Boundary layer approach for a non-Newtonian cross fluid

In this study, the behavior of a non-Newtonian fluid within the boundary layer is analysed. Non-Newtonian fluid is modeled with Cross fluid formula and momentum equations are obtained in selected cartesian coordinates according to our physical problem. Then, boundary layer approach is applied to momentum equations which define this non-Newtonian frictional flow on the plate. The resulting partial differential momentum equations are simplified by the adoption of the boundary layer. The boundary layer equations, which will replace the momentum equations after the assumptions, were dimensioned by means of new variables. The symmetries of these original boundary layer equations, which are specific to the Cross fluid formula, were found by scaling transformation formulas. Ordinary differential equivalent equations of partial differential equations were obtained by means of the symmetries. A numerical solver was applied to the final ordinary differential equations and the effects of Cross fluid parameters on the fluid behavior were interpreted from the graphics which drawned with the obtained numerical data. As a result, viscosity constants of the fluid have similar effects with Newtonian viscosity, while other constants have similarities with the power-law formula which is another non-Newtonian fluid model.