Self pumping magnetic cooling

Efficient thermal management and heat recovery devices are of high technological significance for innovative energy conservation solutions. We describe a study of a self-pumping magnetic cooling device, which does not require external energy input, employing Mn–Zn ferrite nanoparticles suspended in water. The device performance depends strongly on magnetic field strength, nanoparticle content in the fluid and heat load temperature. Cooling (ΔT) by ~20 °C and ~28 °C was achieved by the application of 0.3 T magnetic field when the initial temperature of the heat load was 64 °C and 87 °C, respectively. These experiments results were in good agreement with simulations performed with COMSOL Multiphysics. Our system is a self-regulating device; as the heat load increases, the magnetization of the ferrofluid decreases; leading to an increase in the fluid velocity and consequently, faster heat transfer from the heat source to the heat sink.


Invited by Board Member Sara Majetich
Abstract Efficient thermal management and heat recovery devices are of high technological significance for innovative energy conservation solutions. We describe a study of a self-pumping magnetic cooling device, which does not require external energy input, employing Mn-Zn ferrite nanoparticles suspended in water. The device performance depends strongly on magnetic field strength, nanoparticle content in the fluid and heat load temperature. Cooling (ΔT) by ~20 °C and ~28 °C was achieved by the application of 0.3 T magnetic field when the initial temperature of the heat load was 64 °C and 87 °C, respectively. These experiments results were in good agreement with simulations performed with COMSOL Multiphysics. Our system is a self-regulating device; as the heat load increases, the magnetization of the ferrofluid decreases; leading to an increase in the fluid velocity and consequently, faster heat transfer from the heat source to the heat sink.
Keywords: magnetic nanoparticles, ferrofluid, thermomagnetic convection, thermal management device (Some figures may appear in colour only in the online journal)

Letter
Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. ferrohydrodynamics (FHD), corresponding to the forces of magnetic polarization [10]. Systems based on EHD and MHD have no moving parts and therefore possess a simple structure, however, identifying a working fluid with suitable electrical conductivity is still a challenge. In addition, MHD systems require a high magnetic force to generate significant flow because of high fluid viscosity.
The body force in FHD is the result of a change, in the presence of an applied magnetic field, of the magnetization of the magnetic material with temperature. The mechanics of FHD depends on the physical properties of a colloidal suspension of ferri-or ferromagnetic nanoparticles in a suitable liquid carrier, called a ferrofluid. A ferrofluid experiences a change in magnetization when the fluid temperature changes [11,12]. The magnetization is higher in the low temperature region compared to the high temperature region. Under the influence of an applied magnetic field, a driving force is produced for fluid flow. This ferrofluid can therefore be used as a heat transfer medium. Figure 1 shows a schematic of the system. A cold magnetic fluid (green circle) which has finite magnetization (M > 0) is attracted by the magnetic field. As the fluid enters the thermal field of the heat load, the temperature increases (red circle) beyond the Curie temperature of the magnetic nanoparticles in the ferrofluid. Therefore, in the thermal field, the ferrofluid becomes paramagnetic (M = 0) and is no longer attracted to the magnetic field. This allows ferrofluid continue to move towards the heat sink. The ferrofluid again become ferromagnetic by transferring the heat to the heat sink. The service temperature of the device can be changed by simply changing the Curie temperature of the nanoparticles in the ferrofluid.
Previous studies have referred to this effect as thermomagnetic convection [13][14][15]. Zhou et al proposed an engine whose the performance of the engine can be controlled by an external magnetic field or ferrofluid temperature [16]. Several investigations has been carried out on thermomagnetic convection of magnetic fluids, including for energy transport [13,[17][18][19][20][21][22][23][24][25][26][27]. Lian et al established a mathematical model to predict fluid flow and heat transport of the ferrofluid and to design an energy transport device [11]. Xuan et al designed a cooling device in which waste heat from an electronic device was used as the driving force for fluid flow [14].
There is still considerable scope for improvement of these devices [28,29]. Hence, a device was constructed and experiments conducted to determine the effect of heat load, magn etic particle content and magnetic field on self-pumping magnetic cooling. We fixed the initial temperature of the heat load and examined the temperature drop of the heat load due to the application of magnetic field. For the first time, the switching (application and removal of magnetic field between measurements) effect of magnetic field on cooling was studied. Modeling with COMSOL Multiphysics was also performed. These devices have a wide variety of applications, since no external energy is required for pumping, and there is no noise or vibration. Examples include space craft, server cooling, electronic devices, cold chain systems and for power generation [12,30].

Synthesis of nanoparticles and ferrofluid
Mn x Zn 1−x Fe 2 O 4 nanoparticles (x = 0.3, 0.4 and 0.5) were synthesized via the hydrothermal method. In a typical synthesis manganese (II) chloride tetrahydrate (MnCl 2 · 4H 2 O, 99%), zinc chloride, anhydrous (ZnCl 2 , 98%) and iron (III) chloride hexahydrate, ACS (FeCl 3 · 6H 2 O) were used as starting precursor. Sodium hydroxide (NaOH) was used to adjust the pH value. Each starting precursor was dissolved separately in appropriate molar quantities of purified water. 5M-NaOH was added to the iron chloride solution until the pH value was 8. The precipitate was centrifuged and washed four times with DI water. The salt solutions were then added together and vigorously stirred while adding sodium hydroxide drop wise until the pH of the reaction mixture reached a value of 11. The resulting slurry was decanted into a pressure vessel and placed into an oven at 190 °C for 4 h. The nanoparticles obtained by this method were washed several times with DI water followed by vacuum drying overnight.
Powder x-ray diffraction (XRD) was performed using a Bruker 8D ADVANCE diffractometer. The XRD data was collected from 20° to 70° with a step size of 0.02° and scan rate of 2° min −1 . The instrument was operated at 35 kV and 25 mA using CuKα radiation (λ = 0.154 nm). The Rietveld refinement of x-ray pattern reveals a single phase spinel structure (not shown). To determine the size and crystal structure, transmission electron microscopy (TEM) was carried out using a JEOL 2010 TEM at an operating voltage of 200 kV. Samples were prepared by ultrasonically dispersing a small quantity of powder in hexane, followed by placing a drop of the suspension on a holey carbon-coated copper grid and drying in air. Figure 2 shows a typical bright-field TEM image of the equiaxed Mn 0.4 Zn 0.6 Fe 2 O 4 nanoparticles. The inset of figure 2 shows a histogram of the particle size distribution, revealing an average particle size of ~11 nm. The average size observed from TEM was consistent with the value obtained from x-ray analysis.
Mn 0.4 Zn 0.6 Fe 2 O 4 nanoparticles were used to prepare the ferrofluid. The nanoparticles were coated by a surfactant to prevent their agglomeration in water. The dried nanoparticles were added to a mixture of oleic acid and HNO 3 in the ratio of 1:10, followed by 1 h mechanical stirring at 70 °C. After cooling to room temperature, the nanoparticles were extracted from the excess HNO 3 and oleic acid by a permanent magnet. Finally, the coated particles were dispersed in DI water. The stability of these nanoparticles in the fluid is crucial for self-pumping magnetic cooling. The ratio of thermal energy to magnetic energy results in an expression for particle size d < (6kT/πMH), suggesting that small particles can be suspended in a fluid, even in the presence of high magnetic fields [10,31]. Fe-Ni based nanoparticles have great potential for ferrofluid applications, not only because of their good magnetization but also soft magnetic properties [32][33][34][35][36][37]. However, the long-term stability of metallic nanoparticles in the fluid is a challenge.

Self-pumping magnetic cooling device
To build a self-pumping magnetic cooling device, a 5.2 mm inner diameter, 60 cm circumference polymer tube was used for circular flow. A heat load (electric heater made from Kanthal wires) and a heat sink (ice bath) were placed opposite each other. A Nd-Fe-B permanent magnet which can provide a maximum field of 0.3 T was placed close to the heat load. A temperature data logger with SD card was used to record the temperature as a function of time. The initial temperature of the heat load was tuned by changing the current and the voltage across the wire using a Keithley power supply (Model: 2231 A-30-3). To avoid buoyancy effect, a spirit level was used to fix the device in a horizontal position.
The experiments were carried out for heat load temperature of 64 °C, 74 °C and 87 °C, while heat sink temperature was fixed at a temperature of 0 °C by the use of ice.

Numerical simulation
2D modelling was performed using COMSOL Multiphysics simulation software version 4.4, using the finite element method and extremely fine mesh. The governing equations used in the simulation are given in the following sections.

Fluid flow equation
The value of magnetic susceptibility in the model was calculated from the magnetic susceptibility of the magnetic particles and volume concentration of these particles in the fluid. Water is diamagnetic, the value of volume magnetic susceptibility is −9.0 × 10 −6 . The Navier-Stokes equation describes the incompressible, viscous, laminar flow inside the tube [38][39][40]: where ρ, u, p, η and F f represent the local density of the flow, flow velocity, pressure, fluid viscosity and external volume force vector within each mesh cell, respectively.

Magnetic field equation
To describe the magnetic field, the following equations were used: where χ is the local susceptibility of the ferrrofluid diluted by the carrier fluid. The vector B, M, H, o µ and r µ represent the magnetic flux density, magnetic field strength, magnetization, permeability of vacuum and relative permeability, respectively.

Force calculation
The volume force term F f (N m −3 ) in the Navier-Stokes equation is the sum of the magnetic force vector F m and gravitational force vector F g

F F F
The direction of gravity is perpendicular to the flow plane in our experiments, therefore, its effect is neglected.
In the model, the magnetic fluid is assumed to be a single phase incompressible Newtonian fluid. The no slip boundary condition was applied to the channel walls. The properties of the ferrofluid in the model are taken to be: density ρ = 1044 kg m 3 , specific heat C P = 1616 J kg −1 K −1 and thermal conductivity k = 0.16 W m −1 K −1 . For the thermal boundary condition, a constant surface temperature of 273.15 K was assumed at the heat sink section and at the tube wall in the section where the heat load was placed.
The driving force is the result of magnetic and thermal gradients; the temperature distribution of the fluid can be controlled by changing the applied magnetic field. The effect of magnetic field and load temperature on cooling was studied.

Magnetic properties of nanoparticles
The magnetic properties of the samples were measured using a physical property measuring system (PPM EverCool, Quantum Design USA) equipped with a vibrating sample magnetometer probe. Figure 3 shows the temperature dependence of magnetization M(T) for Mn x Zn 1−x Fe 2 O 4 (x = 0.3, 0.4 and 0.5) nanoparticles at magnetic fields of (a)100 Oe and (b) 500 Oe. In all the samples, magnetization decreases with increasing temperature, this effect is useful for self-pumping magnetic cooling. The ferromagnetic-paramagnetic transition temperature shifts to higher values when the Mn content increases (x increasing from 0.3 to 0.5). For all samples, magnetization is higher when the applied field is 500 Oe compared to the value when the applied field is 100 Oe.

Effect of magnetic field on cooling
Experiments were carried out to determine the effect of magnetic field on cooling. Figure 4 shows the temperature distribution of the fluid in the circular loop with and without magnetic field. From the temperature distribution, it can be concluded that the fluid starts to flow only when the magnetic field is applied i.e. the driving force is the result of both magnetic and thermal fields. Figure 5 shows the effect of magnetic field on the heating coil temperature for a 4.4 W heat load. The initial temperature of the heating coil in the absence of magnetic field was fixed at 74 °C. Magnetic fields of 0 T, 0.2 T, 0.25 T and 0.3 T were applied for both the experiments and the simulations. The magn etic field was tuned by changing the distance of the permanent magnet from the tube. It is evident that the temperature of the heating coil drops with increasing magnetic field, which indicates that thermomagnetic convection, induced by the magn etic field, increases with increasing magnetic field strength.
The combination of temperature gradient and applied magnetic field results in thermomagnetic convection. Since magnetization of the magnetic fluid decreases with increasing temperature, the magnetic fluid in the heat load section possesses lower magnetization compared to other sections. It was reported in our previous work that the magnetization of MnZn ferrite nanoparticles increases with increasing magnetic field [31]. The volume force (F M ) depends on the magnitude of the applied magnetic field; larger magnetic field results in a greater cooling effect. In both experiments and simulations, with non-zero magnetic field, the temperature profiles exhibit a transient behavior (marked by an ellipse in figure 5). This behavior can be understood by the fact that the cold magnetic fluid from the heat sink reaches the hot section only after a transient time. Once the magnetic fluid from the cold section reaches the magnet (and therefore near the heat load), the temperature gradient increases, which results in greater thermomagnetic convection. Xuan et al also reported that the surface temperature of the chip shows a peak before reaching steady state [14]. Jin et al reported an enhancement in heat transfer with increasing applied magnetic field [41]. The temper ature differences after 25 min, for both experiments and simulations, are plotted in figure 6.

Effect of load temperature
To determine the effect of initial temperature of heat load on cooling, the initial temperatures of 64 °C, 74 °C and 87 °C were used. A magnetic field of 0.3 T was applied near the heat load. Figure 7 shows the temperature profiles for the heat load with and without magnetic field of 0.3 T. An obvious reduction in temperature can be seen when the magnetic field is applied. Our experimental results are in good agreement with the simulations, the parameters used in the simulation are the same as those used in the experiments. Figure 8 shows the temperature difference of the heat load with and without magnetic field for average of initial temperatures. The experimental and simulated data are shown by symbols of black square and red circle, respectively. These experimental and simulated results indicate that greater extent of cooling can be attained for higher initial temperature, therefore such devices have an attractive self-pumping regulating feature. However, the temperature limit of such devices is limited to the boiling temperature of the magnetic fluid [42].

Effect of fluid concentration
To examine the effect of volume fraction of the magnetic nanoparticles, we prepared magnetic fluids with 3%, 5%, 7% and 10% of magnetic nanoparticles in water. The initial temper ature of the heat load was 74 °C. Figure 9 shows the effect of particle content on the relationship between the cooling of the heat load and time. As the particle content increases, the assumption that the particles do not aggregate is less valid, weakening the agreement between experiment and simulation.   At high field, particles start to settle in the magnetic field direction after some time, which can decrease the fluid velocity, resulting in reduced cooling. Figure 10 shows the temperature difference of the heat load with different volume fraction of magnetic nanoparticles for experiments (black square) and simulation (red circle). Figure 11 shows the temperature profiles of the heat load when the magnetic field was applied and removed in between the measurements for fixed initial temperature in the absence of magnetic field. After achieving steady state, a magnetic field of 0.3 T was applied; a sharp drop in temperature was obvious in all cases. When the field was removed, the temperature of heat load again increased up to the initial temperature and steady state    was obtained. The cooling (ΔT) increased from ~20 °C to ~28 °C, when the initial temperature of heat load was changed from 64 °C to 87 °C. Interestingly, the temperature drop in every cycle was almost constant for fixed initial temperature. This change in temperature was achieved in less than 3 min.

Conclusions
A self pumping magnetic fluid based cooling device was studied. Chemically synthesized Mn-Zn ferrite nanoparticles were coated by oleic acid and dispersed in the water to prepare a ferrofluid. The ferrofluid was used in a device to examine the cooling of a heat load. The device consists of magnet, heat load, heat sink, polymer tube, connecters and ferrofluid. It was found that the performance of the cooling device depends strongly on the heat load temperature, magnetic particle content in the fluid and the magnetic field strength. A temperature drop of ~16 °C and ~27 °C was achieved by application of 0.3 T magnetic field when the nanoparticle content in fluid was 5% and 10%, respectively. The in situ application and removal of magnetic field of 0.3 T resulted in cooling of ~20 °C, ~24 °C and 28 °C, when the initial temperature was ~64 °C, ~74 °C and ~ 87 °C, respectively. The simulation results were in good agreement with experimental findings. These magnetic cooling devices are self-regulating, i.e. the higher the heat load, the faster the heat transfer.