#### 532.51 Mathematical simulation of non-isothermal steady flow of non-Newtonian fluid by finite element method

##### Dimitrienko Y. I. (Bauman Moscow State Technical University), Li S. -. (Bauman Moscow State Technical University)

###### FINITE ELEMENT METHOD; NON-NEWTONIAN FLUID; NON-ISOTHERMAL FLOW; ITERATIVE ALGORITHM; COMPLEX GEOMETRIC SHAPES, CONVECTION

doi: 10.18698/2309-3684-2018-2-7095

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.

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