Abstract
The velocity field and the adequate shear stress corresponding to the flow of a fractional Maxwell fluid (FMF) between two infinite coaxial cylinders, are determined by means of the Laplace and finite Hankel transforms. The motion is produced by the inner cylinder that at time t = 0+ applies a shear stress fta (a ≥ 0) to the fluid. 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. Similar solutions for ordinary Maxwell and Newtonian fluids are obtained as special cases of general solutions. The unsteady solutions corresponding to a = 1, 2, 3, ... can be written as simple or multiple integrals of similar solutions for a = 0 and we extend this for any positive real number a expressing in fractional integration. Furthermore, for a = 0, 1 and 2, the solutions corresponding to Maxwell fluid compared graphically with the solutions obtained in [1–3], earlier by a different technique. For a = 0 and 1 the unsteady motion of a Maxwell fluid, as well as that of a Newtonian fluid ultimately becomes steady and the required time to reach the steady-state is graphically established. Finally a comparison between the motions of FMF and Maxwell fluid is underlined by graphical illustrations.
Highlights
The motion of a fluid in cylindrical domains has applications in the food industry, oil exploitation, chemistry and bio-engineering [4]
The first exact solutions corresponding to motions of non-Newtonian fluids in cylindrical domains seem to be those of Ting [5] for second grade fluids, Srivastava [6] for Maxwell fluids and Waters and King [7] for Oldroyd-B fluids
The best of our knowledge, the first exact solutions for motions of non-Newtonian fluids due to a shear stress on the boundary are those of Bandelli and Rajagopal [8] and Bandelli et al [9] for second grade fluids and Waters and King [10] for Oldroyd-B fluids
Summary
The motion of a fluid in cylindrical domains has applications in the food industry, oil exploitation, chemistry and bio-engineering [4]. The first exact solutions corresponding to motions of non-Newtonian fluids in cylindrical domains seem to be those of Ting [5] for second grade fluids, Srivastava [6] for Maxwell fluids and Waters and King [7] for Oldroyd-B fluids. A lot of exact solutions corresponding to different motions of non-Newtonian fluids with fractional derivatives have been established, but we mention here only a few in cylindrical domains [15,16,17,18]. T) generalized functions, satisfy both governing equations and all imposed initial and boundary conditions They www.mii.lt/NA can be easy specialized to give the similar solutions for ordinary Maxwell and Newtonian fluids.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
