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Dissipative flow of viscoelastic polymer compound in a porous channel

Baranov A.V.

#### Abstract:

The heat exchange at the flow of non-Newtonian fluid in a flat channel filled with porous material is investigated. Brinkman model is taken as the equation of motion. 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. The flow is described by the Brinkman equation. Phan-Thien-Tanner model is used as a rheological model. There are no transverse normal stresses and no transverse velocity component. When writing the energy equation, a single-temperature model is used. This approach assumes a local thermal equilibrium between the liquid and solid phases. Thermal boundary conditions of the first kind and the energy dissipation are taken into account. The temperature dependence of the viscosity is not considered. 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 solution was analyzed numerically by the finite difference method. Results of calculations have been presented. Accounting for viscoelasticity makes the velocity profile even more flat. A significant effect of Weissenberg and Brinkman numbers on the temperature profile and Nusselt number distribution along the channel has been shown. It was also noted that the inclusion of viscoelasticity with significant values of Weissenberg number tends to reduce dissipative heating of the liquid. This is reflected both in the temperature profiles and the local heat transfer on the channel wall. The calculations show that the impact of elastic properties is so great that neglect of viscoelastic effects can result in significant error.

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