Heat transfer to Herschel–Bulkley materials flowing in the entrance of tubes with an imposed wall temperature profile

Abstract

Heat transfer to the flow of viscoplastic materials in tubes is quite common and its analysis is fundamental to achieve a good performance in many industrial processes. This kind of phenomenon has been successfully studied over the years, but the main results are focused on the two well-known thermal boundary conditions: an imposed constant wall temperature and an imposed constant heat flux. In this work we conduct a numerical study by means of the Galerkin finite element method. The goal here is to investigate the effect of the Reynolds and Peclet numbers together with the rheological properties on the Nusselt coefficient along the tube length when a wall temperature profile is prescribed. This kind of thermal boundary condition is more reliable to characterize the process of pumping oil through risers into the sea. It is worth noting that Nu assumes infinite value at a critical point which is related to changes in the heat direction. As expected, Nu increases as the rheological fluid behavior departs from the Newtonian.