Inertial flow of viscoelastic second-grade fluid in a ciliated channel under a magnetic field and darcy’s resistance

This paper proposes a mathematical analysis of the inertial flow of an MHD second-grade non-Newtonian fluid in a ciliated channel. The two-dimensional flow is modelled under the effect of inertial forces, magnetic field and Darcy’s resistance, which make the system of partial differential equations highly non-linear. To solve the complex system of partial differential equations, the Homo-topy Perturbation Method (HPM) is preferred. The HPM solutions for the velocity profile, stream function and pressure gradient are obtained using the software MATHEMATICA. The significances of the Reynolds number (due to inertial forces), Hartmann number (due to magnetic field), porosity parameter (due to Darcy’s resistance) and fluid parameters (related to the second-grade fluid) on the pressure gradient, stream function and velocity profile are discussed in detail. The pertinent parameters show that the horizontal velocity decays in the presence of a magnetic field, whereas it rises under the effect of inertial forces, Darcy’s resistance and fluid viscosity in the centre of the chan-nel. This research indicates that, for the ciliary flow of a second-grade fluid, a favourable pressure gradient (negative pressure gradient) in the horizontal direction increases when applying a magnetic field, whereas it decreases due to the porous medium. This mathematical model can be helpful to observe ciliary activity under magnetic resonance imaging, when ciliary activity is abnormal.