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Magnetically-driven heat transport device using a binary temperature-sensitive magnetic fluid
Journal of Magnetism and Magnetic Materials 323 (2011) 1378–1383
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Magnetically-driven heat transport device using a binary temperature-sensitive magnetic fluid Yuhiro Iwamoto a,n, Hiroshi Yamaguchi a,b, Xiao-Dong Niu b a b
Department of Mechanical Engineering, Doshisha University, Kyoto 610-0321, Japan Energy Conversion Research Center, Doshisha University, Kyoto 610-0321, Japan
a r t i c l e i n f o
a b s t r a c t
Available online 19 November 2010
The magnetic body force in boiling two-phase temperature-sensitive magnetic fluid (TSMF) flow is known to effectively increase the driving force of magnetic fluid in a non-uniform magnetic field. Based on this mechanism, in the present study, a binary TSMF, which is a mixture of the TSMF and a low-boilingsaturation-temperature organic solution, is proposed to be used in a heat transport device to enhance its circulation. In order to see its performance in the heat transport device, the pressure difference at different heated temperatures, magnetic fields and inclination angles of the heating section are investigated experimentally and theoretically. Results showed that the driving force increases remarkably due to more gas phase appearing in the test fluid and the magnetization of it decreasing. At low magnetic field the driving force is enhanced greatly when the inclination angle is close to 601, while at high magnetic field the driving force is remarkably enhanced due to the effect of the magnetic force in the inclination angle range from 01 to 301 and 601 to 901. & 2010 Elsevier B.V. All rights reserved.
Keywords: Binary temperature-sensitive magnetic fluid Heat transport Two-phase flow
1. Introduction Temperature-sensitive magnetic fluid (TSMF) is a kind of ferrofluid with a property of magnetization strongly dependent of the temperature [1,2]. As energy transfer and flow of the TSMF capable of being controlled with a magnetic field, various applications, ranging from heat transfer technologies [3,4] to astronautic engineering [5], have been explored during the past years. Recent theoretical and experimental studies on the boiling twophase flows of the TSMF in a pipe suggested that the magnetic body force in boiling two-phase flow can effectively increase the driving force of magnetic fluid in a non-uniform magnetic field [6]. Based on these researches, a method of using a binary TSMF, in which a small amount of a low-boiling-saturation-temperature organic solution mixed with the TSMF, in a heat transport device to obtain a large driving force for enhancing the heat transfer has been proposed by one of the authors [7]. Primary investigation [8] showed that an enhancement of the driving force can be achieved with the binary TSMF in a vertical pipe in the non-uniform magnetic fields. In order to obtain the optimal performance of the binary TSMF in the heat transport device, in the present study a systematic investigation of the magnetic body force influencing the driving force are investigated experimentally and theoretically. The final
n
Corresponding author. Tel./fax: +81 774 65 7749. E-mail address: [email protected] (Y. Iwamoto).
0304-8853/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2010.11.050
objective of this study is to provide the fundamental data for optimizing the innovative applications of binary TSMFs in heat transport devices.
2. Experimental study 2.1. Working principle of the present experiment The working principle of the present experimental system is shown schematically in Fig. 1. The magnetic field Hz has a nonuniform distribution along the z coordinate. A binary TSMF is assumed to be heated passing through the point (z¼0) of the maximum magnetic field strength toward the downstream side region (z Z0) and boiled to form a gas–liquid two-phase flow. Under the above conditions, the magnetic body force f of the magnetic fluid is given by f ¼ MUrH
ð1Þ
where H is the magnetic field, and M the magnetization. Due to the magnetization of the fluid dependent on the temperature [9] and the void fraction [8], we have TT0 M ¼ m0 wð1aÞ 1 H ð2Þ TC T0 where m0 is the vacuum permeability, w the magnetic susceptibility, a the void fraction of the gas in the mixture, and T the temperature
Y. Iwamoto et al. / Journal of Magnetism and Magnetic Materials 323 (2011) 1378–1383
with T0 and TC denoting the reference and Curie temperatures, respectively. As shown in Eqs. (1) and (2), the magnetization M(T,H;a) of the working fluid in the heating region (z Z0) decreases when the temperature increases and the gas bubbles appear. As a result, a difference of the magnetization across the point of z ¼0 (Fig. 1) is
Fig. 1. Schematic diagram of the test section and working principle of the system.
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created, leading to an additional driving force formed by the fluid itself.
2.2. Test fluid and experimental set-up The test binary magnetic fluid in the present experiment consists of a base TSMF of TS-50K with concentration 80 wt% and an organic solution of n-Hexane with concentration 20 wt%. The organic fluid has a low-boiling saturation temperature of 342 K. Physical properties of the test fluid and its components at room-temperature condition are listed in Table 1. The experimental set-up of the present study is schematically depicted in Fig. 2, consisting mainly of a test section, a driven pump, an cooling unit, a pre-heater, and a flow meter. The test section (Fig. 1) includes an electromagnet, a heater and a heated body. The temperatures in the test section are measured by using three thermocouples installed at the inlet, outlet, and inner wall of the heated body. The working fluid is filled in the closed copper pipe loop with diameter of 0.01 m and length of 6 m, and is driven by the circular pump which controlled by an inverter. In order to obtain the optimal performance of the magnetic body force of the test fluid affecting the driving force, the test section of the experimental setup is installed to be adjustable from horizontal (y ¼01) setting to vertical (y ¼901) arrangement (see Fig. 1).
Table 1 Physical properties of a binary magnetic fluid at 293 K, 1 atm.
Density r (kg/m3) Viscosity Z (Pa s) Specific heat capacity cp (J/(kg K)) Thermal conductivity l (W/(m K)) Curie temperature TC (K) Saturated temperature TS (K)
TS-50K
TS-50K n-Hexane 20 (wt%)
n-Hexane
1.401 103 1.72 10 2 1387 0.175 477 –
1.143 103 2.35 10 3 1564 0.160 477 358
6.54 102 2.96 10 4 2249 0.126 – 342
Fig. 2. Schematic diagram of the experimental set-up.
1380
Y. Iwamoto et al. / Journal of Magnetism and Magnetic Materials 323 (2011) 1378–1383
Table 2 Experimental conditions. Reynolds number Re (representative) Inclination of the test section y Magnetic field intensity Hz,max Inlet temperature of the fluid Tin Temperature of the heated wall Tiw Diameter of the tube D
100 (dimensionless) 0–90 (deg) 0–1.66 105 (A/m) 307 (K) 337–377 (K) 10 (mm)
2.3. Experimental conditions and evaluation parameter The experimental conditions are given in Table 2. Particularly, the flow Reynolds number and the temperature at the inlet of the test section in the experiment are fixed at Re ¼ rl UD=Zl ¼100 and Tin ¼307 K, respectively; system performance at three temperature differences DT¼30, 50 and 70 K of the inner wall temperature Tiw to the inlet temperature of the test section, and four inclination angles of y ¼01, 301, 601 and 901 are investigated. The enhancement of the driving force due to the magnetization difference created by boiling the binary TSMF is evaluated by the pressure difference DPD measured at the inlet and outlet of the test section using the pressure transmitter. To clearly see the effects of the respective magnetic field and gas phase to the driving force, the pressure difference is written as the following form with three parts:
DPD ¼ DPL þ DPT þ DPM
ð3Þ
where DPL is the pressure difference caused by fluid friction, DPT is the pressure difference due to the gas bubble buoyancy and DPM is the pressure difference due to the magnetic force.
Energy equation for the liquid phase considering the magnetic effect: " !# v2 d rl ð1aÞvl hl þ l dz 2 @M dHz ðiÞ þ Qw a ð1 a ÞT v ¼ rl ð1aÞvl g sin y þ Gl hl þqðiÞ l l @Tl H l dz ð8Þ Magnetic field and Magnetization: h p i 1 TT0 Hz ¼ Hz,max 1 þ cos z ; M ¼ wHz 1 2 L TC T0
where v is the velocity, r the density, P the pressure, h the enthalpy, g the gravitational acceleration, r the mean radius of the bubble defined by Eq. (12) below, FD the drag force, Fvm the virtual mass force considering the expansion of the bubble, q the heat flux through the gas–liquid interface, a the interracial area concentration, Qw the heat transfer rate per unit volume, and G the phase generation rate. The subscripts g and l denote gas and liquid phases, respectively. With the assumption of a spherical bubble with equivalent radius r, and energy transfer caused by the heat transfer between an isothermal spherical bubble and the surrounding liquid, the expression for a is obtained as aðiÞ ¼ 3a=r. To close the above basic equations, the following equations are introduced with assumptions of the perfect gas in the gas phase and the boiling bubbles generated spherically with the minimum radius rmin: Generation rate of the gas phase Gg:
Gg ¼
3.1. Governing equations In the past few years, the governing equations which represent the two-phase flow of a magnetic fluid under a non-uniform magnetic field have been derived and solved numerically with considerations of the effects of evaporation and condensation on the vapor bubbles [6]. In the present study, in order to obtain the detailed information of the flow characteristics, the above model is numerically solved with onedimensional assumption. With the coordinate system set in Fig. 1, the governing equations are given as follows Continuity equation: d d ðr avg Þ ¼ Gg , ðr ð1aÞvl Þ ¼ Gl , Gg þ Gl ¼ 0 dz g dz l
ð4Þ
Momentum equation for the whole two-phase flow considering the magnetic force: i d h dP dH rg av2g þ rl ð1aÞv2l ¼ l ð1aÞrl g sin y þ ð1aÞM z dz dz dz 32 þ Gg ðvg vl Þ 2 ðZg avg þ Zl ð1aÞvl Þ D
Energy equation for the gas phase: " !# v2 d ðiÞ rg avg hg þ g ¼ rg avg g sin y þ Gg hg þ qðiÞ g a dz 2
ð10Þ
ð11Þ
Mass conservation of unit gas bubble with the reference radius r: P 4 d d G P g p ðrg r3 Þ ¼ ð12Þ 3 dz dz Ng Equation of state of gas phase: Pg Pl ¼
2gl r
ð13Þ
Equation of pressure balance between gas and liquid phases: Pg ¼ rg RG Tg
ð14Þ
where RG is the gas constant, gl denotes the surface tension in the liquid phase. In the present study the number of the bubbles nga is set 1.17 106 1/(m2 s), the variance s is assumed to be 0.03 m, the minimum radius of the gas bubble rmin is 0.7 10 3 m and the position of the maximum generation rate of the gas phase zmax is at z¼0.05 m.
ð5Þ
3.2. Calculation conditions and evaluation parameters
ð6Þ
The physical situation used in the theoretical analysis is the same as the present experiments (see Tables 1 and 2). The above basic equations are solved numerically by the Runge–Kutta–Gill method. To see the contributions of the magnetic field, gravity, etc. to the driving force, the components of the total driving pressure difference are calculated, respectively, according to the following formulations:
Momentum equation for the unit spherical gas bubble: dv 4 3 4 dP 4 pr rg vg g ¼ pr 3 l pr 3 rg g sin yFD Fvm 3 3 dz dz 3
4 3 pr r Ng 3 min g
Generation number of the initial bubbles Ng: " # nga ðzzmax Þ2 p ffiffiffiffiffiffi exp Ng ¼ 2s2 2ps
3. Theoretical analysis
ð9Þ
ð7Þ
dðDPT Þ ¼ arl g sin y dz
ð15Þ
Y. Iwamoto et al. / Journal of Magnetism and Magnetic Materials 323 (2011) 1378–1383
dðDPM Þ dH ¼ ð1aÞM dz dz
ð16Þ
dðDPL Þ 32 ¼ 2 ðZg ang þ Zl ð1aÞnl Þ dz D
ð17Þ
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where Pl,in is the pressure at z ¼zin (see Fig. 1).
can observed a remarkable increase of the pressure difference DPD at DT¼70 K comparing to the behaviors at DT¼ 30 and 50 K. To see the performance of the driving force of the test fluid in this heat transport device at different inclination of the test section, Fig. 4 depicts the experimental results of the pressure difference DPD as a function of the axial maximum magnetic intensity Hz,max at different inclinations of the test section at the representative temperature difference of DT¼ 70 K. Shown in Fig. 4, different performances of the pressure difference DPD at low and high magnetic fields are observed. At low magnetic fields, the pressure difference DPD is found to enhance obviously when the inclination angle of the test section varies from 01 to 601, and decreases slightly from the inclination angle of the test section of y ¼601 to 901. On the other hand, at high magnetic fields, the pressure difference DPD is observed to improve remarkably when the inclination angle of the test section varies from 01 to 301 and 601 to 901. In the range y ¼301–601, it is found that the pressure difference DPD decreases at high magnetic fields.
4. Results and discussions
4.2. Theoretical analyses
4.1. Experimental results and discussions
Fig. 4 displays complicated behaviors of the measured pressure difference as the function of the magnetic field and the inclination angle of the test section. In order to clearly explain these experimental observations, an one-dimensional numerical analysis is carried out based on Section 3 at two typical magnetic fields of Hz,max ¼50.9 and 153 kA/m and DT¼70 K. Fig. 5 plots the numerical results of the total pressure difference DPD (Eq. (19)) and its components, DPT, DPM, and DPL (Eqs. (15)–(17)) as a function of the inclination angle of the test section at these two representive magnetic fields and DT ¼70 K. For convenient comparison, experimental results of the pressure difference DPD are also plotted in the figure. As shown in Fig. 5(a), it is observed that the experiment measurement (DPD, Exp.) and numerical simulations (DPD, Theory.) generally agree with each other at low magnetic field in Fig. 5(a). On the other hand, at high magnetic field in Fig. 5(b), it is observed that
where, the pressure difference DPM due to the magnetic force has two components according to the following formulation:
DPM ¼ DPM,l þ DPM,g
ð18Þ
where, DPM,l is the pressure difference due to the temperaturedependent magnetization of the TSMF and DPM,g is the pressure difference due to the magnetization of the test liquid decreased by the gas bubble occurrence. The total pressure difference is expressed as
DPD ¼ Pl rl g sin yðzzin ÞPl,in
ð19Þ
Fig. 3 shows the experimental results of the pressure difference
DPD varying with the magnetic field at different temperature differences DT and the inclination angle of the test section y ¼901. As shown in Fig. 3, increasing the strength of the magnetic field, the axial maximum magnetic intensity Hz,max, enhances the pressure difference DPD. As the temperature in the inner wall of the heated body is increased, the pressure difference DPD is found to increase because the temperature-dependent magnetization decreases in the heated region (zZ0), and causes the pressure difference DPM across the point of z¼0. When the heated temperature increases above the boiling temperature of the test fluid (DT¼70 K), the gas phase will appear in the heated region (zZ0), causing a large reduction of the magnetization and an additional increase of the force due to the gas-phase buoyancy. Therefore, one
500
600
ΔT = 30 [K], Exp.
= 0deg, Exp.
ΔT = 50 [K], Exp.
= 30deg, Exp.
ΔT = 70 [K], Exp.
400
500
Fig.5 (b)
= 60deg, Exp. = 90deg, Exp.
400 ΔPD [Pa]
ΔPD [Pa]
300
200
Fig.5 (a) 300
200 100
100 0 0
50
100 Hz,max [kA/m]
150
Fig. 3. Measured pressure difference DPD varying with the magnetic field at different temperature differences DT and the inclination angle of the test section y ¼90o.
0
50
100 Hz,max [kA/m]
150
Fig. 4. Measured pressure difference DPD as a function of the axial maximum magnetic intensity Hz,max at different inclinations of the test section at DT¼ 70 K.
Y. Iwamoto et al. / Journal of Magnetism and Magnetic Materials 323 (2011) 1378–1383
Total ΔPD , Exp. Total ΔPD , Theory. Component ΔPT , Theory. (1) Component ΔPM , Theory. (2) Component ΔPL , Theory. (3)
ΔPD, ΔPT, ΔPM, ΔPL [Pa]
800
600
400 Total ΔPD, Theory. Total ΔPD , Exp.
200
Total ΔPD, Exp. Total ΔPD , Theory. Component ΔPT , Theory. (1) Component ΔPM, Theory. (2) Component ΔPL , Theory. (3)
800 ΔPD , ΔPT , ΔPM , ΔPL [Pa]
1382
600
Total ΔPD , Theory.
(2)
400
Total ΔPD , Exp. 200
(1)
(1) (2) (3)
0 30
0
60
90
(3)
0
0
[deg]
30
60
90
[deg]
Fig. 5. Pressure differences of DPD, DPT, DPM and DPL as a function of the inclination angle of the test section at magnetic fields of (a) Hz,max ¼50.9 and (b) 153 kA/m, respectively.
Table 3 Calculated DPM,l and DPM,g at different inclinations of the test section at DT¼70 K.
y (deg)
0 30 60 90
Hz,max ¼ 50.9 (kA/m)
Hz,max ¼153.0 (kA/m)
Tout (K)
DPM,l (Pa)
DPM,g (Pa)
Tout (K)
DPM,l (Pa)
DPM,g (Pa)
351.0 348.4 344.2 338.4
86 79 70 57
22 21 20 21
353.4 355.7 346.4 348.4
373 398 302 321
74 71 71 70
there are the quantitative differences between the experimental and numerical results of the pressure difference DPD. The reason is from the numerical model we used in the theoretical analyses. Since we used one-dimensional model, the three-dimensional phenomena, particularly the magnetic interaction effects in the heating section due to the temperature variation and the gas-phase occurrence, are not well considered. However, the numerical results well explain the experimental findings in Fig. 4. As shown in Fig. 5(a) for Hz,max ¼50.9 kA/m, with the increase of the inclination angle of the test section from y ¼01 to 901, the pressure difference DPT due to the buoyancy of the gas phase increases and the pressure difference DPM due to the magnetic force decreases, indicating that at low magnetic field the buoyant effect of the gas phase dominates over that of the magnetic field, and contributes to the enhancement of the total pressure difference DPD. The decrease of the pressure difference DPM in Fig. 5(a) comes from two parts as seen in Eq. (18): the pressure difference DPM,l due to the temperature-dependent magnetization of the TSMF and the pressure difference DPM,g due to the magnetization of test liquid decreased by the gas bubble occurrence. Table 3 shows the effects of these two parts on the pressure difference DPM and the temperature Tout at the outlet of the heated body at DT ¼70 K and Tin ¼307 K for two representive magnetic fields of Hz,max ¼50.9 and 153 kA/m, respectively. As shown in Table 3 for Hz,max ¼50.9 kA/m, with the increase of the inclination angle, the temperature Tout at the outlet of the heated body decreases due to the magnetic ejection effect and the buoyancy force, leading to the magnetization in the heating region (zZ0) increasing and the pressure difference DPM,l decreasing. However, the pressure difference DPM,g
changes little with the outlet temperature Tout variation, indicating that the decrease of DPM is mostly caused by the temperaturedependent magnetization. At high magnetic field, however, as the results displayed in Fig. 5(b), the effect of magnetic field is more dominant than that of the buoyancy of the gas phase because the value of the pressure difference DPM is always larger than that of the pressure difference DPT. The pressure difference DPM varies little in the range of the inclination angle of the test section y ¼ 01–301 and 601–901, but has an obvious decrease from y ¼301 to 601. At the same time, the pressure difference DPT keeps increasing when the inclination angle of the test section varies from 01 to 901. As a result, the pressure difference DPD is observed to increase in the range y ¼01–301 and 601–901, and to decrease in the range y ¼301–601. The complicate behavior of the pressure difference DPM in Fig. 5(b) can be clearly illustrated by Table 3 for Hz,max ¼153 kA/m. As shown in Table 3, with the increase of the inclination angle, the pressure difference DPM,g still changes little like that at Hz,max ¼50.9 kA/m. However, the pressure difference DPM,l increases due to the outlet temperature Tout increase in the range of the inclination angle of the test section y ¼ 01–301 and 601–901, and has a great decrease from y ¼301 to 601, in which the outlet temperature Tout shows a great reduction. This observation suggesting again that the temperaturedependent magnetization is the main role in affecting the complicate behavior of the pressure difference DPM, and further the total pressure difference DPD. Due to the above mentioned driving pressure increase along with the change of inclination angle of the heat transport device, the working fluid, the binary temperature-sensitive magnetic fluid, does circulate by it own driving force, transporting a large latent heat by boiling the organic binary-mixture at heating section to the cooling section. Therefore the test carried out in the present investigation revealed that the configuration of the device, including the magnetic fluid imposition, is effective for that the device transports heat without any external work input.
5. Conclusions A systematic investigation of the performance of the boiling binary temperature-sensitive magnetic fluid in a heat transport
Y. Iwamoto et al. / Journal of Magnetism and Magnetic Materials 323 (2011) 1378–1383
device under a non-uniform magnetic field is performed experimentally and theoretically. The main results obtained here are summarized as follows. (1) From the experimental studies on the pressure difference between the inlet and outlet of the test section, it is clarified that the magnetic body force in boiling binary TSMF flow is effective to increase the driving force of the fluid in a nonuniform magnetic field. The temperature difference between the inner heated wall and the inlet of the test section and the inclination arrangement of the test section strongly influence the performance of the enhancement of the driving force. Both increasing the strength of the magnetic field and the temperature difference between the inner heated wall and the inlet of the test section enhance the pressure difference DPD. At low magnetic field, the pressure difference DPD increases when the inclination of angle of the test section increases. At high magnetic field, the pressure difference DPD increases in the range y ¼01–301 and 601–901, and decreases in the range y ¼301–601. (2) The theoretical studies well explain the experimental findings. The contribution of the driving force enhancement is mainly
1383
from the buoyancy of the gas phase at low magnetic field and the effect of the magnetic field at high magnetic field.
Acknowledgment This work was supported by a grant-in-aid for Scientific Research (C) from the Ministry of Education, Culture, Sports, Science and Technology, Japan.
References [1] R.E. Rosensweig, Ferrohydrodynamics, Cambridge University Press, London, 1985. [2] H. Yamaguchi, Engineering Fluid Mechanics, Springer, Netherlands, 2008. [3] W. Lian, Y. Xuan, Q. Li, J. Heat Mass Transfer 52 (2009) 5451. [4] H. Yamaguchi, X.-D. Niu, K. Yoshikawa, J. Magn. Magn. Mater. 322 (2010) 698. [5] B.M. Berkovsky, Magnetic Fluids Engineering Applications, Oxford University Press, New York, 1993. [6] S. Kamiyama, J. Ishimoto, J. Magn. Magn. Mater. 149 (1995) 125. [7] S. Shuchi, K. Sakatani, H. Yamaguchi., J. Magn. Magn. Mater. 289 (2005) 257. [8] H. Yamaguchi, S. Shuchi, K. Sasatani, S. Enomoto, Trans. Jpn. Soc. Mech. Eng. B 70 (698) (2004) 2591 (in Japanese). [9] E.L. Resler, R.E. Rosensweig, J. AIAA 2 (8) (1964) 1418.
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Magnetically-driven heat transport device using a binary temperature-sensitive magnetic fluid Yuhiro Iwamoto a,n, Hiroshi Yamaguchi a,b, Xiao-Dong Niu b a b
Department of Mechanical Engineering, Doshisha University, Kyoto 610-0321, Japan Energy Conversion Research Center, Doshisha University, Kyoto 610-0321, Japan
a r t i c l e i n f o
a b s t r a c t
Available online 19 November 2010
The magnetic body force in boiling two-phase temperature-sensitive magnetic fluid (TSMF) flow is known to effectively increase the driving force of magnetic fluid in a non-uniform magnetic field. Based on this mechanism, in the present study, a binary TSMF, which is a mixture of the TSMF and a low-boilingsaturation-temperature organic solution, is proposed to be used in a heat transport device to enhance its circulation. In order to see its performance in the heat transport device, the pressure difference at different heated temperatures, magnetic fields and inclination angles of the heating section are investigated experimentally and theoretically. Results showed that the driving force increases remarkably due to more gas phase appearing in the test fluid and the magnetization of it decreasing. At low magnetic field the driving force is enhanced greatly when the inclination angle is close to 601, while at high magnetic field the driving force is remarkably enhanced due to the effect of the magnetic force in the inclination angle range from 01 to 301 and 601 to 901. & 2010 Elsevier B.V. All rights reserved.
Keywords: Binary temperature-sensitive magnetic fluid Heat transport Two-phase flow
1. Introduction Temperature-sensitive magnetic fluid (TSMF) is a kind of ferrofluid with a property of magnetization strongly dependent of the temperature [1,2]. As energy transfer and flow of the TSMF capable of being controlled with a magnetic field, various applications, ranging from heat transfer technologies [3,4] to astronautic engineering [5], have been explored during the past years. Recent theoretical and experimental studies on the boiling twophase flows of the TSMF in a pipe suggested that the magnetic body force in boiling two-phase flow can effectively increase the driving force of magnetic fluid in a non-uniform magnetic field [6]. Based on these researches, a method of using a binary TSMF, in which a small amount of a low-boiling-saturation-temperature organic solution mixed with the TSMF, in a heat transport device to obtain a large driving force for enhancing the heat transfer has been proposed by one of the authors [7]. Primary investigation [8] showed that an enhancement of the driving force can be achieved with the binary TSMF in a vertical pipe in the non-uniform magnetic fields. In order to obtain the optimal performance of the binary TSMF in the heat transport device, in the present study a systematic investigation of the magnetic body force influencing the driving force are investigated experimentally and theoretically. The final
n
Corresponding author. Tel./fax: +81 774 65 7749. E-mail address: [email protected] (Y. Iwamoto).
0304-8853/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2010.11.050
objective of this study is to provide the fundamental data for optimizing the innovative applications of binary TSMFs in heat transport devices.
2. Experimental study 2.1. Working principle of the present experiment The working principle of the present experimental system is shown schematically in Fig. 1. The magnetic field Hz has a nonuniform distribution along the z coordinate. A binary TSMF is assumed to be heated passing through the point (z¼0) of the maximum magnetic field strength toward the downstream side region (z Z0) and boiled to form a gas–liquid two-phase flow. Under the above conditions, the magnetic body force f of the magnetic fluid is given by f ¼ MUrH
ð1Þ
where H is the magnetic field, and M the magnetization. Due to the magnetization of the fluid dependent on the temperature [9] and the void fraction [8], we have TT0 M ¼ m0 wð1aÞ 1 H ð2Þ TC T0 where m0 is the vacuum permeability, w the magnetic susceptibility, a the void fraction of the gas in the mixture, and T the temperature
Y. Iwamoto et al. / Journal of Magnetism and Magnetic Materials 323 (2011) 1378–1383
with T0 and TC denoting the reference and Curie temperatures, respectively. As shown in Eqs. (1) and (2), the magnetization M(T,H;a) of the working fluid in the heating region (z Z0) decreases when the temperature increases and the gas bubbles appear. As a result, a difference of the magnetization across the point of z ¼0 (Fig. 1) is
Fig. 1. Schematic diagram of the test section and working principle of the system.
1379
created, leading to an additional driving force formed by the fluid itself.
2.2. Test fluid and experimental set-up The test binary magnetic fluid in the present experiment consists of a base TSMF of TS-50K with concentration 80 wt% and an organic solution of n-Hexane with concentration 20 wt%. The organic fluid has a low-boiling saturation temperature of 342 K. Physical properties of the test fluid and its components at room-temperature condition are listed in Table 1. The experimental set-up of the present study is schematically depicted in Fig. 2, consisting mainly of a test section, a driven pump, an cooling unit, a pre-heater, and a flow meter. The test section (Fig. 1) includes an electromagnet, a heater and a heated body. The temperatures in the test section are measured by using three thermocouples installed at the inlet, outlet, and inner wall of the heated body. The working fluid is filled in the closed copper pipe loop with diameter of 0.01 m and length of 6 m, and is driven by the circular pump which controlled by an inverter. In order to obtain the optimal performance of the magnetic body force of the test fluid affecting the driving force, the test section of the experimental setup is installed to be adjustable from horizontal (y ¼01) setting to vertical (y ¼901) arrangement (see Fig. 1).
Table 1 Physical properties of a binary magnetic fluid at 293 K, 1 atm.
Density r (kg/m3) Viscosity Z (Pa s) Specific heat capacity cp (J/(kg K)) Thermal conductivity l (W/(m K)) Curie temperature TC (K) Saturated temperature TS (K)
TS-50K
TS-50K n-Hexane 20 (wt%)
n-Hexane
1.401 103 1.72 10 2 1387 0.175 477 –
1.143 103 2.35 10 3 1564 0.160 477 358
6.54 102 2.96 10 4 2249 0.126 – 342
Fig. 2. Schematic diagram of the experimental set-up.
1380
Y. Iwamoto et al. / Journal of Magnetism and Magnetic Materials 323 (2011) 1378–1383
Table 2 Experimental conditions. Reynolds number Re (representative) Inclination of the test section y Magnetic field intensity Hz,max Inlet temperature of the fluid Tin Temperature of the heated wall Tiw Diameter of the tube D
100 (dimensionless) 0–90 (deg) 0–1.66 105 (A/m) 307 (K) 337–377 (K) 10 (mm)
2.3. Experimental conditions and evaluation parameter The experimental conditions are given in Table 2. Particularly, the flow Reynolds number and the temperature at the inlet of the test section in the experiment are fixed at Re ¼ rl UD=Zl ¼100 and Tin ¼307 K, respectively; system performance at three temperature differences DT¼30, 50 and 70 K of the inner wall temperature Tiw to the inlet temperature of the test section, and four inclination angles of y ¼01, 301, 601 and 901 are investigated. The enhancement of the driving force due to the magnetization difference created by boiling the binary TSMF is evaluated by the pressure difference DPD measured at the inlet and outlet of the test section using the pressure transmitter. To clearly see the effects of the respective magnetic field and gas phase to the driving force, the pressure difference is written as the following form with three parts:
DPD ¼ DPL þ DPT þ DPM
ð3Þ
where DPL is the pressure difference caused by fluid friction, DPT is the pressure difference due to the gas bubble buoyancy and DPM is the pressure difference due to the magnetic force.
Energy equation for the liquid phase considering the magnetic effect: " !# v2 d rl ð1aÞvl hl þ l dz 2 @M dHz ðiÞ þ Qw a ð1 a ÞT v ¼ rl ð1aÞvl g sin y þ Gl hl þqðiÞ l l @Tl H l dz ð8Þ Magnetic field and Magnetization: h p i 1 TT0 Hz ¼ Hz,max 1 þ cos z ; M ¼ wHz 1 2 L TC T0
where v is the velocity, r the density, P the pressure, h the enthalpy, g the gravitational acceleration, r the mean radius of the bubble defined by Eq. (12) below, FD the drag force, Fvm the virtual mass force considering the expansion of the bubble, q the heat flux through the gas–liquid interface, a the interracial area concentration, Qw the heat transfer rate per unit volume, and G the phase generation rate. The subscripts g and l denote gas and liquid phases, respectively. With the assumption of a spherical bubble with equivalent radius r, and energy transfer caused by the heat transfer between an isothermal spherical bubble and the surrounding liquid, the expression for a is obtained as aðiÞ ¼ 3a=r. To close the above basic equations, the following equations are introduced with assumptions of the perfect gas in the gas phase and the boiling bubbles generated spherically with the minimum radius rmin: Generation rate of the gas phase Gg:
Gg ¼
3.1. Governing equations In the past few years, the governing equations which represent the two-phase flow of a magnetic fluid under a non-uniform magnetic field have been derived and solved numerically with considerations of the effects of evaporation and condensation on the vapor bubbles [6]. In the present study, in order to obtain the detailed information of the flow characteristics, the above model is numerically solved with onedimensional assumption. With the coordinate system set in Fig. 1, the governing equations are given as follows Continuity equation: d d ðr avg Þ ¼ Gg , ðr ð1aÞvl Þ ¼ Gl , Gg þ Gl ¼ 0 dz g dz l
ð4Þ
Momentum equation for the whole two-phase flow considering the magnetic force: i d h dP dH rg av2g þ rl ð1aÞv2l ¼ l ð1aÞrl g sin y þ ð1aÞM z dz dz dz 32 þ Gg ðvg vl Þ 2 ðZg avg þ Zl ð1aÞvl Þ D
Energy equation for the gas phase: " !# v2 d ðiÞ rg avg hg þ g ¼ rg avg g sin y þ Gg hg þ qðiÞ g a dz 2
ð10Þ
ð11Þ
Mass conservation of unit gas bubble with the reference radius r: P 4 d d G P g p ðrg r3 Þ ¼ ð12Þ 3 dz dz Ng Equation of state of gas phase: Pg Pl ¼
2gl r
ð13Þ
Equation of pressure balance between gas and liquid phases: Pg ¼ rg RG Tg
ð14Þ
where RG is the gas constant, gl denotes the surface tension in the liquid phase. In the present study the number of the bubbles nga is set 1.17 106 1/(m2 s), the variance s is assumed to be 0.03 m, the minimum radius of the gas bubble rmin is 0.7 10 3 m and the position of the maximum generation rate of the gas phase zmax is at z¼0.05 m.
ð5Þ
3.2. Calculation conditions and evaluation parameters
ð6Þ
The physical situation used in the theoretical analysis is the same as the present experiments (see Tables 1 and 2). The above basic equations are solved numerically by the Runge–Kutta–Gill method. To see the contributions of the magnetic field, gravity, etc. to the driving force, the components of the total driving pressure difference are calculated, respectively, according to the following formulations:
Momentum equation for the unit spherical gas bubble: dv 4 3 4 dP 4 pr rg vg g ¼ pr 3 l pr 3 rg g sin yFD Fvm 3 3 dz dz 3
4 3 pr r Ng 3 min g
Generation number of the initial bubbles Ng: " # nga ðzzmax Þ2 p ffiffiffiffiffiffi exp Ng ¼ 2s2 2ps
3. Theoretical analysis
ð9Þ
ð7Þ
dðDPT Þ ¼ arl g sin y dz
ð15Þ
Y. Iwamoto et al. / Journal of Magnetism and Magnetic Materials 323 (2011) 1378–1383
dðDPM Þ dH ¼ ð1aÞM dz dz
ð16Þ
dðDPL Þ 32 ¼ 2 ðZg ang þ Zl ð1aÞnl Þ dz D
ð17Þ
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where Pl,in is the pressure at z ¼zin (see Fig. 1).
can observed a remarkable increase of the pressure difference DPD at DT¼70 K comparing to the behaviors at DT¼ 30 and 50 K. To see the performance of the driving force of the test fluid in this heat transport device at different inclination of the test section, Fig. 4 depicts the experimental results of the pressure difference DPD as a function of the axial maximum magnetic intensity Hz,max at different inclinations of the test section at the representative temperature difference of DT¼ 70 K. Shown in Fig. 4, different performances of the pressure difference DPD at low and high magnetic fields are observed. At low magnetic fields, the pressure difference DPD is found to enhance obviously when the inclination angle of the test section varies from 01 to 601, and decreases slightly from the inclination angle of the test section of y ¼601 to 901. On the other hand, at high magnetic fields, the pressure difference DPD is observed to improve remarkably when the inclination angle of the test section varies from 01 to 301 and 601 to 901. In the range y ¼301–601, it is found that the pressure difference DPD decreases at high magnetic fields.
4. Results and discussions
4.2. Theoretical analyses
4.1. Experimental results and discussions
Fig. 4 displays complicated behaviors of the measured pressure difference as the function of the magnetic field and the inclination angle of the test section. In order to clearly explain these experimental observations, an one-dimensional numerical analysis is carried out based on Section 3 at two typical magnetic fields of Hz,max ¼50.9 and 153 kA/m and DT¼70 K. Fig. 5 plots the numerical results of the total pressure difference DPD (Eq. (19)) and its components, DPT, DPM, and DPL (Eqs. (15)–(17)) as a function of the inclination angle of the test section at these two representive magnetic fields and DT ¼70 K. For convenient comparison, experimental results of the pressure difference DPD are also plotted in the figure. As shown in Fig. 5(a), it is observed that the experiment measurement (DPD, Exp.) and numerical simulations (DPD, Theory.) generally agree with each other at low magnetic field in Fig. 5(a). On the other hand, at high magnetic field in Fig. 5(b), it is observed that
where, the pressure difference DPM due to the magnetic force has two components according to the following formulation:
DPM ¼ DPM,l þ DPM,g
ð18Þ
where, DPM,l is the pressure difference due to the temperaturedependent magnetization of the TSMF and DPM,g is the pressure difference due to the magnetization of the test liquid decreased by the gas bubble occurrence. The total pressure difference is expressed as
DPD ¼ Pl rl g sin yðzzin ÞPl,in
ð19Þ
Fig. 3 shows the experimental results of the pressure difference
DPD varying with the magnetic field at different temperature differences DT and the inclination angle of the test section y ¼901. As shown in Fig. 3, increasing the strength of the magnetic field, the axial maximum magnetic intensity Hz,max, enhances the pressure difference DPD. As the temperature in the inner wall of the heated body is increased, the pressure difference DPD is found to increase because the temperature-dependent magnetization decreases in the heated region (zZ0), and causes the pressure difference DPM across the point of z¼0. When the heated temperature increases above the boiling temperature of the test fluid (DT¼70 K), the gas phase will appear in the heated region (zZ0), causing a large reduction of the magnetization and an additional increase of the force due to the gas-phase buoyancy. Therefore, one
500
600
ΔT = 30 [K], Exp.
= 0deg, Exp.
ΔT = 50 [K], Exp.
= 30deg, Exp.
ΔT = 70 [K], Exp.
400
500
Fig.5 (b)
= 60deg, Exp. = 90deg, Exp.
400 ΔPD [Pa]
ΔPD [Pa]
300
200
Fig.5 (a) 300
200 100
100 0 0
50
100 Hz,max [kA/m]
150
Fig. 3. Measured pressure difference DPD varying with the magnetic field at different temperature differences DT and the inclination angle of the test section y ¼90o.
0
50
100 Hz,max [kA/m]
150
Fig. 4. Measured pressure difference DPD as a function of the axial maximum magnetic intensity Hz,max at different inclinations of the test section at DT¼ 70 K.
Y. Iwamoto et al. / Journal of Magnetism and Magnetic Materials 323 (2011) 1378–1383
Total ΔPD , Exp. Total ΔPD , Theory. Component ΔPT , Theory. (1) Component ΔPM , Theory. (2) Component ΔPL , Theory. (3)
ΔPD, ΔPT, ΔPM, ΔPL [Pa]
800
600
400 Total ΔPD, Theory. Total ΔPD , Exp.
200
Total ΔPD, Exp. Total ΔPD , Theory. Component ΔPT , Theory. (1) Component ΔPM, Theory. (2) Component ΔPL , Theory. (3)
800 ΔPD , ΔPT , ΔPM , ΔPL [Pa]
1382
600
Total ΔPD , Theory.
(2)
400
Total ΔPD , Exp. 200
(1)
(1) (2) (3)
0 30
0
60
90
(3)
0
0
[deg]
30
60
90
[deg]
Fig. 5. Pressure differences of DPD, DPT, DPM and DPL as a function of the inclination angle of the test section at magnetic fields of (a) Hz,max ¼50.9 and (b) 153 kA/m, respectively.
Table 3 Calculated DPM,l and DPM,g at different inclinations of the test section at DT¼70 K.
y (deg)
0 30 60 90
Hz,max ¼ 50.9 (kA/m)
Hz,max ¼153.0 (kA/m)
Tout (K)
DPM,l (Pa)
DPM,g (Pa)
Tout (K)
DPM,l (Pa)
DPM,g (Pa)
351.0 348.4 344.2 338.4
86 79 70 57
22 21 20 21
353.4 355.7 346.4 348.4
373 398 302 321
74 71 71 70
there are the quantitative differences between the experimental and numerical results of the pressure difference DPD. The reason is from the numerical model we used in the theoretical analyses. Since we used one-dimensional model, the three-dimensional phenomena, particularly the magnetic interaction effects in the heating section due to the temperature variation and the gas-phase occurrence, are not well considered. However, the numerical results well explain the experimental findings in Fig. 4. As shown in Fig. 5(a) for Hz,max ¼50.9 kA/m, with the increase of the inclination angle of the test section from y ¼01 to 901, the pressure difference DPT due to the buoyancy of the gas phase increases and the pressure difference DPM due to the magnetic force decreases, indicating that at low magnetic field the buoyant effect of the gas phase dominates over that of the magnetic field, and contributes to the enhancement of the total pressure difference DPD. The decrease of the pressure difference DPM in Fig. 5(a) comes from two parts as seen in Eq. (18): the pressure difference DPM,l due to the temperature-dependent magnetization of the TSMF and the pressure difference DPM,g due to the magnetization of test liquid decreased by the gas bubble occurrence. Table 3 shows the effects of these two parts on the pressure difference DPM and the temperature Tout at the outlet of the heated body at DT ¼70 K and Tin ¼307 K for two representive magnetic fields of Hz,max ¼50.9 and 153 kA/m, respectively. As shown in Table 3 for Hz,max ¼50.9 kA/m, with the increase of the inclination angle, the temperature Tout at the outlet of the heated body decreases due to the magnetic ejection effect and the buoyancy force, leading to the magnetization in the heating region (zZ0) increasing and the pressure difference DPM,l decreasing. However, the pressure difference DPM,g
changes little with the outlet temperature Tout variation, indicating that the decrease of DPM is mostly caused by the temperaturedependent magnetization. At high magnetic field, however, as the results displayed in Fig. 5(b), the effect of magnetic field is more dominant than that of the buoyancy of the gas phase because the value of the pressure difference DPM is always larger than that of the pressure difference DPT. The pressure difference DPM varies little in the range of the inclination angle of the test section y ¼ 01–301 and 601–901, but has an obvious decrease from y ¼301 to 601. At the same time, the pressure difference DPT keeps increasing when the inclination angle of the test section varies from 01 to 901. As a result, the pressure difference DPD is observed to increase in the range y ¼01–301 and 601–901, and to decrease in the range y ¼301–601. The complicate behavior of the pressure difference DPM in Fig. 5(b) can be clearly illustrated by Table 3 for Hz,max ¼153 kA/m. As shown in Table 3, with the increase of the inclination angle, the pressure difference DPM,g still changes little like that at Hz,max ¼50.9 kA/m. However, the pressure difference DPM,l increases due to the outlet temperature Tout increase in the range of the inclination angle of the test section y ¼ 01–301 and 601–901, and has a great decrease from y ¼301 to 601, in which the outlet temperature Tout shows a great reduction. This observation suggesting again that the temperaturedependent magnetization is the main role in affecting the complicate behavior of the pressure difference DPM, and further the total pressure difference DPD. Due to the above mentioned driving pressure increase along with the change of inclination angle of the heat transport device, the working fluid, the binary temperature-sensitive magnetic fluid, does circulate by it own driving force, transporting a large latent heat by boiling the organic binary-mixture at heating section to the cooling section. Therefore the test carried out in the present investigation revealed that the configuration of the device, including the magnetic fluid imposition, is effective for that the device transports heat without any external work input.
5. Conclusions A systematic investigation of the performance of the boiling binary temperature-sensitive magnetic fluid in a heat transport
Y. Iwamoto et al. / Journal of Magnetism and Magnetic Materials 323 (2011) 1378–1383
device under a non-uniform magnetic field is performed experimentally and theoretically. The main results obtained here are summarized as follows. (1) From the experimental studies on the pressure difference between the inlet and outlet of the test section, it is clarified that the magnetic body force in boiling binary TSMF flow is effective to increase the driving force of the fluid in a nonuniform magnetic field. The temperature difference between the inner heated wall and the inlet of the test section and the inclination arrangement of the test section strongly influence the performance of the enhancement of the driving force. Both increasing the strength of the magnetic field and the temperature difference between the inner heated wall and the inlet of the test section enhance the pressure difference DPD. At low magnetic field, the pressure difference DPD increases when the inclination of angle of the test section increases. At high magnetic field, the pressure difference DPD increases in the range y ¼01–301 and 601–901, and decreases in the range y ¼301–601. (2) The theoretical studies well explain the experimental findings. The contribution of the driving force enhancement is mainly
1383
from the buoyancy of the gas phase at low magnetic field and the effect of the magnetic field at high magnetic field.
Acknowledgment This work was supported by a grant-in-aid for Scientific Research (C) from the Ministry of Education, Culture, Sports, Science and Technology, Japan.
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