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Wyświetlanie 1-15 z 26
Tytuł:
Thermal analysis of longitudinal a porous fin with temperature-dependent internal heat generation using the variation of parameters method
Autorzy:
Güngör, Osman
Arslantürk, Cihat
Powiązania:
https://bibliotekanauki.pl/articles/1839762.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
variation of parameters method
porous fin
heat generation
exact solution
metoda wariacji parametrów
żebro porowate
wytwarzanie ciepła
dokładne rozwiązanie
Opis:
The present study investigates the thermal performance of longitudinal a porous fin with temperature-dependent internal heat generation. The Darcy model is utilized to obtain the differential form of the governing equation that solves the nonlinear temperature distribution equation using the method of variation of parameters. Although this method is applied to solve both linear and nonlinear differential equations, there exist rare applications of this method to solve nonlinear heat transfer problems. In the present study, we applied the method to estimate the thermal analysis of the porous fin exposed to convection. The heat generation is assumed as a function of temperature. The effects of the convection parameter Nc, internal heat generation ɛ, porosity Sh, and generation number G parameter on the dimensionless temperature distribution are discussed in detail. The accuracy of the variation of parameters method is verified through comparison with homotopy perturbation method and the Matlab bvp4c solver (NUM). The results have disclosed that the variation of parameters method can be used as a very effective and practical approach for further studies of the porous medium.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 3; 5-16
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solitary wave solution to the nonlinear evolution equation in cascaded quadratic media beyond the slowly varying envelope approximations
Autorzy:
Sarma, A K
Biswas, A.
Powiązania:
https://bibliotekanauki.pl/articles/174484.pdf
Data publikacji:
2014
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
solitons
integrability
exact solution
cascaded quadratic media
Opis:
We report an exact bright and dark soliton solution to the nonlinear evolution equation derived by MOSES and WISE (Phys. Rev. Lett. 97, 2006, 073903) for cascaded quadratic media beyond the slowly varying envelope approximations. The integrability aspects of the model are addressed. The travelling wave hypothesis as well as the ansatz method are employed to obtain an exact 1-soliton solution. Both bright and dark soliton solutions are obtained. The corresponding constraint conditions are obtained in order for the soliton solutions to exist.
Źródło:
Optica Applicata; 2014, 44, 2; 205-212
0078-5466
1899-7015
Pojawia się w:
Optica Applicata
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Singular integral equation with a multiplicative Cauchy kernel in the half-plane
Autorzy:
Karczmarek, P.
Powiązania:
https://bibliotekanauki.pl/articles/255089.pdf
Data publikacji:
2008
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
singular integral equation
exact solution
Cauchy kernel
multiplicative kernel
Opis:
In this paper the explicit solutions of singular integral equation with a multiplicative Cauchy kernel in the half-plane are presented.
Źródło:
Opuscula Mathematica; 2008, 28, 1; 63-72
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Open tandem networks with blocking analysis – two approaches
Autorzy:
Oniszczuk, W.
Powiązania:
https://bibliotekanauki.pl/articles/205602.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
two-node network with blocking
multi-server tandem queues
exact algorithm
product form solution
Opis:
The paper describes an analytical study of open twonode (tandem) network models with blocking. Here, a specific tandem configuration is chosen: the first node is treated as an infinite server (IS - often referred to as the ample-server), meaning that any incoming task can find at least one empty line for service in this node, and the second node has several parallel lines that can serve input task streams simultaneously. Between these two nodes there is a buffer with finite capacity. In this type of network, if the buffer is full, the accumulation of new tasks by the second node is temporarily suspended (blocking factor) and tasks must wait at the first node until the transmission process is resumed. In this paper, the two-node model is investigated using two different methods. The first is the multi-step exact algorithm, involving a numerical part for solving a set of linear equations, and the second is an approximate algorithm using a product form solution. The numerical part is used for solving a system of linear equations and for calculating the state probability vector. Finally, after comparing both algorithms, some recommendations as to when each method can be used are given.
Źródło:
Control and Cybernetics; 2014, 43, 1; 111-132
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the multisummability of WKB solutions of certain singularly perturbed linear ordinary differential equations
Autorzy:
Takei, Y.
Powiązania:
https://bibliotekanauki.pl/articles/255041.pdf
Data publikacji:
2015
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
exact WKB analysis
WKB solution
multisummability
Opis:
Using two concrete examples, we discuss the multisummability of WKB solutions of singularly perturbed linear ordinary differential equations. Integral representations of solutions and a criterion for the multisummability based on the Cauchy-Heine transform play an important role in the proof.
Źródło:
Opuscula Mathematica; 2015, 35, 5; 775-802
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Numerical and analytical calculations of the free surface flow between two semi-infinite straights
Autorzy:
Chedala, Fatma Zohra
Amara, Abdelkader
Meflah, Mabrouk
Powiązania:
https://bibliotekanauki.pl/articles/1839736.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
free surface
flow
surface tension
free streamline theory
exact solution
series truncation
Weber number
numer Webera
napięcie powierzchniowe
dokładne rozwiązanie
przepływ swobodny
Opis:
The problem of two-dimensional flow with the free surface of the jet in a region between two semi-infinite straights intersections at point O is calculated analytically for each angle Beta and numerically for each of the various values of the Weber number and angle Beta. By assuming that the flow is potential, irrotational and that the fluid is incompressible and inviscid, and by taking account only the surface tension for a numerical method using the series truncation, and without the effect of gravity and surface tension for the analytic method utilize the hodograph transformation. The obtained results confirmed a good agreement between them when the Weber number tends to infinity, and the comparison of these surface shapes is illustrated.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 4; 21-32
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Numerical and analytical calculations of the free surface flow between two semi-infinite straights
Autorzy:
Chedala, Fatma Zohra
Amara, Abdelkader
Meflah, Mabrouk
Powiązania:
https://bibliotekanauki.pl/articles/1839739.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
free surface
flow
surface tension
free streamline theory
exact solution
series truncation
Weber number
numer Webera
napięcie powierzchniowe
dokładne rozwiązanie
przepływ swobodny
Opis:
The problem of two-dimensional flow with the free surface of the jet in a region between two semi-infinite straights intersections at point O is calculated analytically for each angle Beta and numerically for each of the various values of the Weber number and angle Beta. By assuming that the flow is potential, irrotational and that the fluid is incompressible and inviscid, and by taking account only the surface tension for a numerical method using the series truncation, and without the effect of gravity and surface tension for the analytic method utilize the hodograph transformation. The obtained results confirmed a good agreement between them when the Weber number tends to infinity, and the comparison of these surface shapes is illustrated.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 4; 21-32
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Mathematical modelling of heat transfer in liquid flat-plate solar collector tubes
Autorzy:
Zima, W.
Dziewa, P.
Powiązania:
https://bibliotekanauki.pl/articles/240431.pdf
Data publikacji:
2010
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
kolektor słoneczny
model matematyczny
rozwiązanie dokładne
stan przejściowy
exact solution
mathematical model
solar collector
transient state
Opis:
The paper presents a one-dimensional mathematical model for simulating the transient processes which occur in the liquid flat-plate solar collector tubes. The proposed method considers the model of collector tube as one with distributed parameters. In the suggested method one tube of the collector is taken into consideration. In this model the boundary conditions can be time-dependent. The proposed model is based on solving the equation describing the energy conservation on the fluid side. The temperature of the collector tube wall is determined from the equation of transient heat conduction. The derived differential equations are solved using the implicit finite difference method of iterative character. All thermo-physical properties of the operating fluid and the material of the tube wall can be computed in real time. The time-spatial heat transfer coefficient at the working fluid side can be also computed on-line. The proposed model is suitable for collectors working in a parallel or serpentine tube arrangement. As an illustration of accuracy and effectiveness of the suggested method the computational verification was carried out. It consists in comparing the results found using the presented method with results of available analytic solutions for transient operating conditions. Two numerical analyses were performed: for the tube with temperature step function of the fluid at the inlet and for the tube with heat flux step function on the outer surface. In both cases the conformity of results was very good. It should be noted, that in real conditions such rapid changes of the fluid temperature and the heat flux of solar radiation, as it was assumed in the presented computational verification, do not occur. The paper presents the first part of the study, which aim is to develop a mathematical model for simulating the transient processes which occur in liquid flat-plate solar collectors. The experimental verification of the method is a second part of the study is not presented in this paper. In order to perform this verification, the mathematical model would be completed with additional energy conservation equations. The experimental verification will be carry out in the close future.
Źródło:
Archives of Thermodynamics; 2010, 31, 2; 45-62
1231-0956
2083-6023
Pojawia się w:
Archives of Thermodynamics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Hypothetical analysis for peristaltic transport of metallic nanoparticles in an inclined annulus with variable viscosity
Autorzy:
Nadeem, S.
Sadaf, H.
Powiązania:
https://bibliotekanauki.pl/articles/201426.pdf
Data publikacji:
2016
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
inclined annulus
viscous nanofluid
peristaltic flow
variable viscosity
exact solution
pierścień
nanofluid
przepływ perystaltyczny
dokładne rozwiązanie
Opis:
The main objective of this article is to present a mathematical model for peristaltic transport in an inclined annulus. In this analysis, two-dimensional flow of a viscous nanofluid is observed in an inclined annulus with variable viscosity. Copper as nanoparticle with blood as its base fluid has been considered. The inner tube is unifom or rigid, while the outer tube takes a sinusoidal wave. Governing equations are solved under the well-known assumptions of low Reynolds number and long-wavelength. Exact solutions have been established for both velocity and nanoparticle temperature. The features of the peristaltic motion are explored by plotting graphs and discussed in detail.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2016, 64, 2; 447-454
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Group invariant solution of some time fractional evolution equations
Autorzy:
Mandal, H.
Bira, B.
Powiązania:
https://bibliotekanauki.pl/articles/122890.pdf
Data publikacji:
2018
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
fractional coupled Burger’s equation
fractional DSSH equations
Riemann Liouville’s fractional derivative
Erdélyi-Kober operator
symmetry analysis
exact solution
równania ewolucji
ułamkowe równania różniczkowe
ułamkowe równania DSSH
pochodna ułamkowa Riemanna Liouville'a
operator Erdélyi-Kober
Opis:
In this paper, we consider some classes of a system of nonlinear fractional differential equations (FDEs) arising in some important physical phenomena. Using symmetry group of transformations, the given systems of fractional partial differential equations (FPDEs) are reduced to systems of fractional ordinary differential equations (FODEs). Further, using the group invariant condition, we solve the reduced systems of FODEs and exact solutions of the given equations are constructed. Finally, the physical significance of the solutions are investigated graphically based on the exact solutions in order to highlight the importance of the study.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2018, 17, 4; 35-46
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Green’s function for a multifield material with a heat source
Autorzy:
Rogowski, B.
Powiązania:
https://bibliotekanauki.pl/articles/279505.pdf
Data publikacji:
2016
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
Green's functions
point heat source
multifield material
magneto-electro-thermo-elastic fundamental solution
multifield composites
exact solution
Opis:
Green’s functions for a multifield material subjected to a point heat source are presented in an explicit analytical form. The study concerns the steady-state thermal loading infi- nite region, half-space region and two-constituent magneto-electro-thermo-elastic material region. The new mono-harmonic potential functions, obtained by the author, are used in the analysis. The elastic displacement, electric potential, magnetic potential and induced by those coupled multifield physical quantities, caused by internal or external heat sources, are limited and presented in a very useful form, exactly and explicitly.
Źródło:
Journal of Theoretical and Applied Mechanics; 2016, 54, 3; 743-755
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Generalized characteristic singular integral equation with Hilbert kernel
Autorzy:
Karczmarek, P.
Powiązania:
https://bibliotekanauki.pl/articles/255057.pdf
Data publikacji:
2008
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
singular integral equation
characteristic equation
exact solution
Hilbert kernel
Opis:
In this paper an explicit solution of a generalized singular integral equation with a Hilbert kernel depending on indices of characteristic operators is presented.
Źródło:
Opuscula Mathematica; 2008, 28, 3; 287-294
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Exact solution of fin problem with linear temperature-dependent thermal conductivity
Autorzy:
Kader, A. H. A.
Latif, A. S. A.
Nour, H. M.
Powiązania:
https://bibliotekanauki.pl/articles/122709.pdf
Data publikacji:
2016
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
exact solution
fin equation
fin efficiency
thermal conductivity
żebro prostokątne
sprawność żebra
wymiana ciepła
przewodność cieplna
Opis:
In this paper, we obtain the general exact solution of a nonlinear fin equation which governs heat transfer in a rectangular fin with linear temperature-dependent thermal conductivity using the partial Noether method. The relationship between the fin efficiency and the thermo-geometric fin parameter is obtained. Additionally, we obtained the relationship among the fin effectiveness, the thermo-geometric fin parameter and the Biot number.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 4; 51-61
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Exact solution for large amplitude flexural vibration of nanobeams using nonlocal Euler-Bernoulli theory
Autorzy:
Nazemnezhad, R.
Hosseini-Hashemi, S.
Powiązania:
https://bibliotekanauki.pl/articles/279261.pdf
Data publikacji:
2017
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
nonlinear free vibration
nonlocal elasticity
nanobeam
exact solution
elliptic integrals
Opis:
In this paper, nonlinear free vibration of nanobeams with various end conditions is studied using the nonlocal elasticity within the frame work of Euler-Bernoulli theory with von K´arm´an nonlinearity. The equation of motion is obtained and the exact solution is established using elliptic integrals. Two comparison studies are carried out to demonstrate accuracy and applicability of the elliptic integrals method for nonlocal nonlinear free vibration analysis of nanobeams. It is observed that the phase plane diagrams of nanobeams in the presence of the small scale effect are symmetric ellipses, and consideration the small scale effect decreases the area of the diagram.
Źródło:
Journal of Theoretical and Applied Mechanics; 2017, 55, 2; 649-658
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Exact controllability of a string to rest with a moving boundary
Autorzy:
Gugat, Martin
Powiązania:
https://bibliotekanauki.pl/articles/970107.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
pde constrained optimization
optimal control of pdes
optimal boundary control
wave equation
analytic solution
exact controllability
moving boundaries
mining elevator
Opis:
We consider the problem of steering a finite string to the zero state in finite time from a given initial state by controlling the state at one boundary point while the other boundary point moves. As a possible application we have in mind the optimal control of a mining elevator, where the length of the string changes during the transportation process. During the transportation process, oscillations of the elevator-cable can occur that can be damped in this way. We present an exact controllability result for Dirichlet boundary control at the fixed end of the string that states that there exist exact controls for which the oscillations vanish after finite time. For the result we assume that the movements are Lipschitz continuous with a Lipschitz constant, whose absolute value is smaller than the wave speed. In the result, we present the minimal time, for which exact controllability holds, this time depending on the movement of the boundary point. Our results are based upon travelling wave solutions. We present a representation of the set of successful controls that steer the system to rest after finite time as the solution set of two point-wise equalities. This allows for a transformation of the optimal control problem to a form where no partial differential equation appears. This representation enables interesting insights into the structure of the successful controls. For example, exact bang-bang controls can only exist if the initial state is a simple function and the initial velocity is zero.
Źródło:
Control and Cybernetics; 2019, 48, 1; 69-87
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 26

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