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1

Application of reconstruction of variational iteration method on the laminar flow in a porous cylinder with regressing walls

Azimi M., Hedesh A. M., Karimian S.

Mechanics and Mechanical Engineering

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2017

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Vol. 21, nr 2

379--387

EN

A study of an incompressible two-dimensional flow in a channel with one porous wall is presented in this research. As usual, the cylindrical propellant grain of a solid rocket motor is modeled as a long tube with one end closed at the headwall, while the other remains open. The governing continuity and momentum equations together with the associated boundary conditions are first reduced to a set of self similar non-linear coupled ordinary differential equations using similarity transformations. Then we solved the ordinary differential equation by RVIM and the numerical method.

2

Computing Simulation of the Generalized Duffing Oscillator Basedon EBM and MHPM

Azimi A., Azimi M.

Mechanics and Mechanical Engineering

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2016

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Vol. 20, nr 4

595--604

EN

This paper is concerned with analytical approximate solutions, to the generalized Duffing oscillation. Modified Homotopy Perturbation Method (MHPM) and Energy Balance Method (EBM) are applied to solve nonlinear equation and consequently the relationship between the natural frequency and the initial amplitude is obtained in an analytical form. The general solution can be used to yield the relationship between amplitude and frequency in different strengths of nonlinearity. To verify the accuracy of the present approach, illustrative examples are provided and compared with exact solutions. The procedure yields rapid convergence with respect to the exact solution obtained by numerical integration.

3

Application of HPM to find analytical solution of coette flow with variable viscosity

Azimi A., Azimi M., Javanfar A.

Acta Mechanica et Automatica

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2015

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Vol. 9, no. 1

5--8

EN

In this paper, the couette flow of fluid with variable viscosity is studied analytically by using Homotopy Pertubation Method (HPM). At first the basic idea of Homotopy Pertubation Method (HPM) is presented. The mathematical formulation and application of HPM to nonlinear problem are presented in section three. In order to check the validity of solution the analytical results are compared with exact ones for various numerical cases. The good agreement between exact method and Homotopy Pertubation Method has been assures us about the solution accuracy.

4

Investigation on the Film Flow of a Third Grade Fluid on an Inclined Plane Using HPM

Azimi M., Azimi A.

Mechanics and Mechanical Engineering

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2014

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Vol. 18, nr 1

5--10

EN

This work concerns the study of the thin film flow problem arising in non–Newtonian fluid mechanics using analytical approach. The governing equations are reduced to ordinary nonlinear boundary value problem by applying the transformation method. Homotopy Perturbation Method (HPM) has been applied to obtain solution of reduced nonlinear boundary value problem. The analytical solutions of the flow velocity distributions for different cases have been presented. The effect of material constant has also discussed. Finally, analytical results have been compared with numerical one obtained by forth order Runge Kutta method. High accuracy and validity are the advantages of present study.

5

Flow Modeling in a Porous Cylinder with Regressing Walls Using Semi Analytical Approach

Azimi M., Hedesh A. M., Karimian S.

Mechanics and Mechanical Engineering

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2014

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Vol. 18, nr 2

77--84

EN

In this paper, the mathematical modeling of the flow in a porous cylinder with a focus on applications to solid rocket motors is presented. As usual, the cylindrical propellant grain of a solid rocket motor is modeled as a long tube with one end closed at the headwall, while the other remains open. The cylindrical wall is assumed to be permeable so as to simulate the propellant burning and normal gas injection. At first, the problem description and formulation are considered. The Navier–Stokes equations for the viscous flow in a porous cylinder with regressing walls are reduced to a nonlinear ODE by using a similarity transformation in time and space. Application of Differential Transformation Method (DTM) as an approximate analytical method has been successfully applied. Finally the results have been presented for various cases.