Fully Developed Laminar Forced Convection in a Circular Duct for Herschel–Bulkley Fluids With Viscous Dissipation and Axial Heat Conduction

The asymptotic behavior of laminar forced convection in a circular duct for a Herschel–Bulkley fluid of constant properties is analyzed. The viscous dissipation and the axial heat conduction effects in the fluid are both considered. The asymptotic bulk and mixing temperature field, and the asymptotic values of the bulk and mixing Nusselt numbers are determined for every boundary condition, enabling a fully developed region. In particular, it is proved that whenever the wall heat flux tends to zero, the asymptotic Nusselt number is zero. The obtained results are compared to other existing solutions in the literature for Newtonian and non-Newtonian cases.