Stokes flow over axisymmetric bodies

Abstract

The present research work is the analytical study of some such problems on Stokes flow in micropolar fluids and Newtonian fluids flow over the different geometries of Reiner Rivlin fluids both in unbounded and confined medium The micropolar fluids are non Newtonian viscous fluids having some additional coefficients of viscosity as compared to usual Newtonian fluids In the micropolar fluid theory by Eringen 1964 to 1966 in addition to the usual classical field of velocity there is one more supplementary field variable the micro-rotation spin which has been introduced to elucidate the kinematics of micromotions A micropolar fluid contains rotating micro constituents that cause the fluid to exhibit non Newtonian behavior Micropolar fluid model has been found useful in the study of flows of exotic lubricants colloidal suspensions polymeric fluids liquid crystals additive suspensions body fluids turbulent shear flows and flows in container and micro channels newlineThe study investigates the analytical solution of few problems for slow steady incompressible and axisymmetric flow of Newtonian fluids and non Newtonian fluids The body couples are neglected in case of micropolar fluids flow The stream functions have been used to reduce the governing field equations of motion into partial differential equations The resulting equations are then solved by the method of separation of variables The appropriate boundary conditions mathematically consistent and physically realistic are employed to determine the arbitrary constants appearing in the solution The numerical results have been deduced and shown both in tabular as well as in graphical forms It has been concluded that our analytical scheme works well to solve various flow problems of Newtonian and micropolar fluids as the result obtained here are in good agreement with the results existing in the literature newline newline