Intensification of heat transfer with an application of strong magnetic gradients

. Experimental analysis of a strong magnetic field influence on heat transfer by paramagnetic fluid was conducted. A rectangular enclosure, filled with working fluid, was placed inside superconducting magnet’s working section in Rayleigh-Bénard configuration and three temperature differences between heated and cooled walls ΔT= 3, 5, 11 [°C] were applied. On the basis of performed measurements heat transfer analysis in the form of Nusselt number, conduction and convection heat fluxes calculations was conducted. Obtained results demonstrated that Nusselt number strongly depends on the temperature difference between thermally active walls as well as on the magnetic induction applied to the system. An application of external high magnetic field from 0 [T] to 10 [T] caused an increase of the heat transfer rate – about 250% for ΔT = 3 [°C] and over 340% for ΔT = 5, 11 and 20 [°C] and can be successfully implemented to heat transfer intensification for paramagnetic fluids.


Introduction
Buoyancy-driven natural convection control in closed system is crucial in many applications, such as: heat exchangers, chemical reactors, space industry or nongravitational state research.
To influence a fluid flow with paramagnetic or diamagnetic properties, a high magnetic field gradient should be applied. Then, depending on mutual configuration of magnetic and gravitational forces, different results could be achieved.
First published results with a paramagnetic fluid convection enhancement and suppression was presented by Braithwaite [1]. Tagawa [2] developed a model equation for thermo-magnetic convection. Bednarz [3] studied thermo-magnetic convection in configuration with one side wall heated and the opposite one cooled. Pyrda et al. investigated heat transfer enhancement in cubical enclosure [4] and developed non-dimensional analysis of paramagnetic fluid in Rayleigh-Bénard configuration [5]. Kenjeres et al. investigated oscillatory states in thermal convection of a paramagnetic fluid in a cubical enclosure subjected to a magnetic field gradient [6] and turbulence pockets in thermal convection of paramagnetic fluid subjected to strong magnetic field gradients [7]. His group performed numerical and experimental study of Rayleigh-Bénard-Kelvin Convection [8].
In present paper authors will focus on heat transfer enhancement with utilization of thermo-magnetic convection of paramagnetic fluid.

Experimental apparatus
Apparatus used to performed experimental analysis of thermo-magnetic convection is shown in Figure 1. It consisted of an experimental enclosure placed in the bore of a superconducting magnet (HF10-100VHT-B, Sumito Heavy Industries, Ltd. Japan), thermostating bath with constant temperature flow, a heater control system, and a data acquisition system connected to a personal computer. The experimental enclosure of dimensions 0.032 x 0.032 [m] in base and 0.016 [m] in height is presented in Figure 2.
Experimental enclosure, heated from one horizontal wall and cooled from the opposite one, consisted of following elements: cooling chamber filled with cold water (     Measuring vessel was placed in the upper half of the superconducting magnet, where gravitational and magnetic forces acted in the same direction, causing enhancement of convective flow, as shown in Figure 3. This position is correlated to the location of a maximal value of grad b 0 , where b 0 stand for magnetic induction, and it was 0.095 [m] from the magnet's top.

Working fluid
As a working fluid, 50% volume glycerol aqueous solution with an addition of 0.8 mol/(kg of solution) gadolinium nitrate hexahydrate Gd(NO3)3•6H2O to make it paramagnetic, was chosen. Properties of the working fluid are listed in Table 1. Assuming one-dimensional conductive heat flow, the heat flux can be calculated from Fourier's law of conduction, and therefore the difference between directly measured heat flux and the heat flux calculated from Fourier's law is the heat loss from the experimental enclosure. The next step was connected with analysis of a thermo-magnetic convection. Experimental enclosure, filled with working fluid, was rotated 180 degrees to Rayleigh-Bénard configuration, with bottom wall heated and the opposite one cooled. The power supply was set to obtain chosen temperature difference between thermally active walls and the setup was left to obtain a stable state. Then temperature, electrical current and voltage were recorded and magnetic field was applied to the system by stages of 1 [T].

Heat transfer analysis
Temperature signals recorded during experimental analysis allowed investigation on a heat transfer rate, which was established by calculation of dimensionless parameter called Nusselt number. This criterion, speaking of a heat transfer in analysed system, can be written as follows: The net convection (Qnet_conv) and net conduction (Qnet_cond) heat fluxes were estimated accrording to method proposed in [9] Assuming that the heat loss depends only on the temperature of the heated wall, conduction measurements were made and heat losses were estimated from : where:   By applying equations (2),( 4) and (5) to (1) expression for Nusselt number can be expressed as follows: The results of heat transfer analysis are presented in Figure 5 -7. According to equation (1) Nusselt number is a ratio of a convective heat flux to a conduction heat flux in the analysed system. Figures 6 and 7  and maximal magnetic induction in the center of the magnet convective heat flux rises over about 250% in comparison to natural convection case. For higher temperature differences this increase is even bigger and equals over 330%.

Summary
In this paper experimental analysis of thermo-magnetic convection of paramagnetic fluid was conducted. Four temperature differences between heated bottom wall and the opposite one cooled were applied and an influence of magnetic field induction on experimental fluid from 0 [T] to 10 [T] was tested. Performed analysis of signals obtained from thermocouples placed in the experimental enclosure enabled calculation of heat transfer indicator in the form of a Nusselt number and conduction and convection heat fluxes. Obtained results led to the following conclusions: (a) the Nusselt number strongly depends on temperature difference between thermally active walls, as well as on magnetic induction in the system; (b) an application of external magnetic field from 0 [T] to 10 [T] causes an increase of the heat transfer rate -about 250% for ΔT = 3 [°C] and over 340% for ΔT = 5, 11 and 20 [°C]; (c) conduction heat flux increase with higher temperature differences, but does not depend on magnetic induction; (d) convective heat flux strongly depends on magnetic induction in the center of the magnet and the increase in its rate with magnetic induction up to 10 [T] is over 250% for every temperature difference; (e) external magnetic field can be successfully implemented to heat transfer intensification for paramagnetic fluids.