On the Taylor–Couette °ow of fractional oldroyd-B °uids in a cylindrically symmetric con¯guration using transforms

The focus in this study is to examine the °ow formation of Taylor–Couette (T–C) for some °uids exhibiting non-Newtonian properties in a region of cylindrical annulus due to the e®ect 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 °uid through the annulus. It is very often when researchers in di®erent ¯elds 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 di®erent ¯elds. 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 ¯eld and the corresponding shear stresses (SS) for the fractional Oldroyd-B °uid (O-B °uid). In the end, a graphical presentation is given for the comparison of the e®ect on °uid motion due to di®erent parameters like fractional parameters, relaxation and retardation times.