Flow of generalized Burgers fluid between parallel walls induced by rectified sine pulses stress

Abstract

This paper presents the unsteady magnetohydrodynamic (MHD) flow of a generalized Burgers' fluid between two parallel side walls perpendicular to a plate. The plate applies a shear stress induced by rectified sine pulses to the fluid. The obtained solutions by means of the Laplace and Fourier cosine and sine transforms are presented as a sum of the corresponding Newtonian and non-Newtonian contributions. The effects of the magnetic field, permeability, and the period of the oscillation have been observed on the fluid motion. Moreover, the influence of the side walls on the fluid motion and the distance between the walls for which the velocity of the fluid in the middle of the channel is negligible are presented by graphical illustrations.

Flow of Generalized Burgers' Fluid between Side Walls Induced by Sawtooth Pulses Stress

“…Kumar and Prasad (2014) presented the MHD pulsatile flow through a porous medium driven by an unsteady pressure gradient between permeable beds of a viscous incompressible Newtonian fluid. Further studies of fluid motions induced by stress may be found in Akhtar et al (2011), Shahid et al (2012), Sultan et al (2014) and Sultan et al (2015).…”

A Strange Result Regarding Some MHD Motions of Generalized Burgers’ Fluids with a Differential Expression of Shear Stress on the Boundary

“…Velocity vector for isothermal motions of the incompressible Newtonian or non-Newtonian fluids between two infinite horizontal parallel plates can be provided by the relation [13][14][15][16][17][18][19][20][21]:…”

“…where T is the stress tensor, T e is the extra-stress tensor, D is the rate of deformation tensor, In the existing literature there are many studies regarding motions of IGBFs in which, velocity, non-trivial shear stress or a differential expression of this shear stress is prescribed on the boundary. Among them we mention those of Zheng et al [12], Jamil [13], Sultan et al [14], Khan et al [15], Khan et al [16], Sultan and Nazar [17], Abro et al [18], Alqahtani and Khan [19], Hussain et al [20] and Fetecau et al [21] which study motions over an infinite flat plate or between two infinite horizontal parallel plates. Early enough, Renardy [22,23] remarked that differential expressions of shear stresses have to be prescribed on the boundary in order to formulate well-posed boundary value problems for motions of rate type fluids like Maxwell and Jeffrey fluids.…”

Rotational motion of fractional Maxwell fluids in a circular duct due to a time-dependent couple

“…Based on the above-mentioned remarks, in the last decade many researchers used the fractional derivatives as a remarkable tool to analyze the properties of viscoelastic fluids [26][27][28][29][30][31][32][33][34]. However, in all these works the motion of the fluid is generated by a cylinder that is rotating around its axis with a given velocity or applies to the fluid a shear stress that is given by a partial differential equation.…”