Heat transfer increase for a laminar pipe flow of a magnetic fluid subjected to constant heat flux: Improvements and additional discussions

This work presents important additional discussions regarding our recent publication: Heat transfer increase for a laminar pipe flow of a magnetic fluid subjected to constant heat flux: an initial theoretical approach. In our first paper we proposed a theoretical law to predict the mean Nusselt number for a laminar pipe flow of a magnetic fluid subjected to a constant heat flux from the walls. We have considered a magnetic fluid flowing inside a small pipe under the action of an uniform magnetic field. From our analysis we have proposed a functional dependency on the mean Nusselt number with respect to magnetic parameters. This increase/decrease in the heat transfer rates inside the pipe arose from a production term in the equation of energy. We have interpreted it as a mechanism related to the deformation of clusters of magnetic particles formed in the microstructure of the fluid. In the present manuscript we present additional physical discussions regarding our previous derivation and propose a correction parameter ζ in this mechanism. This parameter intends to provide a more realistic modeling of this phenomenon, consistent with the restrictive assumptions assumed on our first paper. We also present some new results using Langevin Dynamics to show that this production term spontaneously appear when a non-superparamagnetic fluid is subjected to a shear field under a constant uniform magnetic field.