Analytical and Semi-Analytical Investigation and Solutions for non-Newtonian Micropolar Fluid Flows in Three Different Cases

In this paper, the goal is to provide analytical solutions for the thin film flow of a non-Newtonian fluid in different geometries and boundary conditions. An analytical solution for the non-Newtonian fluids is one of the most important and challenging issues that helps in understanding the physics of these fluids. For this purpose, the theory of micropolar fluids has been used. Thin film in three specific geometries, including flow downward on an inclined surface, flow on a moving ribbon, and flow downward on a vertical cylinder is considered. In order to solve the governing equations and obtaining the velocity and rotational fields, in the first two geometries, an analytical methods and in the third geometry a combined analytic and numerical methods are used with respect to the complexity of the equations. The rotational and velocity fields are plotted for all three cases and the results are discussed for different values of the parameters of a micropolar fluid. Also, the effect of the concentration of microelements in the fluid has been studied. It was observed that with the increase of the micropolar fluid parameter, the magnitude of velocity and rotation decreases.