A new miniaturized engine based on thermomagnetic effect of magnetic fluids

Abstract

A new engine system, essentially consisting of a permanent NdFeB magnet, a kerosene-based magnetic fluid and a rotor, is proposed based on the thermomagnetic effect of a temperature-sensitive magnetic fluid. The rotor was driven by the thermal convection of the magnetic fluid in the presence of a homogeneous external magnetic field. A digital camera was used to record the rotation speed of the rotor to investigate the performance of the engine system under varying conditions such as heat load, heat sink temperature, and magnetic field distribution. The peak angle velocity obtained for the rotor was about 2.1 rad/min. The results illustrate that the rotation speed of the rotor increases as the input heat load increases, or as the heat sink temperature decreases. The performance of the motor is considerably influenced by the magnetic field imposed. Therefore, the performance of such an engine can be controlled conveniently by changing the external magnetic field and/or the temperature distribution in the fluid.

Keywords

magnetic fluid / thermomagnetic effect / engine

Introduction

Magnetic fluid is a colloidal suspension consisting of carrier liquid and magnetic nanoparticles. It possesses not only the flow characteristic of common Newtonian fluids, but also the magnetic features similar to those of bulk magnetic materials. Since magnetic fluid exhibits some unique characteristics under the influence of external magnetic fields such as magneto-viscous effect, magneto-thermal effect and magneto-optical effect, it has found many applications in mechanical engineering, bioengineering, and thermal engineering, etc [1-4].

The temperature-sensitive magnetic fluid induces greater research impulses because of its temperature-dependent magnetization feature and thermomagnetic effect [5-7]. Generally, in the presence of an external magnetic field, the temperature-sensitive magnetic fluid experiences a decrease in magnetization as the local temperature increases, which leads to a smaller magnetic force acting on the fluid (due to the magnetization dependence feature of the magnetic force). As the temperature variation in the temperature-sensitive magnetic fluid takes place in the presence of an external magnetic field, a non-equilibrium state in the magnetization of the fluid arises and a thermomagnetic force is produced. As the column of this fluid is exposed to an external magnetic field and temperature field (as shown in Fig. 1), the fluid on the high temperature side produces a lower magnetization than it does on the low temperature side. Therefore, the magnetic force acting on the warmer fluid is smaller than that on the cooler fluid. The result is straightforward: the fluid can be driven by the field-induced thermomagnetic force, which implies that heat energy can be converted into kinetic energy. Furthermore, the thermomagnetic convection can be enhanced when the magnetic field is strengthened or the temperature gradient increases, so that the thermomagnetic convection may be controlled. Some publications can be found on the investigation of different energy conversion devices based on thermomagnetic effect [8-11].

Matsuki et al. [8] developed an automatic cooling loop consisting of an electromagnet, a heat source, a heat sink and a loop-shape tube containing a temperature-sensitive magnetic fluid. The magnetic fluid was exposed to an external magnetic field, and a thermal field kept flowing in the loop without mechanical parts. Since the magnetic fluid has a Curie temperature much higher than the boiling point of the carrier liquid, it is less sensitive to the fluid temperature compared with the magnetic fluid with a relatively low Curie temperature. Love et al. [9] exposed a simple 2-mm-diameter glass tube with a 40-mm-long column of MF to a uniform magnetic field and a thermal field. The temperature-sensitive Mn-Zn ferrite magnetic fluid which has a low Curie temperature was employed as the working fluid. The fluid was observed to move at a speed of 1-2 mm/s. They developed the constitutive thermal, magnetic, and fluid dynamic equations associated with the magnetocaloric pump. Their experimental data agree with their simulations when they used their finite-element model.

Yamaguchi et al. [10] numerically investigated the performance of an energy conversion device using a temperature-sensitive magnetic fluid, in which the fluid was driven to circulate around a disc as exposed to magnetic and thermal fields. Heat was converted to the kinetic energy of the magnetic fluid and the disc was forced to rotate by the flowing fluid. Fumoto et al. [11] developed an automatic cooling loop consisting of a magnetic fluid, an earth magnet, a heat source, and a heat sink. A circulation flow was maintained inside the loop and the flow rate was measured using an ultrasonic liquid flowmeter. They also examined the relationship between the temperature difference and magnetic energy.

The above investigation efforts indicated the application possibilities of thermomagnetic convection. Since heat can be converted into the kinetic energy of the magnetic fluid, power output can be expected. However, no publication has been found on the power production from the heat, based on the thermomagnetic effect of a temperature-sensitive magnetic fluid.

A newly designed thermomagnetic motor is presented in this paper by introducing an elaborate gearing module into the thermomagnetic convection loop for heat-to-power energy output. The rotation characteristics of the thermomagnetic motor are examined with a digital video camera system. The performance of the rotor, as well as the temperature profiles of the magnetic fluid, is provided for a series of operational conditions. Based on the data, the constitutive thermal, magnetic, and fluid dynamic relationships of the device are discussed. After the experiment, the operation mechanism of the thermomagnetic motor is better understood, the performance of the device is improved, and the reliability of the device is promoted for different application purposes.

Experimental rig

The structure of the loop for thermomagnetic convection is schematically shown in Fig. 2. The 135 mm×125 mm loop (the dimensions of the central axis of the loop channel) is made from a 13-mm-diameter glass tube coated by sponge to reduce the heat loss from the loop to the surroundings. In the heating section, a coil of wire wrapped around the glass tube is used as an electric heater by conducting direct current (DC). In the cooling section, a cooling chamber, 30 mm in outer diameter and 60 mm in length, is integrated with the loop. The coolant of ethylene glycol, which is cooled by a constant low-temperature bath with a fine control uncertainty of ±0.1 K, circulates through the cooling chamber so that heat is transported from the magnetic fluid inside the loop to the coolant. A kerosene-based Mn-Zn ferrite magnetic fluid is employed as the working medium. Some properties of the magnetic fluid are listed in Table 1. At the gearing module, the magnetic fluid flows into a rectangular, aluminum-based channel to drive the rotor. The geometry of the rotor module is described in detail in Section 3. A digital camera is used to record the rotation speed of the rotor. The fluid temperature is measured by the Calibrated K-type thermocouples installed inside the channel near the heater area and the cooler area (as shown in Fig. 2). An NdFeB circle magnet is settled, with its axis perpendicular to the tube axis, 12 mm away from point P (i.e. the intersection between the axis of the magnet and the central axis of the glass tube, as shown in Fig. 2). The variable x (hereafter referred to as the magnet position parameter) represents the distance between the inlet of heating section (point O) and point P. The magnetic induction \mathit{\Lambda } along the axial direction of the loop is measured using a Teslameter (LAKESHORE Inc., Serial 410) with an uncertainty of 2%, and the magnitudes of the corresponding field intensity are illustrated in Fig. 3 (where the magnet position parameter x is 12 mm).

Energy conversion and transfer process

Heat-to-flow energy conversion

Because of the nonequilibrium state in the magnetic force acting on the fluid as the fluid is exposed to proper magnetic and thermal field, a circulation flow inside the loop can be formed, where heat is converted into the flow energy of the magnetic fluid in the absence of a mechanical pump. The driving force produced in the fluid inside the loop is considered based on the thermomagnetic effect. If W denotes the work done by a unit volume of the magnetic fluid, the work differential δW is given by Rosensweig [9]:

(1)\delta W=-{\mu }_{\mathrm{0}}H\left[{\left({\displaystyle \frac{\partial M}{\partial H}}\right)}_{T}dH+{\left({\displaystyle \frac{\partial M}{\partial T}}\right)}_{H}dT\right],

where M and H represent the scalar magnitude of the magnetization and magnetic field intensity, respectively. The force density experienced by the magnetic fluid is so derived as:

(2)\mathit{F}={\mu }_{\mathrm{0}}M\nabla H+{\mu }_{\mathrm{0}}H{\displaystyle \frac{\partial M}{\partial T}}\nabla T,

Here,

-{\displaystyle \frac{\partial M}{\partial T}}

is a material property of the fluid called pyromagnetic coefficient, which indicates the sensitivity of magnetization to temperature. {\mu }_{\mathrm{0}}M\nabla H is the magnetic force induced by the non-uniform magnetic field and {\mu }_{\mathrm{0}}H{\displaystyle \frac{\partial M}{\partial T}}\nabla T is the magnetocaloric force induced by the temperature gradient. For the temperature-sensitive magnetic fluid exposed to a non-uniform magnetic field, both the {\mu }_{\mathrm{0}}M\nabla H and {\mu }_{\mathrm{0}}H{\displaystyle \frac{\partial M}{\partial T}}\nabla T in Eq. (2) contribute to the fluid flow. Apparently, the total driving force on the fluid can be obtained by integrating the force density in the whole loop.

It can be seen that the force acting on the magnetic fluid depends on the synergic effect of the external magnetic field and the temperature gradient inside the fluid. Therefore, the fluid flow may be controlled by the heating or cooling conditions, the field intensity, and gradient produced by the magnet.

Gearing module for power output

Much attention should be given to the design of the miniature rotor for the purpose of producing power effectively with little energy loss because the flow velocity of the thermomagnetic convection is very small (usually several millimeters per second according to publications). Figure 4 shows the schematic layout of the gearing module, where both the rotor and the framework are made of aluminum. However, the axle of the rotor is made of copper to reduce the effect of friction (because the friction coefficient between copper and aluminum is much smaller than that between aluminums).

The rotor may be forced to rotate under such a condition:

(3){TO}_D\ge {TO}_R+{TO}_L,

where TO_D and TO_R are the driving torque and maximum static resisting torque, respectively; and TO_L represents the load torque. If there is no load on the rotor, the driving torque TO_D should overcometo TO_R maintain rotation.

Generally, there are two ways of improving the driving torque TO_D. One is to increase the magnetic pressure generated in the fluid by optimizing the synergy between the magnetic field and thermal field while the other is to make the most use of the flow energy of the fluid, which can be achieved by minimizing the cross-sectional area of the gap (defined as S₂) between the channel and the rotor vane as it is perpendicular to the floor of the channel. The variable \phi, defined as \phi =S_{\mathrm{1}}/(S_{\mathrm{1}}+S_{\mathrm{2}}), is used here to evaluate the effect of the gap (S₁ is the wet area of the vane perpendicular to the floor of the channel, as shown in Fig. 4). In this experiment, \phi takes the value of 95.7%.

The maximum static resisting torque, TO_R, is composed of the friction torque TO_F of the axis and the resisting torque caused by the surface tension of magnetic fluid on the rotor vane, TO_S. Therefore, the following equation can be obtained

(4){TO}_R={TO}_F+{TO}_S.

In this experiment, a fine axis (made of copper) of the rotor is fabricated with a diameter of 0.2 mm and polished to minimize the magnitude of TO_F. Besides, to restrict the friction torque, great efforts are made to cut down the mass of the rotor by making the rotor vane as thin as possible (with a thickness of 0.3 mm for the present device). Furthermore, to reduce the magnitude of TO_S, the rotor vane surfaces are polished, and the rotor is lifted up to decrease the arm of the surface force (as shown in Fig. 4). Consequently, a prototype of the engine is fabricated and the power output from heat input is realized. The performance of this engine system under different operating conditions is experimentally examined.

Results and discussion

Start-up test

After the loop was filled with the studied fluid, a heat load of 3.8 W was imposed on the loop, while the coolant of ethylene glycol started to flow through the heat sink to maintain its temperature at 269 K. As a result, the temperature of the fluid at the measuring points was altered from the original value of 301 K (room temperature). Figure 5 illustrates the temperature variations of the fluid at the measuring points. In this experiment, the magnet position parameter x is 12 mm. The results reveal that the magnetic fluid flow experiences a start-up process in which the fluid temperature changes with time. The readings of these thermocouples just indicate the steady state circulation flow of the magnetic fluid in the loop. Otherwise, if heat conduction was the energy transport mode inside the magnetic fluid, the readings from the two thermocouples symmetrically deployed at the opposite ends of the heater (or cooler) should be the same. In fact, the magnetic fluid moved towards a clockwise flow (A-D-C-B-A) and the rotor was driven by the flowing fluid. The rotation speed of the rotor was measured using a digital camera after the temperatures reached a steady state and the result is shown in Fig. 6.

The fluctuation of the angle velocity of the rotor (about 0.85 rad/min) may have resulted from the resistance caused by the magnetic fluid as the rotor vanes immerge into or emerge from the fluid.

Performance of the motor under different heat loads

As mentioned above, the driving force acting on the magnetic fluid is determined by the synergic effect of the external magnetic field and the temperature gradient inside the fluid. Therefore, the rotation speed of the rotor may be controlled by adjusting the heating or cooling conditions.

By keeping the heat sink temperature at 269 K, a series of experiments were conducted to examine the performance of the motor subjected to different heat loads. Here, the magnet position parameter x is 12 mm. Figure 7 shows the mean angle velocity of the rotor related to different heat loads. Apparently, as the heat load increases, the rotor rotates at a higher speed.

According to experimental data, the temperature difference in the fluid near the magnet increases with the heat load. As a result, the magnetization of the magnetic fluid will increasingly depart from equilibrium, leading to a larger driving force acting on the fluid.

The experimental results indicate that the performance of such a motor system is controlled by the input heat load. As the heat load rises, the magnetic fluid circulates in the loop at a higher speed, and more power is produced as a result.

Effect of heat sink temperature on performance of the motor

Besides the heat load, the heat sink temperature may also affect the flow velocity, since it influences the temperature distribution of the magnetic fluid associated with the magnetic force. In this experiment, the impact of the heat sink temperature on the performance of the motor was examined. Figure 8 shows the values of rotation speed subjected to different cooling conditions. Here the heat load was kept at 15 W and the value of x was 12 mm. It can be seen that as the heat sink temperature increases, the thermomagnetic flow slows down. Therefore, a low heat sink temperature is beneficial to power output.

Effect of magnet position on performance of the motor

In this experiment, the effect of x on the rotation speed of the rotor was investigated, where the heat sink temperature was kept at 269 K. The results are shown in Fig. 9. The angle velocity of the rotor shows a strong dependence on the external magnetic field distribution. The maximum of the angle velocity (2.1 r/min) was achieved as x=0, which may be attributed to the largest temperature gradient in the strong magnetic field region (near the central axis of the magnet).

Therefore, much attention should be given to the design of the magnetic field to optimize the synergy between the magnetic field and the temperature distribution of the fluid in the loop, in which case a driving force as large as possible may be obtained.

Effect of magnetic field intensity on the performance of the motor

In this experiment, each of the other two magnets was used to displace the original one to produce a magnetic field with different intensity. Angle velocity of the rotor as a function of the magnetic field intensity at point P is shown in Fig. 10. Here the heat sink temperature was kept at 269 K and the value of x was 12 mm. The experimental results illustrate that as the external magnetic field intensity increases, a more robust motor is obtained due to the larger magnetic pressure generated in the fluid.

Conclusions

A new miniature motor has been developed based on the thermomagnetic effect of a temperature-sensitive magnetic fluid in a loop-shaped channel where heat is converted into kinetic energy of the fluid and power output is achieved by means of a fine rotor. A prototype motor has been fabricated and tested for several different operating conditions. The performance of the motor system has been experimentally investigated by measuring the angle velocity of the rotor and temperature distribution of the fluid. It has been found that an incessant rotation of the rotor can be maintained as the magnetic fluid is exposed to proper external magnetic field and thermal field, where the driving force is a result of the synergic effect of the magnetic field and temperature gradient in the fluid. A peak angle velocity of 2.1 rad/min was obtained for the present rotor.

The experimental results have suggested that the performance of the motor system can be controlled by adjusting the input heat load. Besides, the heat sink temperature affects the angle velocity of the rotor. Furthermore, the capability of the motor can be strongly influenced by altering the external magnetic field. Therefore, the performance of such a motor system can easily be controlled by adjusting the external magnetic field or the temperature distribution in the fluid.

This type of engine system can utilize waste heat for power conversion or energy harvesting. According to the experimental results, the approach to obtain power output for some practical applications should first be focused on increasing the external magnetic field intensity and optimizing the synergy between the magnetic field and temperature field in the fluid. Since properties of the magnetic fluid also play an important role in the performance of the motor, to maintain a robust power output device, a magnetic fluid with a larger pyromagnetic coefficient, a lower Curie temperature, a higher saturation magnetization, a lower viscosity, and a higher boiling point should be selected.

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