Nonisothermal Channel Flow of a Non-Newtonian Fluid under the Conditions of Chemical Transformations

The processes of hydrodynamics and heat transfer during the flow of a non-Newtonian polymeric medium in a plane channel have been investigated with boundary conditions of the first kind. Consideration was given to a steady-state nonisothermal process with low values of the Reynolds number and high values of the Péclet number, which made it possible to neglect gravity and inertial forces, and also longitudinal thermal conductivity. The Ellis model with a viscosity dependent on temperature, pressure, and the degree of chemical transformation was used as the rheological model. A high-viscosity medium was investigated. Therefore, it is the dissipative term that was taken account of in the energy equation. With the above rheological model, an expression in explicit form was obtained from the equation of motion of such a medium for the velocity profile of its flow. It has been established that the dependence of the viscosity of a medium on its temperature, pressure, and the degree of transformation has an appreciable effect on the distribution of the temperature of the medium and the velocity of its flow along the channel’s length. Taking account of the temperature dependence of the viscosity of the medium leads to a decline in the role of dissipation in the process of its warmup. The dependence of the medium’s viscosity on pressure, conversely, considerably enhances the dissipative effect, which appreciably accelerates the course of a chemical reaction.