Taylor–Couette flow of a generalized second grade fluid due to a constant couple

Abstract

The velocity field and the adequate shear stress, corresponding to the flow of a generalized second grade fluid in an annular region between two infinite coaxial cylinders, are determined by means of Laplace and finite Hankel transforms. The motion is produced by the inner cylinder which is rotating about its axis due to a constant torque f per unit length. The solutions that have been obtained satisfy all imposed initial and boundary conditions. For β → 1 or β → 1 and α1 → 0, the corresponding solutions for an ordinary second grade fluid, respectively, for the Newtonian fluid, performing the same motion, are obtained as limiting cases.

Taylor–Couette flow of a fractional second grade fluid in an annulus due to a time-dependent couple

“…For such flows the constraint of incompressibility is automatically satisfied. The non-trivial shear stress τ (r, t) = S rθ (r, t) corresponding to such a motion of a second grade fluid is given by [23] τ (r,…”

Exact Solutions for the Poiseuille Flow of a Generalized Maxwell Fluid Induced by Time-Dependent Shear Stress

“…In the following section, the fractional partial differential equations (2.3) and (2.4), with appropriate initial and boundary conditions, will be solved by means of the finite Hankel and Laplace transforms. In order to avoid lengthy calculations of residues and contour integrals, the discrete inverse Laplace method will be used [2,5,11,12,16,17,21].…”

“…This generalization allows us to define precisely noninteger order integrals or derivatives. Many 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 [2,5,11,12,16,17,20,21]. Furthermore, the one-dimensional fractional derivative Maxwell model has been very useful in modelling the linear viscoelastic response of some polymers in the glass transition and the glass state [10].…”

Exact Solutions for an Unsteady Flow of Viscoelastic Fluid in Cylindrical Domains Using the Fractional Maxwell Model

“…The velocity field and the associated tangential stress corresponding to the rotational flow of a generalized second grade fluid within an infinite circular cylinder have been obtained by [10]. Various other studies have been done recently on non-Newtonian fluids [11][12][13][14][15][16][17][18].…”