Abstract
In this paper the velocity field and the adequate shear stress
corresponding to the longitudinal flow of a fractional Maxwell fluid, between two infinite coaxial circular cylinders, are determined by applying
the Laplace and finite Hankel transforms. Initially both cylinders are at
rest and at time t = 0+ both cylinders begin to translate along their common axis with different constant accelerations. The solutions that have
been obtained are presented in terms of generalized G functions. The
expressions for the velocity field and the shear stress are in the most simplified form, and the point worth mentioning is that these expressions are
free from integral of the generalized G functions, in contrast with [20], in
which the expression for the velocity field involves integral of the generalized G functions. Moreover, these solutions satisfy both the governing
differential equation and all imposed initial and boundary conditions. The
corresponding solutions for ordinary Maxwell and Newtonian fluids are
obtained as limiting case of general solutions. Furthermore, the solutions
for the motion between the cylinders, when one of them is at rest, can also
be obtained from our results.
A. U. Awan, M. Imran, M. Athar, M. Kamran. (2013) Exact analytical solutions for a longitudinal flow of a fractional Maxwell fluid between two coaxial cylinders, Punjab University Journal of Mathematics, Volume 45, Issue 1.
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