ACCELERATION MOTION OF A SINGLE VERTICALLY FALLING NON-SPHERICAL PARTICLE IN INCOMPRESSIBLE NON- NEWTONIAN FLUID BY DIFFERENT METHODS

摘要

An analytical investigation is applied for acceleration motion of a vertically falling non-spherical particle in a Shear-thinning (n< 1) and Shear-thickening (n> 1) power low fluid. The acceleration motion of a vertically falling non-spherical particle in non-Newtonian fluid can be described by the force balance equation (Basset-Boussinesq-Ossen equation).The main difficulty in the solution of this equation lies in the nonlinear term due to the nonlinearity nature of the drag coefficient. Varinational Iterations Method (VIM) and Numerical Method (Runge- Kutta 4~(th) order method) are used to solve the present problem. The results were compared with those obtained from VIM by R-K 4~(th)order method. We find that VIM which was used to solve such non-linear differential equation with fractional power is simpler and more accurate than other methods. Analytical results also indicate that the velocity in a falling procedure is significantly increased with approaching flow behavior to n → 2 that validated the results obtained by the numerical method. Acceleration motion of a vertically falling single non-spherical particle decreases as the behavior index increases and the particle falling in high behavior index fluid attains its terminal velocity earlier as compared to its motion in a low behavior index fluid. To obtain the results for all different methods, the software MATLAB is used.