Abstract
In the presence of the joint effect of the magnetic field and the porous medium perpendicular to the bottom plate, the velocity field corresponding to the unsteady motion of a Maxwell fluid in a channel is calculated by means of Laplace and Fourier transformations. The fluid movement is created by the plate, which applies an oscillating shear stress to the fluid after time t = 0. The obtained solutions, arranged as a sum of the steady and transient-state solutions, fulfill the governing equation and applied imposed conditions (initial and boundary), which are reduced to analogous corresponded solutions to the motion on an infinite plate in the absence of side walls. As a limiting case lambda -> 0, the unsteady solution for a Newtonian fluid was retrieved by making M, 1/k, and Re zero, zero, and one, respectively. In this article the obtained general solutions are reduced to special cases in the literature. Finally, graphical diagrams demonstrate the effect of related parameters and make a comparison among Maxwell and Newtonian fluids on the components of the velocity profile. Moreover, graphically we have observed some interesting parameters such as k, M, and Re. This explains the physical situation that as k increases, the resistance of the porous medium is lowered, which increases the momentum development of the flow regime and ultimately enhances the velocity field. Physically, it may also be expected due to the fact that the application of a transverse magnetic field M results in a resistive force (called Lorentz force) similar to the drag force, and upon increasing the values of M the drag force increases, which leads to the deceleration of the flow. Although the Reynolds number reflects the ratio of inertial force and viscous force, higher values are thus correlated with greater inertial force, essentially decaying the distribution of velocity. Moreover, it is noted that the ordinary fluid is swift than Maxwell fluid.