EFFECTS OF VISCOUS DISSIPATION AND AXIAL HEAT CONDUCTION ON FORCED CONVECTION DUCT FLOW OF HERSCHEL-BULKLEY FLUID WITH UNIFORM WALL TEMPERATURE OR CONVECTIVE BOUNDARY CONDITIONS

The aim is to study the asymptotic behavior of the temperature field for the laminar forced convection of a Herschel-Bulkley fluid flowing in a circular duct considering both viscous dissipation and axial heat conduction. The asymptotic bulk and mixing Nusselt numbers and the asymptotic bulk and mixing temperature distribution are evaluated analytically in the cases of uniform wall temperature and convection with an external isothermal fluid. In particular, it has been proved that the fully developed value of Nusselt number for convective boundary conditions is independent of the Biot number and is equal to the value of fully developed Nusselt number for uniform wall temperature. The analytical results obtained in the fairly general case of Herschel-Bulkley fluid, which considers both the existence of a yield shear-stress as well as a variable viscosity as a function of shear, are compared with solutions available for the simpler cases of Newtonian fluid and some non-Newtonian fluids with viscous dissipation and/or axial heat conduction taken into account.