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1

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

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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

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

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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

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

Numerical study of coupled oscillator system usingthe classical Euler-Lagrange equations

Shanak H., Khalilia H., Jarrar R., Asad J.

Mechanics and Mechanical Engineering

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2021

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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

Interval Runge-Kutta Methods with Variable Step Sizes

Marciniak A., Szyszka B.

Computational Methods in Science and Technology

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2019

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Vol. 25, No. 1

17--29

EN

In a number of our previous papers we have presented interval versions of Runge-Kutta methods (explicit and implicit) in which the step size was constant. Such an approach has required to choose manually the step size in order to ensure an interval enclosure to the solution with the smallest width. In this paper we propose an algorithm for choosing automatically the step size which guarantees the best (i.e., the tiniest) interval enclosure. This step size is determined with machine accuracy.

6

Numerical approaches to the heat transfer problem in modern electronic structures

Raszkowski T., Samson A.

Computer Science

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2017

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Vol. 18 (1)

71--93

EN

The main aim of this paper is to present a detailed description of the research related to the modeling of heat conduction in modern electronic structures, including special consideration for numerical aspects of analyzed algorithms. The motivation to undertake the research as well as some of the most-important results of the experiments and simulations are also included. Moreover, a numerical approximation of the problem as well as the methodology used and a sample solution of the mentioned problem are presented. In the main part, the discretization techniques, Ordinary Differential Equation algorithms, and simulation results for Runge-Kutta’s and Gear’s algorithms are analyzed and discussed. Additionally, a new effective approach to the modeling of heat transfer in electronic nanostructures is demonstrated.

7

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.

8

Symplectic integrators for cascade of mass-spring system

Jopek H., Stręk T.

Vibrations in Physical Systems

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2006

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Vol. 22

155--160

9

Frictional Auto-vibrations in a Contact Thermoelastic Problem in Wear Conditions

Awrejcewicz J., Pyryev Y.

Vibrations in Physical Systems

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2004

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Vol. 21

79--82

10

Mixed algorithm for solving boundary value problem

Paláncz B., Popper G.

Computer Assisted Mechanics and Engineering Sciences

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1999

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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.