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1
Content available Investigations of Couette flow unsteady radiative convective heat transfer in a vertical channel using the generalized method of lines (MOL)
Sowayan Ahmed S.
International Journal of Applied Mechanics and Engineering
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2022
|
Vol. 27, no. 3
199--211
EN
This study describes a very efficient and fast numerical solution method for the non-steady free convection flow with radiation of a viscous fluid between two infinite vertical parallel walls. The method of lines (MOL) is used together with the Runge-Kutta ODE Matlab solver to investigate this problem numerically. The presence of radiation adds more stiffness and numerical complexity to the problem. A complete derivation in dimensionless form of the governing equations for momentum and energy is also included. A constant heat flux condition is applied at the left wall and a transient numerical solution is obtained for different values of the radiation parameter (R). The results are presented for dimensionless velocity, dimensionless temperature and Nusselt number for different values of the Prandtl number (Pr), Grashof number (Gr), and the radiation parameter (R). As expected, the results show that the convection heat transfer is high when the Nusselt number is high and the radiation parameter is low. It is also shown that the solution method used is simple and efficient and could be easily adopted to solve more complex problems.
2
Content available A study of MHD fluid with second order slip and thermal flow over a nonlinear stretching sheet
Jauhri Shefali, Mishra Upendra
International Journal of Applied Mechanics and Engineering
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2022
|
Vol. 27, no. 2
98--114
EN
An electrically conducted viscous incompressible nanofluid flow caused by the nonlinear stretching surface with stagnation flow has been investigated numerically. The effect of Brownian motion and thermophoresis on the nanofluid is also incorporated. The governing partial differential equations with nonlinear second order boundary conditions are solved by the fourth order Runge-Kutta technique using MATLAB programming. The effect of the radiation parameter (Rd), stretching parameter (n), Brownian motion parameter (Nb), thermophoresis parameter (Nt) on temperature, velocity and mass transfer are shown graphically. The influence of some of these parameters on the local Nusselt number (−𝜃′(0)) and local Sherwood number (−𝜙′(0)) are shown by the graphs.
3
Content available Numerical predictions of laminar flow and free convection heat transfer from an isothermal vertical flat plate
Belhocine Ali, Stojanovic Nadica, Abdullah Oday Ibraheem
Archive of Mechanical Engineering
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2022
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LXIX, nr 4
749--773
EN
In this present work, the laminar free convection boundary layer flow of a two-dimensional fluid over the vertical flat plate with a uniform surface temperature has been numerically investigated in detail by the similarity solution method. The velocity and temperature profiles were considered similar to all values and their variations are as a function of distance from the leading edge measured along with the plate. By taking into account this thermal boundary condition, the system of governing partial differential equations is reduced to a system of non-linear ordinary differential equations. The latter was solved numerically using the Runge-Kutta method of the fourth-order, the solution of which was obtained by using the FORTRAN code on a computer. The numerical analysis resulting from this simulation allows us to derive some prescribed values of various material parameters involved in the problem to which several important results were discussed in depth such as velocity, temperature, and rate of heat transfer. The definitive comparison between the two numerical models showed us an excellent agreement concerning the order of precision of the simulation. Finally, we compared our numerical results with a certain model already treated, which is in the specialized literature.
4
Content available remote Numerical study of coupled oscillator system usingthe classical Euler-Lagrange equations
Shanak H., Khalilia H., Jarrar R., Asad J.
Mechanics and Mechanical Engineering
|
2021
|
Vol. 25, nr 1
1--5
EN
Problems involving vibrations (mechanical orelectrical) can be reduced to problems of coupled oscil-lators. For this, we consider the motion of coupled oscilla-tors system using Lagrangian method. The Lagrangian ofthe system was initially constructed, and then the Euler-Lagrange equations (i.e., equations of motion of the system)have been obtained. The obtained equations of motion are ahomogenous second-order equation. These equations weresolved numerically using the ode45 code, which is basedon Runge-Kutta method.
5
Content available Inundation maps for extreme flood events: Case study of Sidi Bel Abbes city, Algeria
Atallah M., Hazzab A., Seddini A., Ghenaim A., Korichi K.
Journal of Water and Land Development
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2018
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no. 37
19--27
EN
Hydrodynamic modelling is used to analyse the inundation behaviour of Sidi Bel Abbes city (North-West of Algeria) during extreme flood events. The study reach, 5.4 km in length, is a section of Wadi Mekerra through Sidi Bel Abbes city. Land and bathymetric surveys were used to create a digital terrain model (DTM) of the river channel and the floodplain. By coupling the geometry with hydrologic data, a two dimensional hydrodynamic model was built. The model is based on integrating Saint-Venant shallow waters (depth averaged) equations through Runge–Kutta discontinuous Galerkin numerical scheme. It was calibrated in terms of roughness coefficients on measured values of water surface elevation and discharge registered in the Sidi Bel Abbes gauging station. The objective is to draw the flood maps under extreme river flood event. The results are helpful for local authorities in order to take the appropriate defence measures in the future.
PL
Wykorzystano modelowanie hydrodynamiczne do analizy zasięgu ekstremalnych zjawisk powodziowych w mieście Sidi Bel Abbes w północnozachodniej Algierii. Teren badań stanowił odcinek okresowej rzeki Mekerra długości 5,4 km płynącej przez miasto. Badania naziemne i batymetryczne wykorzystano do zbudowania cyfrowego modelu terenu (DTM) koryta rzeki i obszarów zalewowych. Łącząc geometrię z danymi hydrologicznymi, zbudowano dwuwymiarowy model hydrodynamiczny. Model oparto na integracji równań Saint-Venanta (o uśrednionej głębokości) poprzez nieciągły schemat liczbowy Galerkina wg metody Rungego– Kutty. Model był kalibrowany na współczynnik szorstkości dla zmierzonych wysokości poziomu wody i na odpływ rejestrowany w posterunku pomiarowym Sidi Bel Abbes. Celem pracy było sporządzenie map powodzi w warunkach ekstremalnych zjawisk powodziowych. Wyniki mogą być przydatne władzom lokalnym w podejmowaniu odpowiednich zabiegów ochronnych przed powodzią w przyszłości.
6
Content available Effect of viscous dissipation and thermal radiation on heat transfer over a non-linearly stretching sheet through porous medium
Nandeppanavar M. M., Siddalingappa M. N.
International Journal of Applied Mechanics and Engineering
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2013
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Vol. 18, no. 2
461--474
EN
In this present paper, we have discussed the effects of viscous dissipation and thermal radiation on heat transfer over a non-linear stretching sheet through a porous medium. Usual similarity transformations are considered to convert the non-linear partial differential equation of motion and heat transfer into ODE’s. Solutions of motion and heat transfer are obtained by the Runge-Kutta integration scheme with most efficient shooting technique. The graphical results are presented to interpret various physical parameters of interest. It is found that the velocity profile decreases with an increase of the porous parameter asymptotically. The temperature field decreases with an increase in the parametric values of the Prandtl number and thermal radiation while with an increase in parameters of the Eckert number and porous parameter, the temperature field increases in both PST (power law surface temperature) and PHF (power law heat flux) cases. The numerical values of the non-dimensional wall temperature gradient and wall temperature are tabulated and discussed.
7
Content available remote A Résumé on Interval Runge-Kutta Methods
Marciniak A.
Mathematica Applicanda
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2012
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Vol. 40, No. 1
39-52
EN
The paper presents explicit and implicit interval methods of Runge-Kutta type. Such methods introduce the errors of methods. It means that this kind of errors are included in the interval solutions obtained. Applying these methods for solving the initial value problem in floating-point interval arithmetic we can obtain solutions in the form of intervals which contain all possible numerical errors. Numerical examples are presented.
PL
W artykule przedstawiono jawne i niejawne metody przedziałowe typu Rungego-Kutty. Metody takie zawierają w sobie błędy metod, co oznacza, ze ten rodzaj błędów jest uwzględniony w otrzymywanych rozwiązaniach przedziałowych. Stosując te metody do rozwiązywania zagadnienia początkowego w zmiennopozycyjnej arytmetyce przedziałowej otrzymujemy zatem rozwiązania w postaci przedziałów, które zawierają wszystkie możliwe błędy numeryczne. W artykule przedstawiono także przykłady numeryczne
8
Content available remote Równanie Van der Pola
Jendykiewicz P.
Studia i Materiały Informatyki Stosowanej
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2009
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nr 1
49-53
PL
W artykule prezentowana jest metoda badania stabilności obwodu elektrycznego opisanego za pomocą równania różniczkowego. Aby opisać tą metodę wykorzystano oscylator van der Pola. Badania układu opisanego równaniem van der Pola z losowym współczynnikiem tłumienia przeprowadzono za pomocą programu vdP.exe. Na podstawie wizualizacji wyników rozwiązania równania vdP określamy przybliżoną wartości współczynnik tłumienia, przy którym układ traci stabilność. Wykorzystaną metodą numeryczną do obliczeń równania różniczkowego jest metoda Runge-Kutty według schematu cztero poziomowego.
EN
This paper presents the electric circuit stability test method analysed using differential equation. Authors described this method using van der Pol oscillator. Research of the system analysed using van der Pol equation with random damping coefficient has been performed by means of the vdP.exe program. Authors determine approximate value of the damping coefficient for which the system becomes instable on the grounds of the vdP equation visualisation results. The numerical analysis method used to calculate the differential equation is Runge-Kutty method with a four-level pattern.
9
Content available remote Modele rywalizacji i walki w równaniach Lanchestera
Bajek M.
Studia i Materiały Informatyki Stosowanej
|
2009
|
nr 1
39-41
PL
Celem opracowania jest przedstawienie stworzonego przez Lanchestera modelu walki na dowolnym przykładzie. W artykule zamieszczone są informacje na temat samego modelu walki, prezentowany jest ogólny układ równań Lanchestera oraz układ klasyczny i najpopularniejszy. Do komputerowej symulacji wykorzystane będą aplikacje w Excel-u oraz C++ Builder. Układ równań jest rozwiązany metodami numerycznymi z wykorzystaniem czteropoziomowego algorytmu Runge-Kutty
EN
The aim of this study is to present the combat model created by Lanchester using some example. The paper includes information on the combat model itself. The author presents Lanchester's general set of equations as well as classical and most popular sets. The computer simulation uses applications created in Excel and C++ Builder. The set of equations is solved by means of numerical methods using four-level Runge-Kutty algorithm.
10
Content available remote Symplectic integrators for cascade of mass-spring system
Jopek H., Stręk T.
Vibrations in Physical Systems
|
2006
|
Vol. 22
155--160
11
Content available remote Frictional Auto-vibrations in a Contact Thermoelastic Problem in Wear Conditions
Awrejcewicz J., Pyryev Y.
Vibrations in Physical Systems
|
2004
|
Vol. 21
79--82
12
Content available remote Applying the Interval Multistep Methods of Adams Type to Solution Simple Pendulum Problem
Jankowska M.
Vibrations in Physical Systems
|
2004
|
Vol. 21
167--170
13
Wpływ pracy grzejnika konwektorowego na jakość powietrza w ogrzewanym pomieszczeniu
Pełka P.
Ciepłownictwo, Ogrzewnictwo, Wentylacja
|
2003
|
R. 34, nr 7
21-24
PL
W artykule opisano metodykę określania oraz oszacowane wyniki wpływu pracującego grzejnika konwektorowego na transport pyłu zawartego w powietrzu ogrzewanego pomieszczenia. W tym celu dokonano metodą termoanemometryczną pomiaru prędkości konwekcji oraz temperatury powietrza nad grzejnikiem konwektorowym. W drugiej części przeprowadzono obliczenia numeryczne metodą Runge-Kutta IV rzędu w celu wyznaczenia prędkości opadania cząsteczek pyłu.
14
Content available remote Przedziałowe metody całkowania równań dynamiki konstrukcji
Pownuk A.
Zeszyty Naukowe Politechniki Rzeszowskiej. Mechanika
|
1999
|
z. 52 [174]
77-84
EN
In this paper the interval methods for validated solution of ordinary differential equation of dynamics of structures are presented. The interval Euler's method for solving system of ordinary differential equations with automatic determination of guaranteed estimation and high order Taylor series method are described. Using these methods two problems of free vibration are solved.
15
Content available remote Mixed algorithm for solving boundary value problem
Paláncz B., Popper G.
Computer Assisted Mechanics and Engineering Sciences
|
1999
|
Vol. 6, No. 3-4
479-486
EN
Symbolic computation has been applied to Runge-Kutta technique in order to solve two-point boundary value problem. The unknown initial values are considered as symbolic variables, therefore they will appear in a system of algebraic equations, after the integration of the ordinary differential equations. Then this algebraic equation system can be solved for the unknown initial values and substituted into the solution. Consequently, only one integration pass is enough to solve the problem instead of using iteration technique like shooting-method. This procedure is illustrated by solving the boundary value problem of the mechanical analysis of a liquid storage tank. Computation was carried out by MAPLE V. Power Edition package.
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