Micropolarity Ramification of Asymmetric Merging Flow

Abstract

The steady, asymmetric and two-dimensional flow of viscous, incompressible micropolar fluid through a rectangular channel with a splitter (parallel to walls) was formulated and simulated numerically. The plane Poiseuille flow was considered far from upstream and downstream of the splitter. The geometric parameter that controls the position of splitter was defined as splitter position parameter. A numerical scheme that comprises a fourth order method followed by special finite-difference method was used to solve the boundary value problem. This numerical scheme transforms the governing equations to system of finite difference equations which we have solved by SOR iterative method. Moreover, the results obtained were further refined and upgraded by the Richardson extrapolation method. The results were compared on different grid sizes as well as with the existing results for symmetric flow of Newtonian fluids. The comparisons were satisfactory. The microrotation effects on the splitter plate were significantly high as compared to other locations of the channel. This highest value for the asymmetric channel was higher in magnitude as compared to for the symmetric one. Furthermore, the proclivity of rotation of aciculate elements of the fluid about their centroids rises if either the Reynolds' number increases or/and the distance between the upper and splitter plates decreases.