Characterizing Heat Transfer Enhancement in Ferrofluid 2-D Channel Flows Using Mixing Numbers

Ferrofluid channel flows have been used for many non-invasive flow manipulation applications, including drug-delivery, heat transfer enhancement, mixing enhancement, etc. Heat transfer enhancement is one of the most coveted outcomes from novel cooling systems employed for electronic cooling. While using Ferrofluids for heat transfer enhancement, the external magnetic field usually induces Kelvin Body Force, which causes the ferrofluid to swirl or ‘mix’. This mixing process causes extra convection over what is induced through fluid inertia and is responsible for heat transfer enhancement. In order to understand the phenomenon of heat transfer enhancement, it would be logical to view it from the perspective of mixing enhancement. Moreover, channel flows are most common in liquid cooling of electronics equipment, and hence such a fundamental understanding of synergies between mixing and heat transfer enhancement can help pose design rules for advanced cooling configuration for electronics cooling. In this work, a Ferrofluid channel flow is analyzed in the presence of an external magnetic field. A 2-D 90° bend channel ferrofluid flow is considered, with a significant length scale of 0.01 m, where two external current-carrying wires provide an external magnetic field. An external inward heat flux of 1000 W/m2 is applied on the walls of the channel. The channel flow is studied numerically by varying different parameters relating to the external magnetic field and flow conditions. The ferrofluid used is considered magnetite based on water as the carrier fluid, and the properties of which are modeled using appropriate mixture models for nanofluids. The mixing induced in the flow is characterized by using two different mixing numbers based on the flow velocity. This type of characterization is analogous to characterizing flow turbulence. The heat transfer enhancement is characterized using Nusselt numbers. These non-dimensional numbers (mixing) are studied in congruence with the Nusselt number to understand the relationship between the mixing and heat transfer and draw comparative inferences with flow conditions without heat transfer enhancement. Finally, conclusions are drawn between the mixing & heat transfer intensification at local and global levels and choosing the apposite mixing numbers to characterize heat transfer enhancement.