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1
Content available The determinants of the block band matrices based on the n-dimensional Fourier equation
Biernat G., Lara-Dziembek S., Pawlak E.
Journal of Applied Mathematics and Computational Mechanics
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2015
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Vol. 14, nr 3
5--15
EN
This paper contains the method of calculating the determinant of the block band matrix on the example of n-dimensional Fourier equation using the FDM.
2
Content available The n-dimensional Fourier equation with the Robin's boundary condition using the finite difference method
Biernat G., Lara-Dziembek S., Pawlak E.
Journal of Applied Mathematics and Computational Mechanics
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2014
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Vol. 13, nr 3
13--20
EN
The article is a continuation of the considerations on the three-dimensional Fourier equation supplemented by the third boundary condition (the Robin’s condition). The paper is based on the Finite Difference Method.
3
Content available The 3D Fourier equation with the Robin’s boundary condition using the finite difference method
Biernat G., Lara-Dziembek S., Pawlak E.
Journal of Applied Mathematics and Computational Mechanics
|
2014
|
Vol. 13, nr 1
5--11
EN
This article is a continuation of the discussion on the two-dimensional Fourier equation with Robin’s boundary condition. In the paper the Finite Difference Method is applied.
4
Content available The finite difference method in the 2D Fourier equation with Robin’s boundary condition
Biernat G., Lara-Dziembek S., Pawlak E.
Journal of Applied Mathematics and Computational Mechanics
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2013
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Vol. 12, nr 4
5--11
EN
This paper contains the application of the Finite Difference Method in the two-dimensional Fourier equation using Robin’s boundary condition (the third boundary condition).
5
Content available The determinants of the block band matrices based on the n-dimensional Fourier equation. Part 1
Biernat G., Lara-Dziembek S., Pawlak E.
Journal of Applied Mathematics and Computational Mechanics
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2013
|
Vol. 12, nr 3
5--13
EN
This paper contains the method of calculating the determinant of the block band matrix on the example of n-dimensional Fourier equation using the Finite Difference Method.
6
Content available The determinants of the block band matrices based on the n-dimensional Fourier equation. Part 2
Biernat G., Lara-Dziembek S., Pawlak E.
Journal of Applied Mathematics and Computational Mechanics
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2013
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Vol. 12, nr 3
15--20
EN
This work is a continuation of the considerations concerning the determinants of the band block matrices on the example of the n-dimensional Fourier equation (work Part 1). The discussion will concern the special case called the three-dimensional Fourier equation.
7
Content available remote The numerical solution of the transient heat conduction problem using the lattice Boltzmann method
Kałuża G.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2012
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Vol. 11, nr 1
23-30
EN
The implementation of the lattice Boltzmann method (LBM) for the solutionof the transient heat conduction problem is presented. The one dimensional task is considered and the different boundary conditions, specifically the Dirichlet, Neumann and Robin ones are taken into account. The D1Q2 lattice model is applied. To check the accuracy of the LBM algorithm, the same problems have been solved using the explicit variant of the finite difference method. In the final part of the paper, the results of computations are shown and the conclusions are formulated.
8
Content available remote The determinants of the block matrices in the 3D Fourier equation
Biernat G., Lara-Dziembek S., Pawlak E.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2012
|
Vol. 11, nr 4
5-10
EN
In the paper we present the method of calculating the determinant of the block matrix which characterizes internal heat conduction in the 3D case. The Finite Difference Method can be used.
9
Content available remote A new variant of temporary temperature field correction method
Mochnacki B., Majchrzak E., Szopa R.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2012
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Vol. 11, nr 3
125-135
EN
The paper presents the possibilities of numerical solution of the non-linear boundary-initial problem described by the Fourier equation. In particular, the equation containing the temperature-dependent thermophysical parameters (volumetric specific heat and thermal conductivity) is considered. The problem presented in this paper is connected with the artificial linearization of the task discussed (at the stage of numerical computations), in other words, the new numerical procedure which allows one to remodel the solution obtained for linear problem at the time level t + Δ t to the other solution corresponding to nonlinear one. The procedure discussed can be a very effective supplement for different variants of the boundary element method which, as a rule, requires a linear form of the energy equation. In the final part the examples of numerical simulations and the conclusions can be found.
10
Content available remote Finite difference method in Fourier equation internal case : direct formulas
Biernat G., Siedlecka U.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2011
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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.
11
Content available remote Finite difference method in the Fourier equation with Newton's boundary conditions direct formulas
Biernat G., Mazur J.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2008
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Vol. 7, nr 2
123-128
EN
In the paper we gve the direct FDM formulas for the solutions of the Fourier equation with the Newton boundary condition in the (x, t) case.
12
Gruntowe wymienniki ciepła - metody obliczeń
Niezgoda-Żelasko B., Zalewski W.
Inżynieria Chemiczna i Procesowa
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2001
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T. 22, z. 3D
1007--1012
PL
W pracy omówiono metody obliczeń poziomych kolektorów gruntowych. Dokonano porównania wyników obliczeń otrzymanych metodami uproszczonymi z wynikami uzyskanymi na drodze rozwiązania równania Fouriera dla przypadku gruntowego wymiennika ciepła.
EN
In the paper the methods of calculation of the horizontal ground-coupled heat exchangers have been presented. For chosen example the comparison of simplified methods, with calculation results obtained for Fourier equation applied for the ground heat exchangers has been shown.
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