Helical flows of fractionalized Burgers' fluids

Abstract

The unsteady flows of Burgers’ fluid with fractional derivatives model, through a circular cylinder, is studied by means of the Laplace and finite Hankel transforms. The motion is produced by the cylinder that at the initial moment begins to rotate around its axis with an angular velocity Ωt, and to slide along the same axis with linear velocity Ut. The solutions that have been obtained, presented in series form in terms of the generalized Ga,b,c(•, t) functions, satisfy all imposed initial and boundary conditions. Moreover, the corresponding solutions for fractionalized Oldroyd-B, Maxwell and second grade fluids appear as special cases of the present results. Furthermore, the solutions for ordinary Burgers’, Oldroyd-B, Maxwell, second grade and Newtonian performing the same motion, are also obtained as special cases of general solutions by substituting fractional parameters α = β = 1. Finally, the influence of the pertinent parameters on the fluid motion, as well as a comparison among models, is shown by graphical illustrations

Non-linear radiative flow of three-dimensional Burgers nanofluid with new mass flux effect

“…Moreover, Burgers fluid model is one of the most important fluid model which is used to model other geological structures such as Olivine rocks and the propagation of seismic waves in the interior of the earth. Several researchers investigated the Burgers fluid model including Jamil and Khan [17]. The steady flow of Burgers nanofluid over a stretching surface with heat generation/absorption was studied by Khan and Khan [18].…”

Semi Analytical Solutions for Fractional Oldroyd-B Fluid Through Rotating Annulus

“…Recently many researchers have worked on unsteady flow of fractionalized non-Newtonian fluids (second grade, Maxwell, Oldroyed-B and Burgers') and obtained the solutions by using integral transformations. Jamil and Khan studied the unsteady flows of Burgers' fluid with fractional derivatives model, through a circular cylinder, by means of the Laplace and finite Hankel transforms [18]. Qi and Xu discussaed unsteady flow of viscoelastic fluids with the fractional Maxwell model [19].…”