Fully developed laminar forced convection in circular ducts for power-law fluids with viscous dissipation

The asymptotic behaviour of the temperature field for the laminar and hydrodynamically developed forced convection of a power-law fluid which flows in a circular duct is studied. The effect of viscous dissipation is taken into account, while the axial heat conduction in the fluid is considered as negligible. First, it is shown that the sufficient condition for the existence of an asymptotically invariant value of the Nusselt number is less restrictive than that usually employed in the previous literature. Then, both the asymptotic Nusselt number and the asymptotic behaviour of the temperature field for the axial wall heat flux distributions which yield a thermally developed region are determined. Finally, the asymptotic Nusselt number and the asymptotic temperature distribution are evaluated analytically in the cases of either uniform wall temperature or convection with an external isothermal fluid. Copyright © 1996 Elsevier Science Ltd.