An analytical study on motion of a sphere rolling down an inclined plane submerged in a Newtonian fluid

The description of the motion of immersed bodies in fluids is present in several manufacturing processes. In the current study, the unsteady motion of a spherical particle rolling down an inclined plane submerged in a Newtonian environment has been studied using a drag of the form given by Chhabra and Ferreira, for wide range of Reynolds numbers. An analytical solution for velocity, acceleration and position of the particle is derived, using homotopy perturbation method. Equation of motion was solved generally and for some practical conditions. The present investigation shows the effectiveness of HPM and exhibits a new application of this method for nonlinear problems.