2937 words - 12 pages

The article solves the motion of a spherical solid particle in plane coquette fluid flow by using the HPM-Padé technique which is a combination of the Homotopy Perturbation method and Padé approximation. The series solutions of the couple equations are developed. Generally, the truncated series solution is adequately in a small region and to overcome this limitation the Padé techniques, which have the advantage in turning the polynomial approximation into a rational function, are applied to the series solution to improve the accuracy and enlarge the convergence domain. The current results compared with those derived from HPM and the established fourth order Runge–Kutta method in order to ascertain the accuracy of the proposed method. It is found that this method can achieve more suitable results in comparison to HPM.

In the heart of all the different engineering sciences, everything shows itself in the mathematical relation that most of these problems and phenomena are modeled by linear and nonlinear equations. Therefore, many different methods have recently introduced some ways to solve these equations. Analytical methods have made a comeback in research methodology after taking a backseat to the numerical techniques for the latter half of the preceding century. One of the analytical methods of recent vintage, namely, the Homotopy Perturbation Method (HPM) which was firstly proposed by Chinese mathematician Ji-Huan He [1–8] has attracted special attention from researchers as it is flexible in applying and gives sufficiently accurate results with modest effort. This method as a powerful series-based analytical tool has been used by many authors [9–14]. But, the convergence region of the obtained truncated series approximation is limited and in great shape, need of enhancements to enlarge convergence region of the approximate solution. It’s well known that Padé approximations which was presented by Padé in 1892 [15], have the advantage of manipulating the polynomial approximation into a rational function of polynomials. This manipulation provides us with more information about the mathematical behavior of the solution. So, the application of Padé approximations to the truncated series solution obtained by HPM will be an effective way to enlarge the convergence domain and greatly improve the convergence rate of the truncated power series. In recent years, the HPM-Padé method has been successfully employed to solve many types of nonlinear problems [16-17]. Moreover, The Padé techniques have been used before with ordinary differential equations and with partial differential equations [18-22].

Various processes such as filtration, combustion, air and water pollution, coal transport and cleaning, micro contamination control and xerography involve the Particle transport and deposition. There has been renewed interest in the equations of the particle motion, such as work done in [23] where have found that neutrally buoyant...

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