Entropy generation for pipe flow of a third grade fluid with Vogel model viscosity

The flow of fluid-solid mixtures in a pipe can be treated as non-Newtonian fluids of third grade. Depending upon the fluid viscosity, entropy generation in the flow system varies. In the present study, flow of third grade fluid in a pipe is considered. The Vogel model is introduced to account for the temperature-dependent viscosity. Entropy generation due to fluid friction and heat transfer in the flow system is formulated. The influence of viscosity parameters A and B on the entropy generation number is investigated. It is found that increasing viscosity parameter A reduces the entropy generation number and opposite is true for increasing viscosity parameter B.