The finite element method is used to simulate the nonisothermal flow of non-Newtonian viscous fluids in complex geometries. The Carreau-Yasuda model of a non-Newtonian fluid is considered, in which the dependence of the viscosity coefficient on the second invariant of the strain rate tensor has a power form. A variational formulation of the problem of the motion of a non-Newtonian fluid for a plane case is obtained. The iteration algorithm of Newton-Raphson is used to solve the Navier-Stokes equations system, and the Picard iteration algorithm is used to solve the energy equation. The problem of the movement of a polymer mass in a mold of complex variable cross section in the presence of an uneven temperature field is considered. With the help of finite element modeling, a numerical analysis of the effect of various parameters on the movement of a liquid and the heat transfer of a polymer material at different values of external pressure was carried out. It is shown that the nature of the motion of a non-Newtonian fluid essentially depends on the rheological properties of the fluid and the characteristics of the geometric shape, which must be taken into account in technological processes of plastics processing.
Димитриенко Ю.И., Шугуан Ли Конечно-элементное моделирование неизотермического стационарного течения неньютоновской жидкости в сложных областях. Математическое моделирование и численные методы, 2018, № 2, с. 70–95.