Motion analysis of a spherical solid particle in plane Couette Newtonian fluid flow

• Particle's motion in Couette fluid flow is studied.
• DTM–Padé is used to solve this problem.
• The results of DTM–Padé are in excellent agreement with numerical ones.

In this article, the motion of a spherical particle in a plane Couette Newtonian fluid flow is studied. The governing equations of a spherical solid particle's motion in the plane Couette fluid flow are investigated using the Differential Transformation Method (DTM) and a Padé approximant which are an analytical solution technique. For validation of the analytical solution, the governing equation is solved numerically. The horizontal and vertical velocities of spherical solid particle are shown for different fluids and values of the embedding parameters. The DTM–Padé results indicate that the horizontal and vertical velocities of spherical solid particle in water fluid are higher than the glycerin and ethylene-glycol fluids. Also the horizontal and vertical velocities increase with an increase in the particle radius. Comparison of the results (DTM and numerical) was shown that the analytical method and numerical data are in a good agreement with each other.

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