Thermal conduction anisotropy of a magnetic functional fluids utilizing cluster formation of dispersed fine particles (in the case of micron-sized graphite particles)

Abstract

The thermal conductivity of a magnetic fluid is expected to enhance by adding micron-sized particles with high thermal conductivity. The thermal conductivity of the magnetic fluid containing micron-sized graphite particles was investigated experimentally. The shapes of the graphite particles were sphere and flake-like. As the results of visualization experiments using the dark field microscope, the spherical graphite particles form chain-like clusters under applied magnetic field, while the fibrous structure is formed by the flake-like graphite particles, however, chain-like cluster formation cannot be clearly observed. The experiments using the transient hot-wire method showed that the thermal conductivity of magnetic fluid containing graphite particles is enhanced by applying magnetic field and by increasing the volume fraction of graphite particles.

Keywords

Magnetic fluid cluster graphite particle thermal conductivity dark field microscopy

1. Introduction

Recently, exhaust heat generation has become an important problem with rapid development of electric devices such as CPUs and LSIs. Magnetic functional fluids have attracted attention due to their anisotropic thermal conductivity to conduct a large amount of heat in one direction. Magnetic functional fluids are fluids that respond to magnetic field, such as magnetic fluids and magnetorheological (MR) fluids. The magnetic fluid is a suspension in which fine ferromagnetic particles with a diameter of about 10 nm are dispersed stably in a mother liquid such as water or kerosene, while the MR fluid is a fluid in which magnetic particles of submicron to micron size are dispersed in a mother liquid. Thermal conductivity enhancement using the formation of internal structure of magnetic particles induced by applying magnetic field has been investigated recently [1–6]. Magnetic particles in the magnetic functional fluids have much larger heat conductivity comparing with their mother liquids and anisotropic thermal conductivity can be produced effectively by applying magnetic field. Fujita and Mamiya reported that non-magnetic spherical particles in a magnetized magnetic fluid behave like diamagnetic particles in the presence of magnetic field [7]. Thus, micron-sized non-magnetic particles form chain-like clusters in the magnetic fluid under external uniform magnetic field. It can be expected that the thermal conductivity in the direction of magnetic field drastically changes when a magnetic field is applied to the magnetic fluid mixing fine non-magnetic particles with high thermal conductivity.

Table 1
Components of the test fluids

Test fluid Magnetite (vol.%) Graphite particles (vol.%), shape Water (vol.%)

A 4 0, – 96

B 4 4, sphere 92

C 4 8, sphere 88

D 4 12, sphere 84

E 4 16, sphere 80

F 4 4, flake 92

G 4 8, flake 88

H 4 12, flake 84

I 4 16, flake 80

Test fluid	Magnetite (vol.%)	Graphite particles (vol.%), shape	Water (vol.%)
A	4	0, –	96
B	4	4, sphere	92
C	4	8, sphere	88
D	4	12, sphere	84
E	4	16, sphere	80
F	4	4, flake	92
G	4	8, flake	88
H	4	12, flake	84
I	4	16, flake	80

In this study, the thermal conductivity of magnetic fluids containing micron-sized graphite particles were investigated experimentally. Two kinds of micron-sized graphite particles were prepared, i.e., one was the spherical particle and the other was the flake-like particle. As test fluids, seven kinds of magnetic fluids containing graphite particles were prepared. In the presence of magnetic field, the internal structure formed by the suspended particles is effective for the thermal conductivity. Thus, distribution of particles in the magnetic fluid was observed by using the dark field microscope [8]. The thermal conductivity was measured by using the transient hot-wire method [9]. The effects of both volume fraction of graphite particles and shape of particles on the thermal conductivity were investigated.

2. Test fluids

Two kinds of graphite particles were prepared for our experiments: one was the spherical particles whose average diameter was 8.0 μm (Ito Graphite Co. Ltd. SG BH8) and the other was the flake-like particles whose average size was 7.0 μm (Ito Graphite Co. Ltd. CNP7). The base magnetic fluid was the water-based magnetic fluid (Ichinen Chemicals Co. Ltd., W40) in which magnetite nanoparticles were dispersed. Seven test fluids were prepared and their components are shown in Table 1. A sedimentation test was conducted to confirm the sedimentation state of the test fluids. To measure the thermal conductivity by using our experimental apparatus as shown later, it takes about 30 minutes to complete measurement of the thermal conductivity. The state after 30 minutes from the state of sufficiently stirring the fluid was confirmed. As a result, no sedimentation of particles was confirmed as shown in Fig. 1(b). The estimated value of the sedimentation rate of the fluid E is about 2 μm/s by using the theory [2] and the sedimentation is less than 1% of the vessel height in 30 minutes.

Fig. 1.

Sedimentation tests. (a) Initial state and (b) after 30 minutes. (1) Fluid A, B, C, D, E and (2) F, G, H, I, from the left.

3. Visualization experiments and results

3.1. Visualization experiments and discussion

The internal structure formed by the micron-sized nonmagnetic particles in the fluid strongly affects the macroscopic properties such as the thermal conductivity. To visualize the internal structure and distribution of micron-sized graphite particles, the dark field microscopy using Rayleigh light scattering technique was performed. The experimental apparatus consisted of the microscope (Olympus, IX73) and the digital camera (Olympus, DP22). The electromagnet was installed to apply a uniform magnetic field of 24.5 mT to the test fluid. The visualization experiments were performed at room temperature.

Fig. 2.

Dark field microscopy snapshots of the distribution of the micron-sized graphite particles in the test fluids in (1) the initial state and (2) the state after applying magnetic field. The shapes of the particles are (s) sphere and (f) flake, the volume fractions of the particles are (a) 4 vol.%, (b) 8 vol.%, (c) 12 vol.%, (d) 16 vol.%. The length of the white bar in the photos is corresponding to 50 μm and magnetic field is applied in the same direction as the long axis of the white bar.

Figure 2 is the snapshot taken by using the dark field microscopy. As can be seen in Fig. 2(a,b), the spherical graphite particles are randomly dispersed in the initial state, while the chain-like clusters are formed in the magnetic field direction. In the case of high volume fraction, the chain-like clusters are combined each other to form a fibrous structure. From Fig. 2(c,d), the distribution of flake-like graphite particles has changed from the initial state by applying the magnetic field. In the case of low volume fraction of 4 vol.%, many short clusters can be observed. However, the clear chain-like clusters cannot be confirmed in the case of high volume fractions more than 8 vol.%. Since the particle shape is flake-like, the particle is easy to contact with other particles, and it is considered that a fibrous structure is formed by applying magnetic field as in the case of magnetic particles in MR fluid with a relatively high volume fraction. Thus, the chain-like cluster formation cannot be observed clearly.

Fig. 3.

Schematic of the experimental apparatus by using the transient hot-wire method.

4. Thermal conductivity experiments and results

4.1. Transient hot-wire method

The thermal conductivity of the test fluids was measured by using the transient hot-wire method [9] and the thermal conductivity was obtained by using the following equation: 𝜆 = (q∕4π)dT∕d (ln t), where 𝜆 is the thermal conductivity of the fluid, q is the heat flux per unit length and unit time, t is the time and T is the absolute temperature. By measuring the time change of the temperature of the test fluid, the thermal conductivity can be obtained from the above equation. Figure 3(a) shows the schematic of the experimental apparatus. The sensor probe (TPSYS02, Hukseflux) was inserted into the center of the Teflon cylindrical container which was filled with the test fluid. The Helmholtz coil was installed both sides of the container to apply uniform magnetic field of 0, 25, 50, 75 and 100 mT to the test fluids. The test fluid was thoroughly agitated before putting into the container. The thermal conductivity of the fluid is obtained as the gradient of the linear approximation in the gray region shown in Fig. 3(b).

4.2. Experimental results and discussion

Figure 4 shows the thermal conductivity of the magnetic fluid containing spherical graphite particles. The error of the experimental data shown in Fig. 4 is only within the plot display size as in the figures shown below. From Fig. 4(a), the larger the volume fraction of the spherical graphite particles, the larger the thermal conductivity. The thermal conductivity of magnetic fluid mixed with spherical graphite particles increases when a magnetic field is applied, however, even when a magnetic field of 25 mT or higher is applied, the change in thermal conductivity is small and there is no big difference in thermal conductivity. This is because the internal structure of chain-like clusters formed by spherical graphite particles under an external uniform magnetic field is sufficiently formed even with a relatively weak magnetic field of 25 mT. The thermal conductivity of the base magnetic fluid is 0.503 W/m ⋅ K and the maximum thermal conductivity enhancement ratio is 2.207 when the magnetic field of 50 mT is applied to the test fluid E. Figure 4(b) shows the thermal conductivity enhancement ratio of the test fluids containing spherical graphite particles to the thermal conductivity of the base magnetic fluid. From Fig. 4(b), the larger volume fraction of graphite particles, the larger enhancement ratio. From Fig. 4(c), the thermal conductivity enhancement ratio is the highest when the volume fraction of particles is 8 vol.%.

Fig. 4.

The thermal conductivity enhancement of the test fluids containing spherical graphite particles. The applied magnetic fields in (a,c) are as follows: open circle: 0 mT, open triangle: 25 mT, open square: 50 mT, open inverse triangle: 75 mT, open diamond: 100 mT. The volume fractions of particles in (b) are as follows: open circle: 0 vol.%, open triangle: 4 vol.%, open square: 8 vol.%, open inverse triangle: 12 vol.%, open diamond: 16 vol.%. (a) The thermal conductivity and (b,c) the thermal conductivity enhancement ratio to the thermal conductivity of the base magnetic fluid.

When the volume fraction is 4 vol.%, the formed chain-like clusters are short, so the change in thermal conductivity due to the applied magnetic field is small. However, when the volume fraction is 8 vol.%, rather long chain-like clusters are formed under magnetic field and the internal structure changes drastically from the initial state that the particles dispersed randomly. When the volume fraction is larger, the particles are somewhat dense even in the absence of magnetic field, and the internal structure change due to the chain-like cluster formation is considered to be small. Figure 5 shows the thermal conductivity of the test fluids containing flake-like graphite particles. The maximum thermal conductivity enhancement ratio is 3.373, when the magnetic field of 25 mT is applied to the test fluid I. Comparing Fig. 4 and Fig. 5, the fluid containing flake-like particles has higher thermal conductivity than the fluid containing spherical particles. Figures 5(b,c) show the thermal conductivity enhancement ratio by applying magnetic field and increasing volume fraction. As shown in Fig. 2, the flake-like graphite particles form fibrous structure under magnetic field. Thus, the thermal conductivity becomes higher with the volume fraction increases. When the volume fraction is high, the thermal conductivity enhancement ratio increases because a dense fibrous structure is formed by applying magnetic field.

4.3. Anisotropy of the thermal conductivity

The test fluids have the internal structure formed by the graphite particles under magnetic field. Thus, the thermal conductivity of the test fluids under uniform magnetic field is anisotropic and depends on the field direction. However, it is difficult to measure the thermal conductivity in the field direction and in the direction perpendicular to the field separately. By using the transient hotwire method, the thermal conductivity in the radial direction of the sensor probe is obtained and it can be expressed by ${\lambda}=\sqrt{{\lambda}_{1}{\lambda}_{2}}$ where 𝜆₁ is the thermal conductivity in the field direction and 𝜆₂ is that in the direction perpendicular to the field [10]. In the case of spherical graphite particles, the maximum thermal conductivity of the fluid E is 𝜆 = 1.140𝜆₀, where 𝜆₀ is the thermal conductivity of the fluid E in the absence of magnetic field and its value is 1.103 W/m ⋅ K. Since the thermal conductivity of the graphite is much higher than that of the base liquid, the thermal conductivity in the field direction is larger than that without magnetic field, while the thermal conductivity in the direction perpendicular to the field is smaller than that without magnetic field, i.e., 𝜆₁ > 𝜆₀ > 𝜆₂ thus, the thermal conductivities in the direction parallel and perpendicular to the magnetic field can be estimated as 𝜆₁ > 1.300𝜆₀ = 1.434 W/m ⋅ K and 𝜆₂ < 𝜆₀. In the case of flake-like particles, we obtained 𝜆 = 1.166𝜆₀ and 𝜆₁ > 1.359𝜆₀ = 1.667 W/m ⋅ K.

Fig. 5.

The thermal conductivity enhancement of the test fluids containing flake-like graphite particles. The applied magnetic fields in (a,c) are as follows: open circle: 0 mT, open triangle: 25 mT, open square: 50 mT, open inverse triangle: 75 mT, open diamond: 100 mT. The volume fractions of particles in (b) are as follows: open circle: 0 vol.%, open triangle: 4 vol.%, open square: 8 vol.%, open inverse triangle: 12 vol.%, open diamond: 16 vol.%. (a) The thermal conductivity and (b,c) the thermal conductivity enhancement ratio to the thermal conductivity of the base magnetic fluid.

5. Conclusion

The thermal conductivity of the magnetic fluid containing micron-sized graphite particles was investigated experimentally. From the visualization experiments using the dark field microscope, spherical graphite particles in the magnetic fluid form chain-like clusters in the presence of magnetic field, while the flake-like graphite particles do not clearly form chain-like clusters. The thermal conductivity of the magnetic fluid containing graphite particles is enhanced by applying magnetic field. The maximum thermal conductivity in the field direction can be estimated more than 1.359 times of that of the same test fluid in the absence of magnetic field.

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