Analytical solution of settling behavior of a particle in incompressible Newtonian fluid by using Parameterized Perturbation Method

The problem of solid particle settling is a well known problem in mechanic of fluids. The parametrized Perturbation Method is applied to analytically solve the unsteady motion of a spherical particle falling in a Newtonian fluid using the drag of the form given by Oseen/Ferreira, for a range of Reynolds numbers. Particle equation of motion involved added mass term and ignored the Basset term. By using this new kind of perturbation method called parameterized perturbation method (PPM), analytical expressions for the instantaneous velocity, acceleration and position of the particle were derived. The presented results show the effectiveness of PPM and high rate of convergency of the method to achieve acceptable answers.

HOMOTOPY PERTURBATION METHOD AND PARAMETERIZED PERTURBATION METHOD FOR RADIUS OF CURVATURE BEAM EQUATION

In this paper, homotopy perturbation method (HPM) and parameterized perturbation method (PPM) are used to solve the radius of curvature beam equation. This paper compares the HPM and PPM in order to solve the equations of curvature beam. A comparative study between the HPM, PPM and numerical method (NM) is presented in this work. The validity of our solutions is verified by the numerical results. The achieved results reveal that the HPM and PPM are very effective, convenient and quite accurate to nonlinear partial differential equations. These methods can be easily extended to other strongly nonlinear oscillations and can be found widely applicable in engineering and science.

Effect of temperature-dependency of surface emissivity on heat transfer using the parameterized perturbation method

Knowledge of the temperature dependence of the physical properties such surface emissivity, which controls the radiative problem, is fundamental for determining the thermal balance of many scientific and industrial processes. The current work studies the ability of a strong analytical method called parameterized perturbation method (PPM), which unlike classic perturbation method do not need small parameter, for nonlinear heat transfer equations. The results are compared with the numerical Runge-Kutta method showed good Agreement.

SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS

This paper features a survey of some recent developments in asymptotic techniques, which are valid not only for weakly nonlinear equations, but also for strongly ones. Further, the obtained approximate analytical solutions are valid for the whole solution domain. The limitations of traditional perturbation methods are illustrated, various modified perturbation techniques are proposed, and some mathematical tools such as variational theory, homotopy technology, and iteration technique are introduced to overcome the shortcomings. In this paper the following categories of asymptotic methods are emphasized: (1) variational approaches, (2) parameter-expanding methods, (3) parameterized perturbation method, (4) homotopy perturbation method (5) iteration perturbation method, and ancient Chinese methods. The emphasis of this article is put mainly on the developments in this field in China so the references, therefore, are not exhaustive.