Momentum and thermal boundary layer analysis of Carreau-Yasuda fluid

In this study, Carreau-Yasuda formula, a generalized Newtonian fluid model, is adapted to the flow on a plate. After infinite uniform velocity and constant temperature, the fluid comes into contact with the plate and therefore has a two-dimensional velocity and temperature profile due to frictional flow. In order to find the behavior of these profiles mathematically, momentum, continuity and energy equations of the flow have been obtained. All equations are mathematically comprehensive, partial and nonlinear differential equations. In order to simplify these equations, a boundary layer approach compatible with the physics of the problem has been developed. With the boundary layer approach, the flow region was narrowed and important terms in the equations were brought to the fore and some terms were neglected. Thus, the workload required for the solution of the equations without loss of generality is reduced. In spite of the simplification, since the available equations are partial differentials, the symmetries of the equations were calculated to reduce them to ordinary form. Finally, numerical solutions of the system of reduced ordinary differential equations are made. The graphs drawn from the data obtained from this analysis examined the effect of fluid parameters on the flow in the boundary layer. As a result, it has been found that our viscosity properties thicken the boundary layer while slowing down the flow, and the properties of power-law law have the opposite effects.