NUMERICAL STUDY OF A FEW PROBLEMS FOR STEADY AND INCOMPRESSIBLE FLOWS OF MICROPOLAR FLUIDS

Abstract

The present research work is the numerical study of some problems in micropolar fluids flow. The micropolar fluids are viscous fluids having five additional coefficients of viscosity as compared to usual Newtonian fluids. In the micropolar fluid theory, in addition to the usual classical field of velocity, there are two supplementary field variables, the micro-rotation ν (or spin) and the gyration parameter j which have been introduced to elucidate the kinematics of micro-motions. A micropolar fluid contains rotating micro-constituents that cause the fluid to exhibit non-Newtonian behavior. Micropolar fluid model has been found useful in the study of flows of exotic lubricants, colloidal suspensions, polymeric fluids, liquid crystals, additive suspensions, body fluids, turbulent shear flows and flows in capillaries and micro channels. The study investigates the numerical solution of a few problems for steady, laminar and incompressible flow of both the micropolar fluids and Newtonian fluids. The body couples are neglected in case of micropolar fluids flow. The similarity transformations have been used to reduce the governing partial differential equations of motion in to ordinary differential equations. The resulting boundary value problems have been solved by using appropriate numerical techniques. The central differences are applied to these differential equations. The difference equations thus obtained are solved by using Successive Over Relaxation (SOR) method and Simpson’s (1/3) rule. The numerical results have been shown both in tabular as well as in graphical forms. To obtain accuracy of the present numerical results, the computation has been carried out on three different grid sizes. The purpose of this study is to present the numerical solution of different types of flow problems in micropolar fluids as well as in computational fluid dynamics by using appropriate numerical techniques which are straightforward, easy to program and economical. It has been concluded that our numerical scheme works well to solve various flow problems of Newtonian and micropolar fluids. Moreover, the present results of both Newtonian and micropolar fluids are calculated up to six decimal place. The corresponding results of Newtonian fluids for each problem considered have been obtained and presented for comparison purposes.