Magnetohydrodynamic flow induced by ciliary movement: An application to lower respiratory track diseases

•This study deals with the magneto hydrodynamics flow of viscous fluid induced by the ciliary propulsion in a porous medium which has an application to control diseases in respiratory track.•The continuity and momentum equations are simplified under the long wave length and small Reynolds number approximation.•The modelled equations are solved by analytical technique Fourier series expansion method.•If M > 0 and 1/ K > 0 the magnetic field indicate that the horizontal component of the velocity decelerates for the increasing value of magnetic field and dual behaviour is observed for the vertical component of the velocity.•The presence of porous medium shows that velocity profile increases by increasing the volume fraction parameter from 1% to 50%.•The effect of Hartmann number and volume fraction parameter show that fluid is required large amount of power for the flow in the presence of magnetic field and less amount of power is required in the presence of porous medium. This study deals with the magnetohydrodynamics flow of viscous fluid induced by the ciliary propulsion in a porous medium which has an application to control diseases in respiratory track. A symplectic metachronal wave of the micro-organism is considered for the MHD fluid flow. The continuity and momentum equations are simplified under the long wave length and small Reynolds’ number approximation. The modeled partial differential equations are solved by analytical technique Fourier series expansion method. Velocity profile, stream function and pressure gradient are plotted to see the effect of magnetic field and porous medium.