A study on the effects of a generalized newtonian fluid's characteristics on entropy production

In this study, the heat transfer flow of Powell-Eyring fluid, a generalized Newtonian fluid, in a planar channel was investigated. The fluid moves through the gradient of the pressure within the geometry of the channel and is exposed to constant heat flux from the channel surfaces. Even though the flow geometry is two-dimensional, the velocity profile is taken as one dimensional with the hydrodynamically fully developed acceptance. Under these assumptions, the momentum and energy equations giving the velocity and temperature profiles of the fluid were extracted. Since the energy equation has a constant heat flux from the surfaces, the temperature gradient is included in the vertical direction. In addition, the terms related to the heating due to viscous friction were added to the energy equation. For the solution of the nonlinear momentum equation, the Powell-Eyring fluid parameter was considered small and a perturbation technique was used. Using this solution, temperature profiles were found by direct integration of the energy equation. Perturbation solutions are valid in an approximate and limited range due to small parameter acceptance. A numerical algorithm was used to confirm these solutions. The numerical decoder is based on the variable step level 4 and 5 Runge-Kutta-Fehlberg algorithm for initial value problems. Then, with the help of the fluid velocity and temperature profiles, which were confirmed to be accurate, the velocity and temperature of the fluid to the medium were calculated and these expressions were used analytically to remove the Nusselt number. It has been shown that the Nusselt number provides all the frictionless and friction states of the Newtonian fluid found in the literature. The amount of entropy production or irreversibility associated with wasted energy in flow geometry has been studied with the second law analysis. The total amount of entropy was calculated analytically and numerically. The effect of heat transfer and viscous heating due to temperature differences on total entropy production was discussed using Bejan number and all analytical results were confirmed by numerical algorithm.