperature distributions in the hemisphere for various order of time-derivative.
15
Content available Green's function for heat conduction problems in a multi-layered hollow cylinder
63%
Kukla S. , Siedlecka U.
Journal of Applied Mathematics and Computational Mechanics
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2014
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tom Vol. 13, nr 3
115--122
EN
In this paper, derivation of the Green’s function for the heat conduction problems in a finite multi-layered hollow cylinder is presented. Formulation and solution of the problem includes an arbitrary number of the cylinder layers characterized by various thermal properties. At the interfaces perfect thermal contact was assumed. The Green’s function for the three-dimensional heat conduction problems in the cylindrical coordinate has been presented in the form of a product of two other Green’s functions.
16
Content available An analytical solution to the problem of time-fractional heat conduction in a composite sphere
63%
Kukla S. , Siedlecka U.
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2017
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nr 2
17
Content available remote On the modelling of a certain quasi-linear heat conduction problem in a two-phased laminated medium
63%
Siedlecka U. , Woźniak C.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2008
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tom Vol. 7, nr 1
181-184
EN
The aim of the contribution is to obtain a macroscopic model equation for the quasi-linear heat conduction in a two phased-laminated medium. The analysis will be based on the tolerance averaging technique.
18
Content available A solution to the problem of time-fractional heat conduction in a multi-layer slab
63%
Siedlecka U. , Kukla S.
Journal of Applied Mathematics and Computational Mechanics
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2015
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tom Vol. 14, nr 3
95--102
EN
In this paper a solution of the time-fractional heat conduction problem in a multilayer slab is presented. The boundary conditions of the third kind and the perfect contact at the interfaces are assumed. A space-time dependent volumetric heat source in the slab and time dependent surroundings temperatures are taken into account in the formulation of the problem. The solution is obtained in the form of a series expansion with respect to eigenfunctions of an auxiliary problem. A numerical example shows temperature distribution in the slab for various values of the order of the Caputo fractional derivative in the heat conduction equation.
19
Content available Fractional heat conduction in a sphere under mathematical and physical Robin conditions
63%
Kukla S. , Siedlecka U.
Journal of Theoretical and Applied Mechanics
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2018
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tom Vol. 56 nr 2
339--349
EN
In this paper, the effect of a fractional order of time-derivatives occurring in fractional heat conduction models on the temperature distribution in a composite sphere is investigated. The research concerns heat conduction in a sphere consisting of a solid sphere and a spherical layer which are in perfect thermal contact. The solution of the problem with a classical Robin boundary condition and continuity conditions at the interface in an analytical form has been derived. The fractional heat conduction is governed by the heat conduction equation with the Caputo time-derivative, a Robin boundary condition and a heat flux continuity condition with the Riemann-Liouville derivative. The solution of the problem of non-local heat conduction by using the Laplace transform technique has been determined, and the temperature distribution in the sphere by using a method of numerical inversion of the Laplace transforms has been obtained.
20
Content available remote On a macroscopic modelling of nonstationary heat conduction problems in hexagonal - type rigid conductors
63%
Siedlecka U. , Wierzbicki E.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2003
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tom 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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