Heat transfer increase for a laminar pipe flow of a magnetic fluid subjected to constant heat flux: An initial theoretical approach

This work presents a theoretical law to predict the mean Nusselt number for a laminar pipe flow of a magnetic fluid subjected to an uniform magnetic field. The intensity of the field, the magnetic susceptibility of the fluid and the orientation angle formed between the magnet and the direction of the flow appear explicitly in the final expression obtained in this work. The theory developed here considers the superparamagnetism hypothesis, so it can not be applied for magneto-rheological suspensions of large (micrometric) particles. However, it could be used for the vast majority of commercial ferrofluids in conceptual designs of more efficient heat exchangers, specially in microfluidic applications. The limitations of our theory are also discussed. We provide a curve with combinations of operational parameters for which the Nusselt number of the flow may be intentionally controlled in order to increase or decrease the convective heat transfer rates inside the pipe. The breakthroughs and limitations of our theory are also discussed in details as well as some suggestions for future works.