In most polymer processes the quality of the final part stems back in great part to the mixing of the polymer blends and the viscous heating that occurs during the process. To date, these processes have been simulated using the finite difference or finite element methods which rely on cumbersome remeshing techniques, restricting the analysis to simple geometries. However, mathematical manipulation of the governing equations results in boundary integrals, allowing the solution of complicated moving boundary problems without domain meshing. The resulting boundary element model and simulation results of flow with heat transfer and the blending of two or more fluids of different viscosity effects during mixing of polymer blends is presented in this paper. The results give insight to the complex phenomena that take lace during mixing processes.