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

Abstract

Exact solutions for the velocity field and the associated shear stress, corresponding to the flow of a fractional second grade fluid 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 time-dependent torque per unit length 2πR1ft2. The solutions that have been obtained satisfy all imposed initial and boundary conditions. For β → 1, respectively β → 1 and α1 → 0, the corresponding solutions for ordinary second grade fluids and Newtonian fluids, performing the same motion, are obtained as limiting cases.

Thermomechanical Fractional Model of TEMHD Rotational Flow

“…This is due to the reaction of the fluid particles in the outer region on the inner region. Fig 4 Part(a), (c), (d) show the behavior of the stress distribution at small value of time which is compatible with recent work [30]. …”

“…We notice that the magnitude of temperature, velocity and stress were increased with the increasing time [30]. Also from Fig 2 Part(a) for the smallest value of time, the generalized theory with one relaxation time (G- theory) is prominent.…”

“…The oscillating flows in a generalized second grade fluid was studied by Jamil et al [28]. The second grade fluid flow between two cylinders was studied differently, considering the flow of such fluid [29, 30]. Sherief et al derived the fractional order theory of thermoelasticity by using fractional calculus [31].…”

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

“…The first exact solution for motion of non-Newtonian fluids that applies a constant shear stress to the fluid are those of [6] and [7] for second-grade fluids. Exact solutions for Taylor-Couette flow of a fractional second grade fluid in an annulus due to a time-dependent couple have been obtained by [8]. [9] worked on unsteady rotating flows of a viscoelastic fluid with the fractional Maxwell model between coaxial cylinders.…”