Investigation on unsteady fluid flow around an oscillating sphere-A numerical and analytical approach

This article presents the Investigation on unsteady fluid flow around an oscillating sphere-A Numerical and Analytical approach. The analytical expressions for angular velocity and temperature of the fluid around an oscillating sphere have been obtained in form of Bessel functions with suitable assumed boundary conditions. The numerical results in terms of angular velocity, temperature and pressure distribution for various values of the material parameters have been obtained using R-K method of 6th order with shooting methods with the help of MATHEMATICA ND solver. The influence of thermo-viscous flow parameters on angular velocity, temperature, pressure and drag on the boundary have been presented in form of tables and graphs. It may be noticed that the thermo-viscous effects are more predominant in the flow region around the boundary of the oscillating sphere. The R-K method with shooting method is the most powerful and elegant method to solve the governing equations related to the fluid dynamics problems. This method gives the accurate and valid results of highly complex coupled governing equations. The analytical results obtained are validated with this method in the present problem. The results obtained by this method gives more accurate, stable and converging to the analytical results. The numerical solutions of governing equations of present work have been obtained are compared with the existing analytical results and are found to be in excellent agreement. The present theoretical work will be hope fully for the better understanding of researchers and scientists and also it is useful in chemical and nuclear industries.