Y. Rostamiyan¹, S.D.Farahani² , M.R.Davoodabadi³, ¹Islamic azad university, Iran, ²Tehran University, Iran and ³Semnan University, Iran

In this paper, the unsteady motion of a spherical particle rolling down an inclined tube in a Newtonian fluid for a range of Reynolds numbers was solved using a simulation method called the Differential Transformation Method (DTM). The concept of differential transformation is briefly introduced, and then we employed it to derive solution of nonlinear equation. The obtained results for displacement, velocity and acceleration of the motion from DTM are compared with those from numerical solution to verify the accuracy of the proposed method. The effects of particle diameter (size), continues phase viscosity and inclination angles was studied. As an important result it was found that the inclination angle does not affect the acceleration duration. The results reveal that the Differential Transformation Method can achieve suitable results in predicting the solution of such problems.

Spherical particle; Acceleration motion; Inclination angle; Non-linear equation, Differential Transformation Method (DTM).