Development of Finite Element Models for Predicting Velocities and Pressure Distribution for Viscous Fluid Flow between two Parallel Co-Rotating Discs

The study of flow of fluid between two parallel corotating discs continues to be of great concern to engineers and mathematicians. Previous works on this physical phenomenon have extensively applied experimental, analytical and numerical methods such as finite difference, spectral, and boundary element methods of analysis. In this paper we use the Galerkin-weighted residual finite element method to develop models for predicting velocities and pressure distribution for viscous-incompressible-steadylaminar-Newtonian fluid flow between two parallel discs co-rotating at the same angular velocity.

The models in this paper are developed by first reducing the non-linear Navier-Stokes equations to solvable non-dimensional governing differential equations. Galerkin-weighted residual finite element is then used to discretized the governing equations into element equations which are combined to form the domain equations. The domain equation is solved to obtain models to predict velocities and pressures distribution after duly imposing the boundary conditions. The resulting finite element solutions for radial velocity, tangential velocity and pressure are compared to their respective exact solutions.

The results show that as the number of elements is increased the better the finite element solution approximates the exact solution; and the more the radial and tangential velocity profiles assumed better parabolic profile. More so, the results obtained shows that finite element method solutions approximate well the analytical solutions, and the finite element results converge fast as the domain is refined.