Open AccessExact solutions for unsteady axial Couette flow of a fractional Maxwell fluid due to an accelerated shear
Author(s) -
Muhammad Athar,
Constantin Fetecău,
Muhammad Kamran,
Sohail Ahmad,
Muhammad Imran
Publication year - 2011
Publication title -
nonlinear analysis
Language(s) - English
Resource type - Journals
eISSN - 2335-8963
pISSN - 1392-5113
DOI - 10.15388/na.16.2.14101
Subject(s) - herschel–bulkley fluid , laplace transform , newtonian fluid , couette flow , classical mechanics , shear stress , generalized newtonian fluid , fluid motion , mechanics , non newtonian fluid , cylinder , maxwell's equations , physics , boundary value problem , mathematics , mathematical analysis , fluid dynamics , flow (mathematics) , shear flow , fluid mechanics , shear rate , geometry , rheology , thermodynamics
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 ft a (a 0) to the fluid. The solutions that have been obtained, presented under series form in terms of the generalizedG andR 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 fora = 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. Fora = 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