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

Abstract

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.

Keywords

• Entrance region
• Inlet region
• Filled region
• Power-law fluid
• Developing heat transfer
• Nusselt number