Flow on oscillating rectangular duct for Maxwell fluid

Abstract

This paper presents an analysis for the unsteady flow of an incompressible Maxwell fluid in an oscillating rectangular cross section. By using the Fourier and Laplace transforms as mathematical tools, the solutions are presented as a sum of the steady-state and transient solutions. For large time, when the transients disappear, the solution is represented by the steady-state solution. The solutions for the Newtonian fluids appear as limiting cases of the solutions obtained here. In the absence of the frequency of oscillations, we obtain the problem for the flow of the Maxwell fluid in a duct of a rectangular cross-section moving parallel to its length. Finally, the required time to reach the steady-state for sine oscillations of the rectangular duct is obtained by graphical illustrations for different parameters. Moreover, the graphs are sketched for the velocity.

Flow through an Oscillating Rectangular Duct for Generalized Oldroyd-B Fluid with Fractional Derivatives

“…Eliminating 12 , and    between Eqs. in (8) and (9), we obtain the following fractional differential equation…”

“…Nazar, M. et al [8] presented an analysis for the unsteady flow of incompressible Maxwell fluid in an oscillating rectangular cross section. Sultan, Q. et al [10] discussed the analytic solution for the unsteady magnetohydrodynamic (MHD) flow of Oldroyd-B fluid in long porous rectangular cross-section.…”

Unsteady Magnetohydrodynamic Flow of Jeffrey Fluid through a Porous Oscillating Rectangular Duct

“…Fetecau and Fetecau [11] investigated the flows of Oldroyd-B fluid in a channel of rectangular cross-section. Nazar et al [12] examined oscillating flow passing through rectangular duct for Maxwell fluid using integral transforms. Unsteady magnetohydrodynamic flow of Maxwell fluid passing through porous rectangular duct was studied by Sultan et al [13].…”

Flow of Generalized Burgers’ Fluid Induced by Sawtooth Pulses Stress with Quadratic Edges

“…The boundary condition used is of interest as sound waves, light waves, and ocean waves travel like the form of sawtooth pulses. Study of sawtooth pulses flows is also important because of their increasing applications in aerospace science, astrophysics, atmospheric science, and physiological fluid dynamics as by Ghosh [18]. Moreover, a sawtooth wave has strong electromagnetic properties.…”