Analysis of heat transfer for simultaneously developing temperature profile and fluid flow of power-law fluids in the entrance region of a tube

Abstract

• Simultaneously developing power-law fluid flow and heat transfer in a tube is addressed. • The model is based on the inlet-filled region concept. • The heat transfer solution is obtained using an integral method. • The model is validated against published results, and asymptotically against the fully developed solution. • Results include Nusselt number profiles and entrance region length for different values of the power-law fluid index and Prandtl number. Developing heat transfer in a tube subjected to a constant heat flux is investigated in the case of simultaneously developing fluid flow of a power law fluid in a circular duct using an integral boundary layer model. The inlet-filled region concept is used to solve the heat transfer problem with the velocity profile determined from a previously published and validated hydrodynamic model. The thermal entrance region is divided into a thermal inlet-hydrodynamic inlet zone, followed by a thermal inlet-hydrodynamic filled zone, and last a thermally filled-hydrodynamic filled zone. The heat transfer results are validated against published power-law Nusselt number profiles, and published thermal boundary layer thickness and local Nusselt number profiles for Newtonian fluids as a special case. Furthermore, the asymptotically reached values are validated against the fully developed values. The model presented is predominantly analytical and requires minor computational work.