Combined effects of magnetic field and rheological properties on the peristaltic flow of a compressible fluid in a microfluidic channel

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The MHD peristaltic motion of a compressible and electrically conducting Jeffrey fluid induced by a surface acoustic wave in a confined parallel-plane microchannel through a porous medium is analytically investigated. A proper attention is given to the combined effects of physical parameters and magnetic field on the rheological aspects of the considered flow. The slip velocity is considered and the problem is discussed for free pumping case. The wave amplitude is related to the power output of an acoustic source. A perturbation technique is employed to analyze the problem in terms of a small amplitude ratio. In the second order approximation, the net axial velocity is calculated for various values of the fluid parameters. Finally, the effects of the parameters of interest on the mean axial velocity, the reversal flow, and the perturbation function are discussed and shown graphically. The critical value of the magnetic parameter M is discussed such that an optimum M is shown where some physical variables are obtained maximum. It is noticed that, for the Jeffrey fluid, oscillations decay rapidly as we move from the hydrodynamic to the hydromagnetic fluid, and the effect of retardation time becomes weak. It is inferred that increasing the magnetic parameter makes the fluid less prone to nonlinear effects. Several results of other fluid models are deduced as the limiting cases of our problem. This work is the most general model of peristalsis created to date with wide-ranging applications in biological microfluidic networks.