Hodograph transformation methods in non-Newtonian fluids

Solutions for the equations of motion of an incompressible second-grade fluid are obtained by employing hodograph-transformation methods. By introducing a suitable Legendre-transform function the basic equations are recast in terms of this function, and the conditions which this function should satisfy are stated. Several illustrations of the method are considered and the results for stream-lines, velocities and pressure distribution are compared with the corresponding results for viscous fluids.