An Example to the Numerical Processing of Nonisothermal Flow of non-Newtonian Fluids

This chapter discusses the flow of a non-Newtonian fluid round a hot sphere falling along the centre line of a cylindrical tube by using parallel computers. The description of nonisothermal flows not only requires the simultaneous solution of three equations of change (continuity, motion, and energy), but in addition, the temperature dependence of all physical properties, especially that of the viscosity. For polymeric liquids, the shear-rate dependence of the viscosity cannot be neglected. Due to the temperature dependence of the viscosity and constitutive equation coefficients, the equation of motion and energy are strongly coupled. In general, the solution of the set of equations of change cannot be obtained analytically. This problem can be resolved for the isothermal case using the Finite Element Method.