On the Generalized Brinkman Number Definition and Its Importance for Bingham Fluids

In this technical note we discuss the importance of using a generalized Brinkman number definition for laminar pipe flow of a Bingham fluid, when viscous dissipation effects are relevant. We show that adapting the Brinkman number definition commonly used for Newtonian fluids directly to the more general class of non-Newtonian fluids does not calculate correctly the ratio between heat generated by viscous dissipation and heat transfer at the wall and leads to a distortion of the graphical representation of the Nusselt number, Nu, rendering difficult, if not impossible, the comparisons of the Nu behavior between different Brinkman numbers. The use of the proposed generalized Brinkman number removes these problems and simultaneously it has the merit of being independent of any reference apparent viscosities.