Thin film flow of magnetohydrodynamic (MHD) pseudo-plastic fluid on vertical wall

摘要

The effect of the transverse magnetic field on the thin film flow of pseudo-plastic fluid for lifting and drainage on a vertical (wall) surface is investigated. Approximate solutions are obtained analytically and numerically for the resulting non-linear and inhomogeneous ordinary differential equations arising from the constitutive equation of the pseudo-plastic fluid. Physical quantities such as the velocity profile, volume flux, average velocity, shear stress, vorticity and the force exerted by fluid on the belt surface respectively for lift and drainage are calculated. The condition for the net upward flow for lift case has also been investigated. The effect of different parameters such as the magnetic effect M2, the non-Newtonian parameter β, the Stokes number St on velocity profiles and shear stress are presented via graphs. The analysis for the analytical solution is carried out for small value of β. The analogy of the velocity profiles of MHD pseudo-plastic and MHD Newtonian fluids reveals that the MHD pseudo-plastic fluid drains down the upward moving belt faster than the MHD Newtonian fluid whereas in drainage, the behavior of the velocity profiles is vice versa. In other words, the applied magnetic field generally reduces the flow velocity in the lifting case, while, in the drainage case, the magnetic field and the velocity field are shown to have a direct relation.