Solution of boundary layer flows in fluids mechanics by using finite difference method

In this study, two dimensional, steady flow, laminar boundary layer equations of a modified power-law fluid of third grade are treated. The model is a combination of power-law and third grade fluid which the fluid may exhibit normal stresses, shear thinning (n<0) or shear thickening (n>0) behaviors. The equations of motion are derived for power-law and third grade fluids. Acceleration terms, viscous term, power-law and third grade fluid terms are calculated for Cartesian coordinates. These equations and boundary conditions have been made dimensionless to be able to generalize results. The coupled partial differential equation system is transformed into an ordinary differential equation system via similarity transformation. Classical boundary layer conditions are considered, and a numerical finite difference scheme is used to integrate the equations. Effect of power-law index n and third grade coefficient on the boundary layer solutions is investigated. x and Y component of velocities are drawn for various n values. For shear thickening n values, a decrease in both the component of velocities is observed for increasing n. Whereas, for shear thinning n values, a increase in both the component of velocities is observed for decreasing n. As the third grade fluid coefficient increases, the boundary gets thicker.