Abstract
The focus in this study is to examine the flow formation of Taylor-Couette (T-C) for some fluids exhibiting non-Newtonian properties in a region of cylindrical annulus due to the effect of imposed stresses on the periphery of the inner cylinder while the outer cylinder is hanging around inert. This tangential shear will be liable for the motion of the fluid through the annulus. It is very often when researchers in different fields like engineering, mathematics and physics come across the complexity that the given mathematical model cannot be solved in the existing space and requires to be transformed in the space in which it can be easily solved. Thus, transforms are being used as a key tool for solving many dominant problems in different fields. Many transformations have been introduced by researchers but for solving problems in this study, we will make use of Hankel transform and Laplace transform to obtain the velocity field and the corresponding shear stresses (SS) for the fractional Oldroyd-B fluid (O-B fluid). In the end, a graphical presentation is given for the comparison of the effect on fluid motion due to different parameters like fractional parameters, relaxation and retardation times.