Influence of Temperature and Pressure on Viscoelastic Fluid Flow in a Plane Channel
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Journal of Engineering Physics and Thermophysics, Vol. 93, No. 5, September, 2020
TRANSFER PROCESSES IN RHEOLOGICAL MEDIA INFLUENCE OF TEMPERATURE AND PRESSURE ON VISCOELASTIC FLUID FLOW IN A PLANE CHANNEL A. V. Baranov
UDC 532.135:536.242:678:065
The hydrodynamics of a steady-state nonisothermal flow of a viscoelastic polymer medium in a plane channel and heat transfer in it under boundary conditions of the first kind have been investigated. Fluid flow with a low Reynolds number and a high Péclet number was investigated, which made it possible to neglect the gravity and inertial forces, as well as the longitudinal thermal conductivity of the medium. From the rheological viewpoint, the polymer melt represents a viscoelastic fluid; therefore the Phan-Thien–Tanner fluid model was used as a rheological model of the fluid, with viscosity depending on temperature and pressure. A high-viscosity medium was considered; therefore a dissipation term was included into the equation of the energy of its flow. With the use of the indicated rheological model the velocity profile of fluid flow was obtained in an explicit form from the equation of fluid motion. It has been established that the dependence of the fluid viscosity on temperature and pressure exerts a noticeable influence on the distribution of the Nusselt number and of bulk temperature of the fluid along the channel length. It is shown that account for the temperature dependence of fluid viscosity leads to a decrease in the role of energy dissipation of its flow in the process of flow heating and that, conversely, the dependence of the fluid viscosity on pressure considerably enhances the dissipation effect. The problem has been solved numerically by the method of finite differences. Keywords: viscoelastic fluid, heat exchange, nonisothermal flow, dissipation. Introduction. Numerous publications, a partial survey of which is presented in work [1], are devoted to investigation of the processes of nonisothermal non-Newtonian media flow in various channels. In the present work, flow of high-viscosity polymer composite in a plane channel is considered (Fig. 1) on the assumption that the temperature of the medium T0 and the temperature of the channel walls Tw do not coincide and that Tw exceeds T0. This means that as the composite flows in the channel it will heat up from both the hot walls of the channel and due to the energy dissipation of its flow. The flow of viscoelastic composites is accompanied by clearly manifested highly elastic effects. In the mathematical model of such flow the first difference of normal stresses becomes significant, which requires incorporation of the rheological equation of nonlinear viscoelastic medium into this model. It is considered at the present time that the best results in describing the flows of nonlinear viscoelastic media are yielded by rheological models of relaxation (velocity) type. Often, especially in the foreign literature, they are also called differential. One of the most efficient models of this type is the Phan-Thien–Tan
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