Modelling of non-Newtonian fluids

The problem of the non-Newtonian fluid flow is solved. The basic equations are derived based on the Newtonian fluid flow but using special constitutive equation for the viscosity. The spatial discretization is done using the finite element method (FEM). The algorithm is tested on a simple axial symmetric flow in a horizontal tube and comparison to Newtonian fluid is stated. Application for the synovial fluid flow modelling in the total knee replacement is presented. The model is simplified as a planar model and the pressure distribution due to the interaction between femur and tibia in the synovial fluid is computed.