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.
This paper presents the unsteady magnetohydrodynamic (MHD) flow of a generalized Burgers' fluid between two parallel side walls perpendicular to a plate. The flow is generated from rest at time 0 t induced by sawtooth pulses stress applied to the bottom plate. The solutions obtained by means of the Laplace and the Fourier cosine and sine transforms in this order are presented as a sum between the corresponding Newtonian and non-Newtonian contributions. We investigate the effect of magnetic field and permeability on the fluid motion by a numerical procedure for the inverse Laplace transform, namely Stehfest's algorithm. Moreover, the influence of side walls on the fluid motion, the effect of pulse period, magnetic and porosity parameters and material parameters is presented by graphical illustrations.
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.
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