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1

The effect of temperature-dependent viscosity and thermal conductivity on velocity and temperature field: an analytical solution using the perturbation technique

Panahi-Kalus H., Ahmadinejad M., Moosaie A.

Archives of Mechanics

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2020

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Vol. 72, nr 6

555--576

EN

This paper proposes a general form of the perturbation expansion method for the governing equations of viscous flow coupled to the temperature evolution. The effect of the variations of viscosity and thermal conductivity with temperature on the temperature and velocity fields in a steady two-dimensional Couette–Poiseuille flow is examined. The presented analytical solution by the perturbation method is validated against a finite difference solution of the governing equations. The numerical and analytical solutions are in good agreement.

2

Perturbation solutions for magnetohydrodynamics (MHD) flow of in a non-Newtonian fluid between concentric cylinders

Yurusoy M., Guler O. F.

International Journal of Applied Mechanics and Engineering

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2019

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Vol. 24, no. 1

199--211

EN

The steady-state magnetohydrodynamics (MHD) flow of a third-grade fluid with a variable viscosity parameter between concentric cylinders (annular pipe) with heat transfer is examined. The temperature of annular pipes is assumed to be higher than the temperature of the fluid. Three types of viscosity models were used, i.e., the constant viscosity model, space dependent viscosity model and the Reynolds viscosity model which is dependent on temperature in an exponential manner. Approximate analytical solutions are presented by using the perturbation technique. The variation of velocity and temperature profile in the fluid is analytically calculated. In addition, equations of motion are solved numerically. The numerical solutions obtained are compared with analytical solutions. Thus, the validity intervals of the analytical solutions are determined.

3

Propagation of shear waves in viscoelastic medium at irregular boundaries

Chattopadhyay A., Gupta S., Sharma V.K., Kumari P.

Acta Geophysica

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2010

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Vol. 58, no. 2

196-214

EN

The aim of the paper is to study the shear wave propagation in a viscoelastic layer over a semi-infinite viscoelastic half space due to irregularity in the viscoelastic layer. It is of great interest to study the propaga-tion of shear waves in the assumed medium having a non planar boundary due to its similarity to most of the real situations. The perturbation method is applied to find the displacement field. The effect of complex wave number on dissipation factor is analysed. Finally, as an application, the result obtained has been used to get the reflected field in viscoelastic layer when the shear wave is incident on an irregular boundary in the shape of parabolic irregularity as well as triangular notch. It is observed that the amplitude of this reflected wave decreases with increasing length of the notch, and increases with increasing depth of the irregularity.

4

Thermal radiation effects on hydromagnetic flow

Abdelkhalek M. M.

Computer Assisted Mechanics and Engineering Sciences

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2007

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Vol. 14, No. 3

471-484

EN

Numerical results are presented for the effects of thermal radiation, buoyancy and heat generation or absorption on hydromagnetic flow over an accelerating permeable surface. These results are obtained by solving the coupled nonlinear partial differential equations describing the conservation of mass, momentum and energy by a perturbation technique. This qualitatively agrees with the expectations, since the magnetic field exerts a retarding force on the free convection flow. A parametric study is performed to illustrate the influence of the radiation parameter, magnetic parameter, Prandtl number, Grashof number and Schmidt number on the profiles of the velocity components and temperature. The effects of the different parameters on the velocity and temperature profiles as well as the skin friction and wall heat transfer are presented graphically. Favorable comparisons with previously published work confirm the correctness of numerical results.

5

Onset of surface-tension-driven convection in superposed layers of fluid and saturated porous medium

Shivakumara I. S., Suma S. P., Chavaraddi K. B.

Archives of Mechanics

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2006

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Vol. 58, nr 2

71-92

EN

The onset of surface-tension-driven convection is studied in a two-layer system comprising an incompressible fluid-saturated porous layer over which lies a layer of the same fluid. The lower rigid surface of the porous layer is either perfectly heat conducting or insulating, while the upper heat insulating fluid boundary is free and at which the surface tension effects are allowed for. At the contact surface between the fluid-saturated porous medium and the adjacent bulk fluid, both Beavers-Joseph and the Jones conditions are employed. The resulting eigenvalue problem is solved exactly. Besides, analytical expression for the critical Marangoni number is obtained for insulating boundaries by using regular perturbation technique. The effect of variation of different physical parameters on the onset of Marangoni convection is investigated in detail. It is found that the parameter ..., the ratio of the thickness of the fluid layer to that of the porous layer, has a profound effect on the stability of the system.

6

Application of modified homotopy perturbation method to nonlinear oscillations

Marinca V.

Archives of Mechanics

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2006

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Vol. 58, nr 3

241-256

EN

The purpose of this paper is to apply a version of homotopy technique to nonlinear problems. The modified version of homotopy perturbation method is applied to derive highly accurate analytical expressions for periodic solutions or for approximate formulas of frequency. In contrast with the traditional perturbation methods, the proposed method does not require any small parameter in the equation. The proposed algorithm avoids the complexity provided by other numerical approaches. The analysis is accompanied by three numerical examples. The results prove that this method is very effective and simple.

7

Zastosowania metody perturbacji do oszacowania wartości własnych układów dynamicznych o parametrach niepewnych

Skrzypczyk J., Liszka T.

Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska

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2004

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z. 23

369-374

PL

Metoda perturbacji pozwala na szybkie oszacowanie wartości własnych w układach poddanych zaburzeniom. Uogólniając tą metodę na liczby przedziałowe można wykorzystać ją do oszacowania wszystkich wartości własnych przedziałowego zadania własnego [A]x=Alfa[B]x a także zadania własnego drugiego stopnia Alfa2[A]x + Alfa[B]x+[C]x = 0. W teorii konstrukcji tą metodę możemy wykorzystać do oszacowania częstości drgań własnych wielowymiarowych układów dynamicznych o parametrach niepewnych oraz częstości drgań swobodnych w układach z tłumieniem.

EN

Method of perturbation makes possible quick estimation of eigenvalues of systems imposed on a perturbations. Extension of this method over interval numbers gives possibility to estimate all eigenvalues of interval generalized eigenvalue problem [A]x=Alpha[B]x end second degree eigenvalue problem Alpha2[A]x +Alpha[B]x + [C]x = 0, In theory of structures this method can be used for eigenfrequency estimation of multidimensional dynamic systems with interval parameters end frequency of free vibration in systems with damping.

8

Magnetodynamic stability of bounded hollow jet pervaded by varying magnetic field

Radwan A. E., Elazab S. S., Hydia W. M.

Mechanics and Mechanical Engineering

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2000

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Vol. 4, nr 2

213--223

EN

The problem is formulated and solved based on the linear perturbation technique. The stability criterion is derived and discussed. The analytical results are confirmed numerically. The uniform magnetic fields interior and exterior the jet have stabilizing influences for all modes of perturbation. The varying transverse magnetic field interior the model is stabilizing or not according to restrictions. The radii ratio of the gas-liquid cylinder has a tendency for stabilizing the model. As the axial magnetic fields intensities interior and exterior the gas jet are so much strong than that of the transverse magnetic field and adapting the cylinders radii ratio the instability of the model is suppressed and stability sets in.