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  1. 7 Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
  2. 7 Scientific Research of the Institute of Mathematics and Computer Science
  3. 2 International Journal of Applied Mechanics and Engineering
  4. 2 Journal of Power Technologies
  5. 2 Problems of Applied Sciences
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  1. 1 2023
  2. 1 2022
  3. 2 2019
  4. 2 2018
  5. 1 2017
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  1. 4 Majchrzak E.
  2. 2 Czajkowski A. A.
  3. 2 Drozdek J.
  4. 2 Freus K.
  5. 2 Hussain A.
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1
Analiza rozruchu termicznego wysokoobrotowego wymiennika ciepła
100%
Wilk J.
Prace Naukowe Instytutu Techniki Cieplnej i Mechaniki Płynów Politechniki Wrocławskiej. Konferencje
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1998
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tom Vol. 53, nr 9
874-879
PL
Przeprowadzono obliczenia czasu rozruchu termicznego wysokoobrotowego ssąco-tłoczącego wymiennika ciepła. Dokonano analizy tego czasu pod względem intensywności zachodzących procesów niestacjonarnych. Zastosowano metodę różnic skończonych w numerycznym rozwiązaniu równania nieustalonego przewodzenia ciepła w materiale wirnika regeneratora. Przeanalizowano jeden typ porowatego wirnika z promieniowo usytuowanymi kanalikami o stałym kołowym polu przekroju powierzchni, wirującego ze stałą określoną prędkością obrotową. Uwzględniono wpływ wirowania na wielkość współczynnika wymiany ciepła przy powierzchni kanalika wirnika.
EN
The numerical analysis was applied for transient heat transfer conduction in the rotor of high-speed sucking and forcing heat exchanger. The calculations were referred to the porous rotor with radial ducts of constant cross-section area and constant rotional speed. The influence of the rotating on the value of the heat transfer coefficient in the duct of the rotor was taken into accound. The finite difference method was used. As a result the characteristics of the changes of the rotor temperature during the thermal starting time was obtained. The analysis of the intensity of nonstationary processes was done.
2
Numeryczne rozwiązanie kwaziliniowego zagadnienia początkowo-brzegowego dla równania typu parabolicznego
100%
Boychuk V.
Zeszyty Naukowe. Matematyka / Politechnika Opolska
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2001
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tom z. 17
113-118
PL
W artykule rozważano numeryczne rozwiązanie niestacjonarnego kwaziliniowego zagadnienia brzegowego typu parabolicznego. Zaproponowano algorytm rozwiązywania i podano wyniki przykładowych obliczeń.
EN
Numerical solution for non-stationary quasi-linearly parabolic initial-boundary-valued problem is considered. Algorithm for its solution and some results of calculations are presented.
3
Content available remote Numerical solution of fractional Euler-Lagrange equation with multipoint boundary conditions
88%
Błaszczyk T. , Ciesielski M.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2011
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tom Vol. 10, nr 2
43-48
EN
In this paper we consider an ordinary fractional differential equation containing a composition of left and right fractional derivatives. This type of equation is known in literature as the boundary conditions. We proposed a numerical scheme using the finite difference method. In the final part of the paper, examples of the solutions are shown.
4
Content available remote Numerical solution of heat diffusion equation using the generalized FDM
75%
Lara-Dziembek S. , Pawlak E.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2007
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tom Vol. 6, nr 1
117-125
EN
In the paper the numerical solution of boundary-initial problem described by the Fourier equation and adequate conditions is discussed. The algorithm bases on the concept of generalized finite difference method (GFDM). In the first part the mathematical formulation of the problem and a short description of GFDM algorithm are presented. In the second part the examples of numerical computations are shown. On the stage of computation the explicit version of GFDM is used.
5
Content available remote Numerical solution of bioheat transfer equation by means of the dual reciprocity BEM
75%
Drozdek J. , Majchrzak E.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2007
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tom Vol. 6, nr 1
47-56
EN
Application of the standard boundary element method for numerical solution of the bioheat transfer equation requires discretization not only the boundary but also the interior of the domain considered. It results from the presence of internal heat sources in the biological tissue (metabolic and perfusion sources). In this paper the variant of the BEM which is connected only with the boundary discretization is presented. It is the essential advantage of the algorithm proposed in comparison with the classical one. As example, the problem of temperature field computations in heating biological tissue domain is solved.
6
Content available remote Application of the BEM for numerical solution of nonlinear diffusion equation
75%
Majchrzak E. , Freus K. , Freus S.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2007
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tom Vol. 6, nr 1
159-167
EN
In the paper the nonlinear diffusion equation is considered, this means the volumetric specific heat and thermal conductivity are temperature dependent. To solve the problem by means of the boundary element method the Kirchhoff transformation is introduced and for each time step the mean values of these parameters are taken into account. In the final part of the paper the results of computations are shown.
7
Content available remote The stability of motion of slab in continuous casting of steel forced by oscillating caster
75%
Ciekot A.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2004
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tom Vol. 3, nr 1
19--26
EN
In this paper the motion of the slab has been analysed. The equation of motion for the slab was solved numerically. The stability of the obtained solutions was determined with regard to the dependence of the casting speed and the intensity of heat exchange in the primary and secondary cooling zone.
8
Content available Non-perturbative solution for hydromagnetic flow over a linearly stretching sheet
75%
Makinde O. D. , Mahabaleswar U. S. , Maheshkumar N.
International Journal of Applied Mechanics and Engineering
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2013
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tom Vol. 18, no. 3
935--943
EN
In this paper, the Adomian decomposition method with Padé approximants are integrated to study the boundary layer flow of a conducting fluid past a linearly stretching sheet under the action of a transversely imposed magnetic field. A closed form power series solution based on Adomian polynomials is obtained for the similarity nonlinear ordinary differential equation modelling the problem. In order to satisfy the farfield condition, the Adomian power series is converted to diagonal Padé approximants and evaluated. The results obtained using ADM-Padé are remarkably accurate compared with the numerical results. The proposed technique can be easily employed to solve a wide range of nonlinear boundary value problems.
9
Content available remote Analiza opływu układów 3-wymiarowych w oparciu o metodę Eulera
75%
Kubryński K.
Zeszyty Naukowe. Cieplne Maszyny Przepływowe - Turbomachinery / Politechnika Łódzka
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2000
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tom nr 117, vol. 1
79-84
PL
Referat omawia analizę 3-wymiarowego opływu ściśliwego w oparciu o równania Eulera. Schemat numeryczny oparto na metodzie Roe rozdzielania różnic strumieni Dla uzyskania nieoscylacyjnego rozwiązania drugiego rzędu zastosowano schemat MUSCLE z ogranicznikami strumieni, zmodyfikowanymi dla zachowania drugiego rzędu dokładności w obszarach gładkich ekstremów. Pozwoliło to zmniejszyć dysypację i poprawić dokładność wyznaczenia oporu. Siatka obliczeniowa generowana jest w oparciu o metodę algebraiczną (transfinite interpolation) i shemat wieloblokowy, pozwalając na łatwą generację siatki dla złożonych układów.
EN
The paper describes the method for analysis of 3-dimensional compressible flow using Euler equations Solution is based on Roe flux difference spliting method To find non-oscilatory sulution the second order MUSCLE scheme with flux luniters is applied, with modifications for preserving higher order solution m the regions with smooth extrema. As result the dissipation is reduced and the drag is more accurate compared to the basic scheme. The computational grid is generated using algebraic transfinite interpolation method and multi-block topology.
10
Content available remote Numerical solution of the inverse parametric problem using the boundary element method
75%
Majchrzak E. , Freus K.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
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2002
|
tom Vol. 1, nr 1
125--132
EN
In the paper the application of the boundary element method for numerical solution of the inverse parametric problem is presented, this means the temperature dependent thermal conductivity is identified. The thermal conductivity of the material appears in the fundamental Fourier law and also in the basic energy equation (the Kirchhoff-Fourier equation). This parameter is determined on the basis of physical experiments. The numerical identification of the thermal conductivity is possible on the basis of the knowledge of temperature field in the\ domain considered.
11
Content available remote Application of the multiple reciprocity BEM for numerical solution of bioheat transfer equation
75%
Majchrzak E. , Drozdek J. , Kałuża G.
Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
|
2002
|
tom Vol. 1, nr 1
113--124
EN
Application of the standard boundary element method for numerical solution of the bioheat transfer equation requires discretization not only the boundary but also the interior of the domain considered. In this paper the variant of the BEM which is connected only with the boundary discretization is presented. It is the essential advantage of the algorithm proposed in comparison with the classical one. As the example, the problem of the pair of vessels (artery and vein) surrounded by the tissue is analyzed, and the temperature field in the tissue sub-domain is found.
12
Content available remote The Analysis and Applicability Conditions of Tshebyshev’s Theory Concerning Garment Patterns
63%
Raszka J. , Kobza W.
Fibres & Textiles in Eastern Europe
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2005
|
tom Vol. 13, no. 3 (51)
41--43
EN
Many publications related to the garment industry refer to Tshebyshev’s works about garment patterns. This is because his point of view allows us to hope that an engineering method for garment design can someday be created. This work is an attempt to verify the equations Tshebyshev obtained, and to compare their precision with a numerical solution. To this end, the value of the deformation angle of the network determined in accordance with Tshebyshev’s theory was compared with the deformation angle obtained by the same method but using modern computer systems. The results obtained form the conclusions to this work.
PL
Wiele publikacji, dotyczących przemysłu odzieżowego, odwołuje się do pracy Czebyszewa związanej z konstrukcją odzieży. Jest to wynikiem tego, że punkt widzenia Czebyszewa daje nam nadzieję na opracowanie inżynierskiej metody konstrukcji odzieży. Praca ta omawia próbę zweryfikowania równań przedstawionych przez Czebyszewa oraz porównanie dokładności ich rozwiązań z obliczeniami numerycznymi. W pracy porównano kat deformacji według teorii Czebyszewa z kątem deformacji otrzymanym tą samą metodą, lecz przy zastosowaniu nowoczesnych systemów komputerowych. Otrzymane wyniki zostały przedstawione w pracy.
13
Content available remote A new approach for solving Bratu’s problem
63%
Ghomanjani F. , Shateyi S.
Demonstratio Mathematica
|
2019
|
tom Vol. 52, nr 1
336--346
EN
A numerical technique for one-dimensional Bratu’s problem is displayed in this work. The technique depends on Bernstein polynomial approximation. Numerical examples are exhibited to verify the efficiency and accuracy of the proposed technique. In this sequel, the obtained error was shown between the proposed technique, Chebyshev wavelets, and Legendre wavelets. The results display that this technique is accurate.
14
Content available remote Numerical modelling of effect of drying rate on kaolin fracturing
63%
Musielak G. , Śliwa T. , Stasiak M.
Materiały Ceramiczne
|
2013
|
tom T. 65, nr 1
61--64
EN
Non-uniform distributions of moisture inside the porous materials during drying results in compressive stresses inside the material and tensional ones close to the surface. The tensional stresses together with brittleness of dry material are the reasons of fracturing of the material. In the paper the model describing the fracturing is used to examine the influence of the drying rate on fracturing. It is shown that slow drying does not involve any cracks. The quicker drying generates higher risk of fracturing, and the final fracture pattern is more complicated.
PL
Niejednorodny rozkład wilgoci wewnątrz porowatych materiałów podczas suszenia wywołuje naprężenia ściskające wewnątrz materiału i rozciągające w pobliżu powierzchni. Naprężenia rozciągające wraz z kruchością suchego materiału są przyczyną jego pękania. W artykule wykorzystano model opisujący pękanie do zbadania wpływu szybkości suszenia na pękanie. Wykazano, że powolne suszenie nie pościąga za sobą powstawania pęknięć. Szybsze suszenie powoduje większe ryzyko pękania, a końcowy obraz przebiegu pęknięć jest bardziej skomplikowany.
15
Content available Application of analytical solution for extended surfaces on curved and squared ribs
63%
Brestovič T. , Jasminská N. , Lázár M.
Acta Mechanica et Automatica
|
2015
|
tom Vol. 9, no. 2
75--83
EN
The presented article discusses how to increase heat transfer through ribbed surfaces and it is oriented to the mathematical representation of temperature fields and the total thermal flow. The complexity of solving for some types of ribs with variable cross-section requires the application of numerical methods, which are applied consequently to the planar rib as well. In this case there was chosen the finite-difference method (FDM). During solution of the cylindrical ribs the FDM method is preferably used directly with regard to the complexity of solving for infinite sums and improper integrals in Bessel functions. In conclusion is assessed the application suitability of the calculation procedure applied to curved ribs. This procedure is usually used to planar ribs. At the same time it is pointed out the possibility of using this method for calculation of the total thermal flow through cylindrical ribs, which have got the squared form.
16
Content available remote Eigenvalue approach to study generalized thermoelastic problem for an infinitely long circular cylinder
63%
Lahiri A. , Sarkar N.
International Journal of Applied Mechanics and Engineering
|
2011
|
tom Vol. 16, no 3
731-745
EN
In this work, a one-dimensional problem for an infinitely long circular cylinder is solved by an eigenvalue approach. The outer surface of this cylinder is traction free and subjected to a thermal shock. The problem is in the context of the theory of generalized thermoelasticity with one relaxation time parameter. The Laplace transform technuiqe is used. The solution in the transformed domain is obtained by a direct eigenvalue approach. The inversion of the Laplace transform solution is evaluated numerically. Numerical results are obtained and represented graphically for two cases and finally compared with the current results available in the literature.
17
Content available remote Numerical solution of a Casson nanofluid flow and heat transfer analysis between concentric cylinders
63%
Hussain A. , Javed F. , Nadeem S.
Journal of Power Technologies
|
2019
|
tom Vol. 99, nr 1
25--30
EN
The current investigation deals with heat transfer of a non-newtonian fluid between two concentric cylinders. To describe the behavior of non-Newtonian fluid casson fluid model is used because of its various useful applications. The governing partial differential equations suchlike continuity, momentum, energy, solute concentration and nano-particle fraction equations are transubstantiated into non-linear ordinary differential equations with the assistance of resemblance alteration. Then those are numerically solved by the very efficient shooting method. Additionally, influences of distinct involved parameters are interpreted graphically. It is adhered that the velocity field shows inclined behavior due to the increment in the values of the casson parameter, so long as enhancing the temperature.
18
Content available Modelowanie i symulacja numeryczna pękania materiałów porowatych podczas procesu suszenia
63%
Musielak G. , Śliwa T.
Inżynieria i Aparatura Chemiczna
|
2010
|
tom Nr 3
81-82
PL
Naprężenia suszarnicze indukowane wewnątrz kruchego (suchego) materiału są przyczyną jego pękania. W pracy wykorzystano prosty model transportu masy dla uzyskania rozkładu wilgoci w materiale. Następnie materiał zamodelowano w postaci cząstek połączonych między sobą sprężyście. Parametry materiałowe określono doświadczalnie. Rozwiązano dwuwymiarowy problem początkowo-brzegowy, którego rezultaty pokazują możliwą drogę inicjacji i wzrostu pęknięć podczas suszenia.
EN
The drying induced stresses inside brittle (dry) material are responsible for its fracturing. A simple model of mass transfer is used to obtain the moisture content distribution. Then, material is modelled as a set of small particles interconnected elastically. The dependencies between material parameters and the moisture content were determined experimentally. The two-dimensional initial-boundary problem was solved. The results show possible way of drying induced cracks initiation and generation.
19
Content available remote Mathematical analysis of mass and heat transfer through arterial stenosis
51%
Hussain A. , Sarwar L. , Akbar S. , Malik M. Y.
Journal of Power Technologies
|
2022
|
tom Vol. 102, nr 3
88--95
EN
The article investigates the steady state flow of an incompressible fluid which is treated as a Williamson fluid through a stenoised region in the shape of cosine constriction. Blood is taken as a Williamson fluid. Mathematical formulation leads us to nonlinear compatibility and energy equations, which are then deciphered by the shooting technique to obtain the numerical solution. Suitable resemblance transformations are used to change partial differential equations into an embellished form of ordinary differential equations. Further, the consequences of the different parameters involved are shown by graphs and a conclusion is presented. Velocity and temperature fields are canvassed graphically for the distinct values of emerging parameters and discussed in tabular form. Skin friction and the coefficient of heat transfer are also covered in the discussion. The resulting Nusselt number curve exhibits negative deflection for variational values of λ and height of the stenosis δ.
20
Content available remote Influence of boundary conditions on 2D wave propagation in a rectangle
51%
Ashirbayev N. K. , Ashirbayeva J. N.
Journal of Mathematics and Applications
|
2013
|
tom Vol. 36
27--33
EN
Work is devoted to generalization of a differential method of spatial characteristics to case of the at task about distribution of waves in rectangular area of the final sizes with gaps in boundary conditions. On the basis of the developed numerical technique are received the settlement certainly - differential ratios of dynamic tasks in special points of front border of rectangular area, where boundary conditions on coordinate aren't continuous. They suffer a rupture of the first sort in points in which action P - gurative dynamic loading begins. Results of research are brought to the numerical decision.
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