Solutions of equations of motion of incompressible fluid with general function of degree five

AbstractNavier–Stokes Equations (NSE) are considered as basics of different fields of science and engineering. This study discusses exact solution of incompressible fluids with variable viscosity of specified fluid flow in the absence of external forces. Exact solutions of NSE describe the dynamics of fluid flow in a better way than other approximate methods. In this study fluid flow with the general function of degree five has been discussed through the solution of ordinary differential equations. Martin’s coordinates and von Mises variables are used to transform NSE into more simple system of ordinary differential equations, which then provide exact solutions subject to different cases. Final solutions are simplified using MATLAB routine. Streamline pattern for the fluid flows is also plotted for different cases