Taylor-Couette Flow of an Oldroyd-B Fluid in an Annulus Subject to a Time-dependent Rotation

Abstract

Abstract:In this paper the velocity field and the adequate shear stress corresponding to the rotational flow of an Oldroyd-B fluid, between two infinite coaxial circular cylinders, are determined by applying the finite Hankel transforms. The motion is produced by the inner cylinder that, at time t = 0 + , is subject to a time-dependent rotational shear stress. The solutions that have been obtained are presented under series form in terms of Bessel functions, satisfy all imposed initial and boundary conditions. Moreover, these solutions satisfy both the governing differential equations and all imposed initial and boundary conditions. The corresponding solutions for Maxwell, second grade and Newtonian fluids are obtained as limiting case of general solutions. Finally, the influence of the pertinent parameters on the velocity and shear stress of the fluid is analyzed by graphical illustrations.

Investigating Magnetohydrodynamic Motions of Oldroyd-B Fluids through a Circular Cylinder Filled with Porous Medium

“…Owing to the shear, the fluid begins to move and its velocity vector w is characterized by Equation (7). The governing equations corresponding to this motion are given by Relations (8)- (10), while the initial and boundary conditions are…”

“…The first exact solutions for unsteady motions of these fluids in cylindrical domains seem to be those of Waters and King [3]. Interesting results regarding unsteady motions of incompressible Oldroyd-B fluids in such a domain have been obtained by Rajagopal and Bhatnagar [4], Wood [5], Fetecau [6], Fetecau et al [7], McGinty et al [8], Khan et al [9], Imran et al [10] and Ullah et al [11].…”

The Effect of MHD on a Longitudinal Flow of a Fractional Maxwell Fluid between Two Coaxial Cylinders

“…Fluids are classified into Newtonian and non-Newtonian where in the second case the relation between the rate of strain and shear stress is nonlinear. Newtonian fluids can be describe by Navier-Stokes equations, for more detail see (1,2). A thermodynamic framework has been put into place to develop a rate type model known as Maxwell which is non-Newtonian model, in which the ordinary Maxwell model has been replaced by the Maxwell model with fractional calculus such that the time derivative of an integer order replacing by the so-called Riemann-Liouville fractional differential operator (3,4,5,6).…”

Oscillating Motion of an Oldroyd-B Fluid with Fractional Derivatives in a Circular Cylinder

“…Exact solutions for the motion due to time-dependent shear to a nonNewtonian fluid have been discussed by Fetecau and Kannan (2005). Rotational motion within annulus of an Oldroyd-B fluid is discussed by Imran et al (2015). Some important attempts to get exact solutions of fractional non-Newtonian fluid models are listed here ), Tong et al (2005, Sultan and Nazar (2016)).…”