TY - JOUR
TI - On analytical study of factional Oldroyd-B flow in annular region of two torsionally oscillating cylinders
AU - Mahmood Amir
JN - Thermal Science
PY - 2012
VL - 16
IS - 2
SP - 411
EP - 421
PT - Article
AB - The velocity field and the associated shear stress corresponding to the  torsional oscillatory flow of a fractional Oldroyd-B fluid, also called  generalized Oldroyd-B fluid (GOF), between two infinite coaxial circular  cylinders, are determined by means of the Laplace and Hankel transforms.  Initially, the fluid and cylinders are at rest and after some time both  cylinders suddenly begin to oscillate around their common axis with different  angular frequencies of their velocities. The exact analytic solutions of the  velocity field and associated shear stress, that have been obtained, are  presented under integral and series forms in terms of generalized G and R  functions. Moreover, these solutions satisfy the governing differential  equation and all imposed initial and boundary conditions. The respective  solutions for the motion between the cylinders, when one of them is at rest,  can be obtained from our general solutions. Furthermore, the corresponding  solutions for the similar flow of classical Oldroyd-B, generalized Maxwell,  classical Maxwell, generalized second grade, classical second grade and  Newtonian fluids are also obtained as limiting cases of our general  solutions.