Heat transfer for Herschel–Bulkley fluids in the entrance region of a rectangular duct

In this study, we present a numerical solution for combined laminar fluid flow and heat transfer of Herschel–Bulkley non-Newtonian fluids in the entrance region of a rectangular duct. The governing equations are solved iteratively by using finite difference method to obtain temperature, bulk temperature, and Nusselt number. Two cases of the thermal boundary conditions are considered; (i) T thermal boundary condition “constant temperature at the wall” and (ii) H2 thermal boundary condition “constant heat flux at the wall”. The results are presented in tables and figures for different parameters for the fluid and the duct geometry.