Unsteady Helical Flow of Giesekus Viscoelastic Fluid between Two Concentric Cylinders

Abstract

In this paper the unsteady helical flow of Giesekus fluid between two concentric cylinders is investigated numerically. The flow is impressed by inner cylinder's rotation and the outer cylinder's sliding or oscillating movement along its axial direction. The effects of Weissenberg number, the mobility parameter of Giesekus model, and frequency of oscillations on velocity field and shear stresses are studied. These results affirm the shear thinning behavior of Giesekus fluid. Also it was found that tangential shear stress at inner cylinder's surface, axial shear stress at outer cylinder's surface, and first normal stress difference decrease by increasing the mobility parameter and the approach of axial velocity or shear stresses to their steady periodic state values is postponed by decreasing the Reynolds number.

The Role of Fox-H Function in Analytic and Fractional Modeling of Helicity of Cylinder: Fractional Generalized Burger Fluid

“…At t = 0 + the cylinder starts to rotate around its axis r = 0 with w 1 (R, t) = ΩRH(t)sin(ωt) or w 1 (R, t) = ΩRH(t)cos(ωt) (angular velocity) and to oscillate along with the same axis w 1 (R, t) = UH(t)sin(ωt) or w 2 (R, t) = UH(t)cos(ωt) (linear velocity). Fluid is gradually moved due to shear stress; while the velocity assumed of the form (3) 1 having the governing partial differential equations (7)- (10). Such type of flow generates helices (flow in helicity); in general, its streamlines yield helices (see Fig.…”

“…Applying Laplace transform on Eqs. (9) and (10) and implementing initial and boundary conditions Eqs. (13) and 14, we find that…”