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Non-isothermal flow of reacting viscoelastic polymer compounds in a flat channel

Baranov A.V.

#### Abstract:

Mathematical model of non-isothermal flow of non-Newtonian fluid in a flat channel is presented. Many assumptions were made on the basis of the fact that the flow occurs at low values of the Reynolds number and at a high Peclet number. This allows us to neglect inertia terms in the equation of motion and ignore axial thermal conductivity in the energy equation. Phan-Thien-Tanner model is used as a rheological model. Thermal boundary conditions of the first kind and the energy dissipation are taken into account. The flow is accompanied by a chemical reaction that leads to a sharp increase in viscosity. The viscosity is considered to depend on the temperature and the degree of conversion. This, in turn, led to the inclusion of the kinetic equation of a chemical reaction in the mathematical model. It is believed that a chemical reaction takes place in one stage and can be described using a single parameter – the degree of conversion. When a certain critical degree of conversion is reached, the viscosity rushes to infinity and the compound loses its fluidity. The fluid temperature at the inlet of the channel and the temperature of the walls of the channel are different. This means that the composition in the channel will be heated both because of hot channel walls and due to energy dissipation. The heat output at a chemical reaction is not taken into account. The solution was analyzed numerically by the finite difference method according to the iterative scheme. Results of calculations have been presented. The significant influence of various factors on the velocity profiles, as well as on the distribution of pressure and mass-average temperature along the channel is shown. From the made calculations, it can be seen that the dependence of viscosity on temperature and the degree of conversion can significantly change the entire hydrodynamic and thermal situation in the channel. Thus, when calculating the mass-average temperature, ignoring the energy dissipation and the dependence of the viscosity on the degree of conversion leads to a significant error, which is growing as the dimensionless length increases.

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