Start-off MHD electrokinetic Couette flow in an annulus: A Riemann-sum approximation approach

Abstract

The time dependent Couette flow of an electrically conducting fluid in a horizontal annulus in the presence of electric potential and accelerated motion of the outer cylinder is investigated. The governing electric field potential as well as the momentum equations are obtained from Poisson–Boltzmann and Navier-Stokes equations respectively. As a promising tool for solving time-dependent problems, the Laplace transform technique is used to obtain analytical solution for electric field and velocity profile in Laplace domain. Using the Riemann-sum approximation simulation, the results are obtained numerically in time-domain. In the course of numerical and graphical representations of results, it is found that the magnitude of electrokinetic effect as well as Debye-Hückel parameter play important role in flow formation and mass flow rate in the horizontal annulus. Further, velocity, skin-friction and mass flow-rate decrease with increase in Debye-Hückel parameter at all-time regardless of the mode of application of magnetic field. In addition, mass flow-rate can be enhanced with increasing Hartmann number when the magnetic field fixed relative to the moving cylinder.