A Study On Creeping Flow of Micro Polar Fluid Past a Fluid Sphere using Slip Condition

Abstract

Polar fluids contain suspensions of hard or deformable molecules in viscous fluid, newlineplasma, and other physiological fluids. Micropolar fluids are special case of polar fluids with molecules having hard spherical structure. Micropolar fluid flow past a fluid newlinesphere/liquid drop at low Reynolds numbers had wide applications in the areas such as newlineradial drift, paint rheology, tainted and pure engine solvents and cervical streams, biological and industrial applications and many other related fields. Studies of fluid sphere has applications in spray drying, petroleum refining, internal combustion engines, steam condensation and related streams. A fluid sphere, which is fixed in an incompressiblesteady and axisymmetric flow, is considered for analysis. A study of uniform flow/oscillatory flow of micropolar fluid with slip condition past a fluid sphere/ partially contaminated fluid sphere is investigated in this thesis. The entire flow region is divided into two regions i.e., external and internal region to the fluid sphere. A uniform flow of micro-polar fluid past a fluid sphere and partially contaminated fluid sphere filled with newlineviscous fluid and viscous fluid over micropolar fluid sphere vice versa were studied. newlineFor oscillatory flow past a fluid sphere and partially contaminated fluid sphere both the newlinedual flow of viscous and micropolar fluid were studied. The momentum equations are newlinederived for these situations. The velocities for the internal and external regions were newlineexpressed in terms of stream functions. In order to meet the regularity condition far newlineaway from the body they are expressed in terms of Gegenbeuer polynomial. The stream newlinefunctions and angular velocities are obtained using impermeability condition at the sur- newlineface, interfacial slip condition and shear stress continuity condition on the interface, newlineand zero angular velocity condition at the surface. The stream functions and drag co- newlineefficient acting on the surface are computed analytically. The numerical results were newlineobtained using MATLAB and represent