ANALYTIC SOLUTIONS FOR THE UNSTEADY LONGITUDINAL FLOW OF AN OLDROYD-B FLUID WITH FRACTIONAL MODEL |
| |
| Authors: | M Nazar A Mahmood M Athar M Kamran |
| |
| Affiliation: | 1. Centre for Advanced Studies in Pure and Applied Mathematics , Bahauddin Zakariya University , Multan , Pakistan mudassar_666@yahoo.com;3. Department of Mathematics , COMSATS Institute of Information Technology , Lahore , Pakistan;4. Abdus Salam School of Mathematical Sciences , GC University , Lahore , Pakistan;5. Department of Mathematics , COMSATS Institute of Information Technology , Wah Cantt , Pakistan |
| |
| Abstract: | The unsteady flow of an Oldroyd-B fluid with fractional derivative model, between two infinite coaxial circular cylinders, is studied by using finite Hankel and Laplace transforms. The motion is produced by the inner cylinder that, at time t = 0+, is subject to a time-dependent longitudinal shear stress. The solutions that have been obtained, presented under series form in terms of the generalized G and R functions, satisfy all imposed initial and boundary conditions. The corresponding solutions for ordinary Oldroyd-B and generalized and ordinary Maxwell and Newtonian fluids, performing the same motion, are obtained as limiting cases of our general solutions. Finally, the influence of the pertinent parameters on the fluid motion, as well as a comparison between models, is shown by graphical illustrations. |
| |
| Keywords: | Fractional calculus Generalized Oldroyd-B fluid Integral transforms Shear stress Velocity field |
|
|
