Magnetohydrodynamic (MHD) flows of viscoelastic fluids in converging/diverging channels

摘要

The present work is a theoretical investigation of the applicability of magnetic fields for controlling hydrodynamic separation in Jeffrey-Hamel flows of viscoelastic fluids. To achieve this goal, a local similarity solution was found for laminar, two-dimensional flow of a viscoelastic fluid obeying second-order/second-grade model as its constitutive equation with the assumption being made that the flow is symmetric and purely radial. These assumptions enabled a third-order nonlinear ODE to be obtained as the single equation governing the MHD flow of this particular fluid in flow through converging/ diverging channels. With three physical boundary conditions available, Chebyshev collocation-point method was used to solve this ODE numerically. Results are presented in terms of parameters such as Reynolds number, Weissenberg number, channel half-angle, and the magnetic number. It was found that these parameters all have a profound effect on the velocity profiles in Jeffrey-Hamel flows. The effect of magnetic field was found to be more striking in that it is predicted to force fluid elements near the wall to exceed centerline velocity in converging channels and to suppress separation in diverging channels. Interestingly, the effect of the magnetic field in delaying flow separation is predicted to become more pronounced the higher the fluid's elasticity.