Asymptotic analysis of MHD viscous fluid flow due to a rotating disc and a radially stretching-shrinking disc with Navier slip condition

摘要

This paper presents the impact of magnetic field on partially slip flow of viscous fluid between two parallel discs separated by distance h where the lower disc rotates at the rate Omega about a fixed axis and the upper disc stretches or shrinks radially at the rate a. A similarity reduction reduces the Navier-Stokes equation with their boundary conditions into a pair of coupled differential equations and reduced boundary condition having four parameters i.e. M = sigma*h(2)B(0)(2)/rho nu, lambda = N/h, R = vertical bar a vertical bar h(2)/nu and sigma = Omega/vertical bar a vertical bar where sigma*, rho, nu and B-0 are electrical conductivity, density, kinematics viscosity of fluid and magnetic field strength. The influence of magnetic field and slip boundary condition on radial velocity profile and azimuthal velocity profile are discussed for both cases of the upper disc i.e. stretching upper disc and shrinking upper disc. Solutions for low Reynolds number (R) are obtained by perturbation technique which, along with the large-R asymptotic behaviors, are compared with the numerical results for discs shear stress parameters. The results show that slip parameter and magnetic field can be used to reduce the shear stress and control the boundary layer that develops on the discs.