Numerical simulation of flow of a micropolar fluid between a porous disk and a non-porous disk

Abstract

Two dimensional steady, laminar and incompressible motion of a micropolar fluid between an impermeable disk and a permeable disk is considered to investigate the influence of the Reynolds number and the micropolar structure on the flow characteristics. The main flow stream is superimposed by constant injection velocity at the porous disk. An extension of Von Karman’s similarity transformations is applied to reduce governing partial differential equations (PDEs) to a set of non-linear coupled ordinary differential equations (ODEs) in dimensionless form. An algorithm based on finite difference method is employed to solve these ODEs and Richardson’s extrapolation is used to obtain higher order accuracy. The numerical results reflect the expected physical behavior of the flow phenomenon under consideration. The study indicates that the magnitude of shear stress increases strictly and indefinitely at the impermeable disk while it decreases steadily at the permeable disk, by increasing the injection velocity. Moreover, the micropolar fluids reduce the skin friction as compared to the Newtonian fluids. The magnitude of microrotation increases with increasing the magnitude of R and the micropolar parameters. The present results are in excellent comparison with the available literature results.