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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.

2

The least squares stochastic finite element method in structural stability analysis of steel skeletal structures

Kamiński M., Szafran J.

International Journal of Applied Mechanics and Engineering

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2015

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Vol. 20, no. 2

299--318

EN

The main purpose of this work is to verify the influence of the weighting procedure in the Least Squares Method on the probabilistic moments resulting from the stability analysis of steel skeletal structures. We discuss this issue also in the context of the geometrical nonlinearity appearing in the Stochastic Finite Element Metod equations for the stability analysis and preservation of the Gaussian probability density function employed to model the Young modulus of a structural steel in this problem. The weighting procedure itself (with both triangular and Dirac-type) shows rather marginal influence on all probabilistic coefficients under consideration. This hybrid stochastic computational technique consisting of the FEM and computer algebra systems (ROBOT and MAPLE packages) may be used for analogous nonlinear analyses in structural reliability assessment.

3

Hartmann two-fluid Poiseuille-Couette flow in an inclined channel

Umavathi J. C., Sridhar K. S. R.

International Journal of Applied Mechanics and Engineering

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2009

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Vol. 14, no 2

539-557

EN

A numerical and analytical study of a two fluid magnetohydrodynamic Poiseuille-Couette flow in an inclined channel is investigated. The fluids in both the regions are incompressible, electrically conducting and the transport properties are assumed to be constant. The channel walls are assumed to be electrically insulating. Separate solutions for each fluid are obtained and these solutions are matched at the interface using suitable matching conditions. The governing equations of motion are solved analytically and are valid for small Eckert numbers and numerically valid for large . Solutions for large show a marked change on the velocity and temperature profiles. The results are presented graphically for various Hartmann number, Grashof number, angle of inclination and also for various ratios. It is found that the flow can be controlled effectively by a suitable choice of values of ratios of electrical conductivities, widths, viscosities and thermal conductivities.

4

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.