Heat transfer through thermomagnetic convection in magnetic ﬂuids induced by varying magnetic ﬁelds
Szabo, Peter Sebastian Benedek
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Magnetic ﬂuid ﬂow by thermomagnetic convection with and without buoyancy was studied in experiments and computational simulations. A mineral oil based ferro magnetic ﬂuid was subjected to varying magnetic ﬁelds to induce thermomagnetic convection. As such ﬂuids are mainly developed to increase heat transfer for cooling the fundamental eﬀects on magnetic ﬂuid ﬂow was investigated using various magnetic ﬁeld distributions. Computational simulations of natural and thermomagnetic convection are based on a Finite-Element technique and considered a constant magnetic ﬁeld gradient, a realistic magnetic ﬁeld generated by a permanent magnet and alternating magnetic ﬁelds. The magnetic ﬁeld within the ﬂuid domain was calculated by the magneto-static Maxwell equations and considered in an additional magnetic body force known as the Kelvin body force by numerical simulations. The computational model coupled the solutions of the magnetic ﬁeld equations with the heat and ﬂuid ﬂow equations. Experiments to investigate thermomagnetic convection in the presence of terrestrial gravity used infrared thermography to record temperature ﬁelds that are validated by a corresponding numerical analysis. All conﬁgurations were chosen to investigate the response of the magnetic ﬂuid to the applied body forces and their competition by varying the magnetic ﬁeld intensity and its spatial distribution. As both body forces are temperature dependent, situations were analysed numerically and experimentally to give an indication of the degree by which heat transfer may be enhanced or reduced. Results demonstrate that the Kelvin body force can be much stronger than buoyancy and can induce convection where buoyancy is not able to. This was evident in a transition area if parts of a ﬂuid domain are not fully magnetically saturated. Results for the transition from natural convection to thermomagnetic convection suggest that the domain of inﬂuence of the Kelvin body force is aligned with the dominance of the respective body force. To characterise the transition a body force ratio of the Kelvin body force to buoyancy was developed that identiﬁed the respective driving forces of the convection cells. The eﬀects on heat transfer was quantiﬁed by the Nusselt number and a suitable Rayleigh number. A modiﬁed Rayleigh number was used when both body forces were active to deﬁne an eﬀective body force by taking the relative orientation of both forces into account. Results for the alternating magnetic ﬁeld presented ﬂow ﬁelds that altered with the frequency of the applied magnetic ﬁeld but with varying amplitude. This aﬀected the heat transfer that alternated with the frequency but failed to respond instantaneously and a phase lag was observed which was characterised by three diﬀerent time scales.