Numerical solution of the flow of a second-order fluid under an enclosed rotating disc

The solution of a non-linear boundary value problem arising due to the steady flow of an incompressible second-order fluid (flowing with a small mass rate of symmetrical radial outflow in, taken negative for a net radial inflow) under finite rotating disc (enclosed within a co-axial cylindrical casing) has been obtained numerically using finite difference method. The resulting equations are converted into a set of difference equations. Starting from the known values of flow functions for small values of the Reynolds number, the solution is extended for larger Reynolds number by making use of Newton-Raphson iterative method and Gauss elimination method. Effects of second order forces in the flow on the velocity field have been investigated in detail in the regions of recirculation and no-recirculation for the cases of radial outflow and inflow and illustrated graphically. Such flows are useful in mechanical and chemical industries.