Effects of MHD and Porosity on Jeffrey Fluid Flow with Wall Transpiration

Abstract

In this research work, the velocity of Jeffrey fluid flow which is unsteady in nature, over an infinite horizontal porous plate, is considered, and also, the influence of MHD and porosity on the velocity of the fluid is investigated. The major objective of this research paper is to achieve the analytical solution for the incompressible transient flow of MHD (magneto hydrodynamic) Jeffrey fluid above an accelerating porous plate. The fluid flows above the plate at $y>0$ , and the plate is infinite in the x-direction $\left(y=0\right)$ and gives an oscillatory motion. For the occurrence of both injection and suction phenomena, porous plate is used. The governing equation of the model becomes dimensionless by using the appropriate set of nondimensional variables. With the help of Laplace transformation and perturbation methods, these nondimensional differential equations of Jeffrey fluid are solved. The effects of different parameters on velocity are studied. These parameters include ω (oscillating frequency), λ1 (ratio of relaxation and retardation time), β (Jeffrey fluid parameter), γ (wall transpiration parameter), t (time), k (porosity parameter), and Ha (magnetic parameter). We found that velocity declines as we increase the values of ratio of relaxation and retardation times, Jeffrey fluid parameter, wall transpiration parameter, and magnetic parameter. The effect of time, oscillation frequency, and porosity on velocity profile is opposite as that of other parameters. We take $\beta <1$ , as $\beta$ represents perturbed parameter. Graphs are plotted for various values of these parameters with the help of Mathcad software and talk over these graphs in detail.