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Energy transport in cooling device by magnetic fluid
Journal of Magnetism and Magnetic Materials 431 (2017) 229–236
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Energy transport in cooling device by magnetic fluid Hiroshi Yamaguchi a,n, Yuhiro Iwamoto b a b
Department of Mechanical Engineering, Doshisha University, Kyo-tanabe, Kyoto 610-0321, Japan Department of Electrical and Mechanical Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Aichi 466-8555, Japan
art ic l e i nf o
a b s t r a c t
Article history: Received 30 June 2016 Received in revised form 22 August 2016 Accepted 26 August 2016 Available online 27 August 2016
Temperature sensitive magnetic fluid has a great potential with high performance heat transport ability as well as long distance energy (heat) transporting. In the present study experimental set-up was newly designed and constructed in order to measure basic heat transport characteristics under various magnetic field conditions. Angular dependence for the device (heat transfer section) was also taken into consideration for a sake of practical applications. The energy transfer characteristic (heat transport capability) in the magnetically-driven heat transport (cooling) device using the binary TSMF was fully investigated with the set-up. The obtained results indicate that boiling of the organic mixture (before the magnetic fluid itself reaching boiling point) effectively enhances the heat transfer as well as boosting the flow to circulate in the closed loop by itself. A long-distance heat transport of 5 m is experimentally confirmed, transferring the thermal energy of 35.8 W, even when the device (circulation loop) is horizontally placed. The highlighted results reveal that the proposed cooling device is innovative in a sense of transporting substantial amount of thermal energy (heat) as well as a long distance heat transport. The development of the magnetically-driven heat transport device has a great potential to be replaced for the conventional heat pipe in application of thermal engineering. & 2016 Published by Elsevier B.V.
Keywords: Long distance energy transport Binary temperature-sensitive magnetic fluid Heat transfer Boiling two-phase flow Heat pipe
1. Introduction Since electro and/or mechanical devices were rapidly developed in recent years and their operating temperature has reached almost critical, a high performance heat transport (cooling) device is urgently demanded in the field of thermal engineering. In practice, for example, the power density (heat flux) of Central Processing Units (CPUs) is estimated to reach 1000 kW/m2 due to the high density integration of transistors [1]. Owing to the reasons, long distance energy (heat) transport device with high ability of transporting thermal energy has attracted extensive attention in recent years. Typically the most known device, which has been used and yet been studied, is the heat pipe [2]. With modern technology applying to heat pipes the technical challenge [2] is activity under way, where the some (prototype) heat pipe device [3] is able to transport heat as far as around 10 m distance. In competing the long distance heat transport device (heat pipe), the device using magnetic fluid, particularly which has a strong temperature sensitivity, so called the temperature-sensitive magnetic fluid (TSMF), has a great potential with high performance heat transport ability as well as long distance energy (heat) transporting. The TSMF is a type of magnetic fluid, in which low-Curie n
Corresponding author. E-mail address: [email protected] (H. Yamaguchi).
http://dx.doi.org/10.1016/j.jmmm.2016.08.083 0304-8853/& 2016 Published by Elsevier B.V.
temperature magnetic nanoparticles of such Mn–Zn ferrite are stably dispersed in a carrier liquid. One of the most interesting features of TSMF is that the flow can be induced by input of thermal energy, with which imposing a magnetic field excretes magnetic pressure and transports thermal energy at the same time from hot source to cold heat sink. The energy conversion device (using the principle) with smartly imposing magnetic field enables the design of magnetically-driven heat transport (cooling) device, which as well can transfer heat for a long distance without any mechanical pump. In series of research works [4–8], the authors have developed a device with proposing an innovative energy carrier of a binary TSMF. The binary TSMF used to date is a mixture of kerosene based TSMF with a low-boiling-saturation-temperature organic solution of n-Hexane. The binary TSMF can facilitate the enhancement of the magnetic driving pressure together with high level heat transfer mode, effectively utilizing the boiling gasbubble kinematics and its latent heat. The original concept of energy conversion using TSMF was due to Resler and Rosensweig [9], where they proposed a new thermal engine (power cycle). In the proposed power cycle, the working fluid of TSMF was thought to be operated by applying appropriate magnetic field, and with which the cycle transfers the heat from the heat source to the radiator without any mechanical pumps, generating mechanical power output. They carried out the cycle simulation, suggesting a possibility of MHD power generation system. Namely, in the cycle the thermal energy is converted into
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the kinetic energy of TSMF, and then the kinetic energy is finally converted into the mechanical power output by MHD power generator. After the original report on the energy conversion principle using TSMF, several experimental and theoretical research and works, related to the energy conversion in application of power device or heat transport device, have been reported [10– 21]. As for design of heat transport (cooling) device, not for the power cycle application, it is thought that the boiling heat transfer (latent heat) is a key factor to enhance the heat transfer of TSMF. Nevertheless, till recent years most of the researches have focused on the heat transport by a single-liquid phase flow of TSMF [10– 18], and a very few research was reported in literature under the condition of a gas-liquid boiling two-phase flow [4–8,19–21]. Among those, Kamiyama et. al. [20] investigated the effect of boiling two-phase flow in consideration of magnetic pressure. In their experimental research, TSMF was directly heated by a laser beam power device, in which visualized distribution of the boiling gas-bubbles in the presence of a non-uniform magnetic field was reported. In their results, they showed that the boiling gas-bubble effectively enhanced the magnetic pressure to drive a flow of TSMF. However, no heat transfer characteristic was reported. This was mainly due to the fact that the basic researches conducted in previous years were chiefly oriented to develop a power (generating) cycle. For the aim to develop a heat transport (cooling) device using a magnetic fluid, although the essence of the theory behind it is the same as power cycle, the authors have proposed an innovative energy transport (cooling) device using a binary temperaturesensitive magnetic fluid (binary TSMF) with a thought for realizing long distance heat transport system. The smart energy conversion using the binary TSMF enables to design an innovative magnetically-driven heat transport (cooling) device with advantages listed as follows:
Entirely no external electric energy consumption to drive the
energy carrier. A large amount of energy (heat) transport with phase change. A long distance of energy (heat) transport. Simple configuration which enables the deice to miniaturize. No directional limit for heat transport, horizontal direction to vertical position.
In the present work, some details of the experimental set-up, which was newly designed and constructed so as to obtain basic heat transfer data with the binary TSMF, is introduced. The set-up was designed to take measurements when boiling takes place under various magnetic field imposition. From experimental results phenomenological explanation is given to the heat transfer characteristics of the set-up. The set-up is also constructed, in view of practical application, in consideration of changing the angle of heat transfer section toward the gravity direction. With various angle positions, basic operating performance is obtained under self-circulation condition in the closed loop (with actually driving the binary TSMF) by purely excreted magnetic pressure at the test section. As a challenging thermal application of this set-up (to be extended to realize a practical cooling device) in comparison with heat pipe, some discussions are given in the proceeding sections for a possibility of achieving long distance heat transport.
2. Experimental apparatus and procedure 2.1. Test fluids TSMF used in the present study is commercially supplied magnetic fluid, which is composed of the low-Curie temperature
Table 1 Physical properties of TSMF, n-Hexane and binary temperature-sensitive magnetic fluid at 1 atm, 293 K. TSMF
Binary TSMF
n-Hexane
Density ρ [kg/m3] Viscosity η [Pa s] Specific heat cp [J/(kg K)]
1.401 103 1.72 10 2 1387
1.143 103 2.35 10 3 1564
6.540 102 2.96 10 4 2249
Thermal conductivity λ [W/(m K)] Thermal expansion β [1/K] Curie temperature TC [K]
0.175 6.4 10 4 526
0.160 8.9 10 4 526
0.126 1.36 10 3 –
Saturated temperature TS [K]
377–523
358
342
40
Magnetization M [kA/m]
230
796 [kA/m] 1592 [kA/m] 2388 [kA/m] 3184 [kA/m] 3980 [kA/m]
30
20
10 Room Temperature 0
300
350 400 Temperature T [K]
450
Fig. 1. TSMF, magnetization relation versus temperature.
magnetic nanoparticles of Mn–Zn ferrite dispersed in carrier liquid of Kerosene. The magnetization of TSMF is sensible with temperature in a room temperature range. The proposed binary TSMF used, as a reference in the present study, is a mixture of TSMF with a low-boiling-saturation-temperature organic solution of n-Hexane (with 20 wt% concentration). The physical thermal properties of TSMF, the binary TSMF and n-Hexane at 1 atm and 293 K are listed in Table 1. In Fig. 1, the magnetization of TSMF is plotted versus temperature. It is seen from Fig. 1 that the magnetization of TSMF decreases substantially as temperature being increased, where almost maximum 67% reduction is evident within the room temperature (300 K–400 K) range. 2.2. Experimental set-up In view of constructing a practical cooling device in competition with heat pipe (considering long distance heat transport device), the experimental set-up is manufactured as 5 m loop length (with connection pipe of 10 mm diameter). Angle dependence of core heating section with electric magnetic coil (named test section), where the binary TSMF is driven by magnetic pressure, is examined in order to verify the fact whether if the system may circulate (and transport heat) with its own magnetic driving pressure at different setting angle. The schematic diagram of the experimental set-up with the closed loop structure is shown in Fig. 2(a). The apparatus is mainly composed of the test section (heating and imposing magnetic field section), radiator, pre-heater and mass flow meter. The above mentioned components are connected by copper pipes of diameter 10 mm with 5 m total
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Fig. 2. (a): Schematic diagram of experimental set-up. (b): Schematic diagram of test section. (c): Angle θ dependence testing.
length, in which the working fluid of the binary TSMF is full-filled in the closed loop. The detailed test section is schematically depicted in Fig. 2(b). The test section is mainly composed of a solenoidal electromagnet (coil), two heaters and a heated body. With supplying DC power (0–60 V, 10–10 A) to the solenoid coil, the
solenoidal magnetic field is induced with maximum magnetic field strength of Hx, max ¼155 kA/m. A typical magnetic field distribution (solenoidal field) imposing to the binary TSMF is displayed in Fig. 3, noting that the directional magnetic field Hx( x ) is the actually measured magnetic field, Hx( x ) is used to estimate the
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reading. The temperatures in the test section are measured by thermocouples installed at the inlet, the outlet and representative points at inner wall of the heated part. 2.3. Evaluation parameters and experimental conditions The heat transfer characteristics of the binary TSMF under nonuniform magnetic field (Fig. 3) are evaluated by the local Nusselt ¯ . As number Nu( x ) together with the averaged Nusselt number Nu shown in Fig. 2(b), four inner wall temperatures at A2, B2, C2, D2 positions are measured by thermocouples, where the heat transfer coefficient are evaluated at each representing point x . With the assumption of a constant heat flux along the channel axis of the test section, the local heat transfer coefficient at position x is defined as
h( x) =
q( x) Tiw( x) − Tm( x)
(1)
where Tiw is the inner wall temperature and q is the heat flux. The liquid bulk temperature Tm is calculated by Fig. 3. Axial magnetic field distribution Hx( x ) .
Tm( x) = Tin + magnetic (driving) pressure lately in the following sections. A Coriolis-type flow meter is used to measure the mass flow rate. To control the temperature at the inlet of the test section, a pre-heater is installed so that precise local heat transfer along the test section can be measured at controlled conditions (by controlling inlet temperature to the test section). In order to obtain consistent data (with rigorous precision in data acquisition) of the heat transfer coefficient, an inverter controlled circulation pump (with volumetric flow control function) is installed as shown in Fig. 2(a). By controlling the circulation pump (controlling the flow rate), the circulating flow Reynolds number at the test section can be fixed during the heat transfer (temperature) measurements (by fixing electric power heater input). Applying magnetic field will cause the driving pressure rise of circulating working fluid (the binary TSMF); the test section does act alike a line pump while by the circulation pump the flow rate is controlled to be constant. In the present study, as mentioned before, the circulating flow rate is originally controlled to obtain unified heat transfer coefficient (for fixed Reynolds number). The inclination angle of the test section, in consideration whether if the closed loop (system) can transport heat at various angle position under effect of the gravity, is made variable as indicated in Fig. 2(c). In the present study, θ ¼0° (horizontal position), 30°, 60° and 90° (vertical position) are examined representatively. The self-circulating performances are then recorded with each angle position, taking heat transfer (energy transport) measurements as well as magnetic driving pressure data at the same time. In the test section (Fig. 2(b)), the test fluid is heated, while passing through the point ( x ¼0) of the maximum magnetic field strength toward the downstream side region ( x > 0). After the test section, the heated magnetic fluid is cooled and the generated gasbubbles in the test section are condensed in the cooling unit, which is installed in the closed loop (as shown Fig. 2(a)). In the test section, as shown in Fig. 2(b), the heated part (at the test section as indicated in Fig. 2(b)) is made of brass metal and has the following dimensions; 10.0 mm inner diameter, 5.0 mm wall thickness and 100.0 mm length. AC power supplies are connected to inside and outside heaters to provide the necessary heat flux to the working fluids. Two thermocouples are installed between the inside and the outside heaters. In order to minimize heat loss to the surroundings, the outside heater is controlled to make both measured temperatures the same value by monitoring thermocouple
πD ∫ q( x)dx cpG
(2)
where Tin is the temperature at the inlet of the heated body (position I1 in Fig. 2(b)), D is the inner diameter of the heated body, cp is the specific heat and G is the mass flow rate measured by the mass flow meter. The local Nusselt number Nu( x )and the averaged ¯ can be defined as Nusselt number Nu
h( x)D λ
Nu( x) =
¯ = 1 Nu L
∫ Nu( x)dx
(3)
(4)
where λ is the thermal conductivity and L is the length of the heated body. To characterize the measured data, the Reynolds number Re and the magnetic pressure number Rp are defined as follows
Re =
Rp =
ρUD η
(5)
μ 0 χ0 Hx2, max ρU2
(6)
where g is the gravitational acceleration, ρ is the density, β is the thermal expansion coefficient, U is the averaged velocity, η is the viscosity, ΔT is the reference temperature under constant heat flux which is express as follow
ΔT =
qD λ
(7)
3. Results and discussion 3.1. Basic feature in heat transfer characteristics – influence of boiling heat transfer at the presence of magnetic field Although utilization of TSMF as well as the binary TSMF for heat transport (cooling) device without mechanical pump has been found to be feasible [4–8], the basic feature with respect to the heat transfer of the binary TSMF has not been fully examined
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233
Inner wall temperature [K]
66 36
64 36
62 36
60 36 0
500
1000 Time [s]]
1500
Fig. 4. Inner wall temperature T of heating body with Hx, max ¼ 28.0 kA/m; Re ¼ 100 and heat flux of q ¼18.7 W/m2.
2000 elapsed
time;
yet. Before designing in a practical magnetically-driven heat transport device with the binary TSMF, it is essential to give substantial discussion on basic heat transfer characteristics (presented ¯ ) as well as magnetic driving pressure (presented as Nu( x ) and Nu as Δp and self-circulating flow Reynolds number Re ). Before discussing the basic heat transfer (and heat transport) characteristics, examining primitive temperature information is helpful to understand the flow state inside of the test section, in which no flow visualization is possible. The primary experiment was conducted with the binary TSMF at a representative experimental condition, in which the test fluid (binary TSMF) was driven by the mechanical pump; where Reynolds number was fixed to 100 and the device was horizontally placed, i.e. θ ¼0°. Fig. 4 shows the inner wall temperature variation measured at position T2 (in Fig. 2(b)) with time elapse after relatively weak magnetic field of 28.0 kA/m being imposed. The heat flux input was set as 18.7 kW/m2. From the figure, it is clearly observed that the inner wall temperature rapidly drops from 366.1 K to 359.9 K, dropping 6.2 K after imposing the weak magnetic field. The data indicates that the test fluid is accelerated by the magnetic (driving) pressure
Δp =
∫1
2
MdH
(8)
where 1 and 2 in the integration is the reference position as indicated in Fig. 3. Thus, it is confirmed that the flow of test fluid cools the test section (and transport the heat energy toward the direction to the cooling unit, circulating in the closed loop). Furthermore in order to see the influence of the magnetic field on the temperature drop ΔT as well as associated average Nusselt num¯ , Fig. 5 shows a typical trend of ΔT and Nu ¯ when imposing ber Nu the magnetic field by varying the strength from 0 to 155 kA/m. As shown in the figure, the inner wall temperature is found to decrease largely (plotted as increasing order) with the increase of the magnetic field intensity. Owing to the temperature drop, the average Nusselt number increases with the increase of the magnetic field strength. When the magnetic field of 155 kA/m as the maximum value is imposed, the temperature drop ΔT and the ¯ are observed to become maximum as averaged Nusselt number Nu 20.1 K and 38.8, respectively. This result reveals that imposing magnetic field greatly enhances the heat transfer and effectively cools the heating part. The important information that is con¯ in Fig. 5, is that the order of Nu ¯ is in the range of heat tained in Nu
Fig. 5. The magnitude of temperature drop and average Nusselt number by imposing magnetic field Hx, max ; Reynolds number of Re ¼ 100 and heat flux of q ¼18.7 kW/m2.
transfer with phase change, i.e. in the case of present set-up condition this is in the subcooled boiling region. It is mentioned that Fig. 5 indicates the magnetic driving pressure does effect the heat transfer (vice versa) allowing the test fluid to boil. Retailed discussion for the magnetic (driving) pressure Δp will be given in later section. The influence of the magnetic field on the flow behavior of the binary TSMF is evident and the boiling occurrence does drive the fluid and transports the thermal energy. In order to discuss the effect of the boiling occurrence and the heat transfer enhancement, the local Nusselt numbers at the presence of magnetic field is investigated for representative conditions, where the test fluid is also circulated by the circulation pump at Reynolds number of Re ¼100. Fig. 6 shows the local Nusselt number Nu( x+) by varying the magnetic field strength (represented as magnetic pressure number Rp ) for the binary TSMF. The horizontal axis is the nondimensional length from the inlet of the test section, defined as
x+ =
x 1 D RePr
(
(9)
)
where Pr =ηcp/λ is Prandtl number. The solid line indicates an approximate expression on a reference local Nusselt number for single-phase laminar flow given by Shah and London [22], 3
Nu( x+)
10 ⎫ 10 ⎧ ⎛ 220x+ ⎞− 9 ⎪ ⎪ = 5.364⎨ 1 + ⎜ ⎟ ⎬ − 1.0 ⎝ π ⎠ ⎪ ⎪ ⎩ ⎭
(10)
As shown in Fig. 6(a), it is mentioned that the experimental results and the approximation (10) quantitatively agree with each other at the absence of the magnetic fluid, i.e. Rp ¼0. It is observed, however, that there are quantitative differences between the experimental results and the approximation as data being larger (along tube length). The reason can be speculated from the effect of natural convection on the heat transfer, since the flow speed of the test fluids is low enough, Re ¼ 100, that there may be quite effect from natural connection taking place, while the approximation formula does not consider the effect of natural convection in heat transfer. However for Rp ¼ 0 in Fig. 6(b) when sub-cooled liquid enters the heated tube, the heat transfer coefficient dramatically increases along the tube length, when the first bubbles appear on the wall in sub-cooled flow boiling process [23]. In order to verify quantitative trend to verify the contribution
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80
80
70
approximation formula Rp = 0 [-] Rp =1598 [-] Rp =4066 [-] Rp =7022 [-]
50
60 Nu (x+) [-]
Nu (x+) [-]
60
40 30
approximation formula Rp = 0 [-] Rp =1598 [-] Rp =4066 [-] Rp =7022 [-]
40
20
20 10 0
0.001
0.002 0.003 + x [-]
0.004
0
0.001
0.002
0.003
0.004
+
x [-]
Fig. 6. Local Nusselt number at heat fluxes of (a) 6.6 kW/m2 and (b) 34.2 kW/m2 with variation of magnetic pressure number Rp ; Reynolds number Re ¼ 100. Solid line represent the calculated local Nusselt number from approximation formula given by formula (10) [22].
of the magnetic field to the heat transfer characteristics, Fig. 6 further presents the experiment results of local Nusselt at (a) 6.6 kW/m2 (liquid single-phase flow) and (b) 34.2 kW/m2 (boiling gas-liquid two-phase flow). As shown in Fig. 6(a), the local Nusselt numbers at every temperature measuring points are increased by imposing the magnetic field. Our previous numerical investigation of the thermal flow behavior of single-phase TSMF under a non-uniform magnetic field revealed that the flow is accelerated near the heating wall and is decelerated close to the center of the heating tube due to the effect of the temperaturedependent magnetization in TSMF [24]. Therefore, in the present experiment, it can be easily speculated that the flow is accelerated (as the magnetic field strength presented by Rp is increased) near the heating wall under the non-uniform magnetic field, enhancing the heat transfer. When the flow regime is in the boiling twophase flow (Fig. 6(b)), the local Nusselt number substantially increases with increase of the magnetic field strength (presented by Rp). It is further noted that in addition to the effect of the temperature-dependent magnetization as likely observed in the liquid single-phase flow in Fig. 6(a), the effect of the magnetic buoyancy force (repelling force for bubbles in magnetic field) acting on the boiling gas-bubbles would pay dominant role when strong magnetic field gradients is affected. Due to the above mentioned heat transfer characteristic and driving flow mechanism along with the change of the magnetic field strength, the binary TSMF transports a large amount of latent heat by boiling the organic binary-mixture at heating section. The fundamental test carried out in the present investigation revealed that the configuration of the device, including the configuration of the magnetic field imposition, is effective as the heat transports device, and resultantly heat flux of 34.2 kW/m2 (total energy input of 107 W) can be transported by magnetic driving pressure (the test section acts as a linepump boosting pressure against the circulation pump). To the next step of experiment in the present study, the circulation pump is by-passed (shut down the circulation pump) and the set-up is operated by setting the angle position of the test section for given magnetic field strength ( Hx, max ¼0, 51, 102, 123 and 155 kA/m). Mass flow rate (presented as Re ) is measured for each experimental condition, when self-circulation by its own
magnetic driving pressure is identified. Though the direct measurement of Δp (the magnetic driving pressure) was partly carried out, due to small range of pressure difference Δp"311 Pa, Δp can be estimated from Re and from known associated parameters. 3.2. Influence of inclination angle on the flow rate and the heat transfer in the magnetically-driven self-circulation loop One of the most interesting feature of utilization of the binary TSMF as the working fluid in the heat transport (cooling) device is that the device can be magnetically driven without any mechanical work input (without the circulation pump) by absorbing and transporting thermal energy. When establishing the automatic heat transport device (self-circulation loop), identifying the selfcirculating mass flow rate (presented as Reynolds number at the test section), the effect of the gravity (inclination angle of the test section) on the heat transfer characteristics should be discussed. Fig. 7(a) and (b) show respectively resultant Reynolds number and average Nusselt number with varying the inclination angle ( θ ¼0°, 30°, 60°, and 90°) of the test section under various magnetic field strength. As shown in Fig. 7(a), even when relatively weak magnetic field ( Hx, max ¼51 kA/m) is imposed, the device can be operated evidently at the inclination angle after θ ¼ 30°. Reynolds number (derived from the circulation volumetric flow rate) increases with increase of the inclination angle. This is due to the buoyancy force acting on the rising boiling gas bubble, which facilitates to drive the working fluid upward against gravity. This effect is observed for all the cases on the inclination angle as it is increased to the vertical position θ ¼90°. It is noted that no selfcirculation is observed, when the heat transport device is horizontally placed at weakly imposing magnetic field strength of 0 and 51 kA/m. On the other hand, when relatively strong magnetic field (above 122 kA/m) is imposed, it is evident that the device can be operated even when the test section is placed horizontally, i.e. θ ¼0°. Reynolds number is increased with increasing magnetic field strength up to Reynolds number of 22.0 at θ ¼0°. This result implies that the proposed magnetically-driven heat transport (cooling) device is feasible and is able to transport the heat energy with the long-distance of 5 m with the magnetic driving force. The maximum Reynolds number was measured as
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235
Fig. 7. (a) Variation of Reynolds number and (b) average Nusselt number with variation of inclination angle of and magnetic field intensity; heat flux, 11.4 kW/m2.
40.1, when the device was vertically placed with the magnetic field intensity of 155 kA/m. Similarly, Fig. 7(b) shows the average Nusselt number as the function of the inclination angle of the test section with varying the strength of the imposed magnetic field. Owing to the fact that the flow rate depends on the strength of the magnetic field and the inclination angle, the heat transfer is strongly related with the flow rate; the value of the average Nusselt number tends to decrease at around 20–40 in a range of 30° ≤ θ ≤ 90°and 102 kA/ m o Hx, max o155 kA/m as the inclination angle is increased. While the device is horizontally placed, Nusselt number dramatically increases. This is because of the large latent heat from active boiling process (nucleate boiling phenomena) taking place, enhancing the heat transfer due to the low flow rate at θ ¼ 0°. As mentioned previously, when θ is increased, the average Nusselt ¯ decreases (for a given heat flux, q ¼34.2 kW/m2; heat number Nu flux controlled experiment). This is entirely due to increasing flow rate (as observed in Fig. 7(a)), shifting the two-phase heat transfer mode (i.e. boiling heat transfer) to sub-cooled heat transfer and further toward single-phase heat transfer mode as clearly observed in Fig. 7(b). Similar trend of the heat transport of the device is observed and with the maximum magnetic field intensity of Hx, max ¼155 kA/m, the maximum heat flux q ¼34.2 kW/m2 (the thermal energy of 107 W) can be transported with distance of 5 m when the set-up (device) is placed horizontally, θ ¼0°. It is easily speculated from the results displaced in Fig. 7(a) and (b), that when heat flux at the test section is increased, the trend of heat transport capability can become substantially strong, increasing the magnetic driving pressure (promising further long distant heat transport capability) at any inclination angle setting.
applied magnetic field strength is increased. Also as mentioned earlier, it was quite difficult to measure the precise pressure rise Δp, due to small magnetic pressure (measurement Δp is too small with some degree of fluctuation) that conventional pressure transducer could not yield precision measurement. In the present study, however, Δp can be estimated with reasonable degree of accuracy by employing the formulation (8), knowing M = M ( T , H ; x ) as T = T ( x ) and H = H ( x ). Fig. 8 is a simple schematic of the magnetic field Hx( x ) derived from the present solenoid coil used in the set-up. Thus, from the formula (9), the integration Δp =
2
∫1 MdH can be sub-divided into 1-2-3
to yield the Δp ;
Δp =
∫1
2
MdH −
∫2
3
MdH
where the position 1-2 (at the test section) implies the section of non-heating region, while the position 2-3 is the heating section, where at the position 2 the peak value of the magnetic field strength exists. Assuming H1≈0 kA/m and H3≈0 kA/m (assuming H1 and H3 are far apart from the effective magnetic field), formula (12) gives Δpcal. ¼188 Pa in the case of θ ¼0° with Hx, max ¼102 kA/m. The direct measurement of Δpexp. for the experimental condition was approximately Δpexp. ¼242 Pa, resulting in reasonable account of formula (11). Though as mentioned previously, the direct
3.3. Discussion of long distance heat transport of magnetically-driven heat transport device using binary temperature-sensitive magnetic fluid In competing with an advance heat pipe [3], it is worthy discussing the feasibility of the present heat transport device (if this set-up is manufactured as actual practical device) based on the experimental results gained in the previous sections. As observed in Fig. 7(a), the device does work as (self-circulating) heat transport device, knowing that flow rate (presented as Re ) increases as
(11)
Fig. 8. Schematic diagram of simplify solenoidal magnetic field.
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measurement of Δp is difficult, the preliminary measurement of Δp yielded for the case of θ ¼0°, as Δpexp. ¼ 271 Pa and Δpexp. ¼311 Pa with Hx, max ¼123 kA/m and Hx, max ¼155 kA/m respectively, while the estimated magnetic driving pressure calculated from formula (11)) are Δpcal. ¼279 Pa and Δpcal. ¼ 420 Pa, respectively. Similarly reasonable estimation of formula (11) is evident. 2
L=
ΔpD 32μ 0 u¯
(12)
Using representative value of Δpcal. ¼188 Pa (above mentioned value) at θ ¼0°and Hx, max ¼102 kA/m, the ideal heat transport distance L (based on Newtonian pipe flow, the diameter D ¼ 0.01 m and Newtonian viscosity and μ0 ¼2.35 10 3 Pa s u¯ ¼3.71 10 3 m/s as average flow speed obtained from measured Re) can be calculated by formula (12) to give L ¼40.7 m, meaning that the device based on this set-up can carry heat as far as 40.7 m long distance at ideal condition. In comparison with advanced heat pipe (in competing heat pipe), whose limitation of heat transport distance is approximately 10 m for conditions of volumetric was flow rate of carrier fluid as 1.32 kg/min [25]. Using this value for an estimation of the heat transport distance L of the present device (based on the present set-up), it will be L ¼12.2 m when Hx, max ¼ 400 kA/m is assumed, indicating that the device should be feasible and competitive against the heat pipe in consideration of the long distance heat transport.
4. Conclusions An experimental investigation of the heat transfer characteristic of the binary TSMF is performed. The main results obtained here are summarized as follows. 1. Inner wall temperature of test section rapidly decreases when an external non-uniform magnetic field is applied, indicating that the working fluid is driven by the magnetic driving pressure. This implies that the constructed device (the set-up) does perform and has a potential as a heat transport device (cooling device). 2. Averaged Nusselt number increases with increase of the magnetic field strength. Particularly, averaged Nusselt number dramatically increase when subcooled boiling occurs in the test section, boosting the magnetic driving pressure to circulate in the closed loop. 3. The evaluation of the long distance heat transport on the present set-up yields that the set-up is feasible to design an actual heat transport device in competition with heat pipe.
Acknowledgment The work was supported by a grant-in-aid for Scientific
Research (c) from the Ministry of Education, Culture, Sports, Science and Technology (Grant No. 26420126), Japan.
References [1] A. Danowitz, K. Kelley, J. Mao, J.P. Stevenson, M. Horowitz, CPU DB: Recording Microporocessor Histroy, Queen-Processors, Vol. 10, 2012, pp. 1–18. [2] A. Faghri, Review and advances in heat pipe science and technology, J. Heat. Transf. 134 (2012) 123001. [3] M. Mitomi, H. Nagano, Long-distance loop heat pipe for effective utilization of energy, Int. J. Heat. Mass Transf. 77 (2014) 777–784. [4] S. Shuchi, T. Mori, H. Yamaguchi, Flow boiling heat transfer of binary mixed magnetic fluid, IEEE Trans. Magn. 38 (2002) 3234–3236. [5] S. Shuchi, K. Sakatani, H. Yamaguchi, Boiling heat transfer characteristics of binary magnetic fluid flow in a vertical circular pipe with a partly heated region, Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 218 (2004) 223–232. [6] Y. Iwamoto, H. Yamaguchi, X.D. Niu, Magnetically-driven heat transport device using a binary temperature-sensitive magnetic fluid, J. Magn. Magn. Mater. 323 (2011) 1378–1383. [7] Y. Iwamoto, Y. Fuji, K. Takeda, X.-D. Niu, H. Yamaguchi, Application of a binarysensitive magnetic fluid for a mini magnetically-driven heat transport device, J. Jpn. Soc. Exp. Mech. 13 (2013) s18–s23. [8] H. Yamaguchi, Y. Iwamoto, Heat transport with temperature-sensitive magnetic fluid for application to micro-cooling device, Magnetohydrodynamics 49 (2013) 448–453. [9] E.L. Resler, R.E. Rosensweig, Magnetocaloric Power, AIAA J. 2 (1964) 1418–1422. [10] E.L. Resler, R.E. Rosensweig, Regenerative thermomagnetic power, J. Eng. Power 89 (1967) 399–406. [11] H. Yamaguchi, A. Sumiji, S. Shiuchi, T. Yonemura, Characteristics of thermomagnetic driven motor using magnetic fluid, J. Magn. Magn. Mater. 272–276 (2004) 2362–2364. [12] K. Fumoto, H. Yamagishi, M. Ikegawa, A mini heat transport device based on thermo-sensitive magnetic fluid, Nano. Micro. Therm. Eng. 11 (2007) 201–210. [13] K. Fumoto, M. Ikegawa, T. Kawanami, Heat transfer characteristics of a thermosensitive magnetic fluid in micro-channel, J. Therm. Sci. Technol. 4 (2009) 332–339. [14] Y. Xuan, W. Lian, Electric cooling using an automatic energy transport device based on themomagnetic effect, Appl. Therm. Eng. 31 (2011) 1487–1494. [15] W. Lina, Y. Xuan, Q. Li, Characterization of miniature automatic energy transport devices based on the thermomagnetic effect, Energy Convers. Manag. 50 (2009) 35–42. [16] W. Lian, Y. Xuan, Q. Li, Design method of automatic energy transport devices based on the thermomagnetic effect of magnetic fluids, Int. J. Heat Mass Transf. 52 (2009) 5451–5458. [17] Y. Mitamura, E. Okamoto, Numerical analysis of the effects of a high gradient magnetic field on flowing erythrocytes in a membrane oxygenator, J. Magn. Magn. Mater. 380 (2015) 54–60. [18] A.N. Afifah, S. Syahrullail, NAC Sidik, Magnetoviscous effect and thermomagnetic convection of magnetic fluid: a review, Renew. Sustain. Energy Rev. 55 (2016) 1030–1040. [19] J. Ishimoto, M. Okubo, S. Kamiyama, M. Higashitani, Bubble behaviour in magnetic fluid under a nonuniform magnetic field, Jpn. Soc. Mech. Eng. Int. J. Ser. B 38 (1995) 382–387. [20] S. Kamiyama, J. Ishimoto, Boiling two-phase flows of magnetic fluid in a nonuniform magnetic field, J. Magn. Magn. Mater. 149 (1995) 125–131. [21] E. Aursand, M.A. Gjennestad, K.Y. Levag, H. Lund, A multi-phase flow model with equation of state for thermomagnetic pumping and heat transfer, J. Magn. Magn. Mater. 402 (2016) 8–19. [22] R.K. Shah, A.L. London, Laminar Flow Forced Convection in Ducts, Academic Press, New York, 1978. [23] C.T. Crowe, Multiphase Flow Handbook, CRC Press, Boca Raton, 2006. [24] Y. Iwamoto, H. Ishizuka, X.-D. Niu, H. Yamaguchi, T. Kuwahara, Active Flow Control of Ferrofluids using External Magnetic Fields, in: Proceedings of the 20th MAGDA Conference in Pacific Asia, 2011, pp. 309–314. [25] N.A. Avgerions, D.P. Margaris, D.T. Tsahalis, Effect of the working liquid to the capillary pumped loop performance, Int. J. Low.-Carbon Technol. 0 (2013) 1–7.
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Energy transport in cooling device by magnetic fluid Hiroshi Yamaguchi a,n, Yuhiro Iwamoto b a b
Department of Mechanical Engineering, Doshisha University, Kyo-tanabe, Kyoto 610-0321, Japan Department of Electrical and Mechanical Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Aichi 466-8555, Japan
art ic l e i nf o
a b s t r a c t
Article history: Received 30 June 2016 Received in revised form 22 August 2016 Accepted 26 August 2016 Available online 27 August 2016
Temperature sensitive magnetic fluid has a great potential with high performance heat transport ability as well as long distance energy (heat) transporting. In the present study experimental set-up was newly designed and constructed in order to measure basic heat transport characteristics under various magnetic field conditions. Angular dependence for the device (heat transfer section) was also taken into consideration for a sake of practical applications. The energy transfer characteristic (heat transport capability) in the magnetically-driven heat transport (cooling) device using the binary TSMF was fully investigated with the set-up. The obtained results indicate that boiling of the organic mixture (before the magnetic fluid itself reaching boiling point) effectively enhances the heat transfer as well as boosting the flow to circulate in the closed loop by itself. A long-distance heat transport of 5 m is experimentally confirmed, transferring the thermal energy of 35.8 W, even when the device (circulation loop) is horizontally placed. The highlighted results reveal that the proposed cooling device is innovative in a sense of transporting substantial amount of thermal energy (heat) as well as a long distance heat transport. The development of the magnetically-driven heat transport device has a great potential to be replaced for the conventional heat pipe in application of thermal engineering. & 2016 Published by Elsevier B.V.
Keywords: Long distance energy transport Binary temperature-sensitive magnetic fluid Heat transfer Boiling two-phase flow Heat pipe
1. Introduction Since electro and/or mechanical devices were rapidly developed in recent years and their operating temperature has reached almost critical, a high performance heat transport (cooling) device is urgently demanded in the field of thermal engineering. In practice, for example, the power density (heat flux) of Central Processing Units (CPUs) is estimated to reach 1000 kW/m2 due to the high density integration of transistors [1]. Owing to the reasons, long distance energy (heat) transport device with high ability of transporting thermal energy has attracted extensive attention in recent years. Typically the most known device, which has been used and yet been studied, is the heat pipe [2]. With modern technology applying to heat pipes the technical challenge [2] is activity under way, where the some (prototype) heat pipe device [3] is able to transport heat as far as around 10 m distance. In competing the long distance heat transport device (heat pipe), the device using magnetic fluid, particularly which has a strong temperature sensitivity, so called the temperature-sensitive magnetic fluid (TSMF), has a great potential with high performance heat transport ability as well as long distance energy (heat) transporting. The TSMF is a type of magnetic fluid, in which low-Curie n
Corresponding author. E-mail address: [email protected] (H. Yamaguchi).
http://dx.doi.org/10.1016/j.jmmm.2016.08.083 0304-8853/& 2016 Published by Elsevier B.V.
temperature magnetic nanoparticles of such Mn–Zn ferrite are stably dispersed in a carrier liquid. One of the most interesting features of TSMF is that the flow can be induced by input of thermal energy, with which imposing a magnetic field excretes magnetic pressure and transports thermal energy at the same time from hot source to cold heat sink. The energy conversion device (using the principle) with smartly imposing magnetic field enables the design of magnetically-driven heat transport (cooling) device, which as well can transfer heat for a long distance without any mechanical pump. In series of research works [4–8], the authors have developed a device with proposing an innovative energy carrier of a binary TSMF. The binary TSMF used to date is a mixture of kerosene based TSMF with a low-boiling-saturation-temperature organic solution of n-Hexane. The binary TSMF can facilitate the enhancement of the magnetic driving pressure together with high level heat transfer mode, effectively utilizing the boiling gasbubble kinematics and its latent heat. The original concept of energy conversion using TSMF was due to Resler and Rosensweig [9], where they proposed a new thermal engine (power cycle). In the proposed power cycle, the working fluid of TSMF was thought to be operated by applying appropriate magnetic field, and with which the cycle transfers the heat from the heat source to the radiator without any mechanical pumps, generating mechanical power output. They carried out the cycle simulation, suggesting a possibility of MHD power generation system. Namely, in the cycle the thermal energy is converted into
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the kinetic energy of TSMF, and then the kinetic energy is finally converted into the mechanical power output by MHD power generator. After the original report on the energy conversion principle using TSMF, several experimental and theoretical research and works, related to the energy conversion in application of power device or heat transport device, have been reported [10– 21]. As for design of heat transport (cooling) device, not for the power cycle application, it is thought that the boiling heat transfer (latent heat) is a key factor to enhance the heat transfer of TSMF. Nevertheless, till recent years most of the researches have focused on the heat transport by a single-liquid phase flow of TSMF [10– 18], and a very few research was reported in literature under the condition of a gas-liquid boiling two-phase flow [4–8,19–21]. Among those, Kamiyama et. al. [20] investigated the effect of boiling two-phase flow in consideration of magnetic pressure. In their experimental research, TSMF was directly heated by a laser beam power device, in which visualized distribution of the boiling gas-bubbles in the presence of a non-uniform magnetic field was reported. In their results, they showed that the boiling gas-bubble effectively enhanced the magnetic pressure to drive a flow of TSMF. However, no heat transfer characteristic was reported. This was mainly due to the fact that the basic researches conducted in previous years were chiefly oriented to develop a power (generating) cycle. For the aim to develop a heat transport (cooling) device using a magnetic fluid, although the essence of the theory behind it is the same as power cycle, the authors have proposed an innovative energy transport (cooling) device using a binary temperaturesensitive magnetic fluid (binary TSMF) with a thought for realizing long distance heat transport system. The smart energy conversion using the binary TSMF enables to design an innovative magnetically-driven heat transport (cooling) device with advantages listed as follows:
Entirely no external electric energy consumption to drive the
energy carrier. A large amount of energy (heat) transport with phase change. A long distance of energy (heat) transport. Simple configuration which enables the deice to miniaturize. No directional limit for heat transport, horizontal direction to vertical position.
In the present work, some details of the experimental set-up, which was newly designed and constructed so as to obtain basic heat transfer data with the binary TSMF, is introduced. The set-up was designed to take measurements when boiling takes place under various magnetic field imposition. From experimental results phenomenological explanation is given to the heat transfer characteristics of the set-up. The set-up is also constructed, in view of practical application, in consideration of changing the angle of heat transfer section toward the gravity direction. With various angle positions, basic operating performance is obtained under self-circulation condition in the closed loop (with actually driving the binary TSMF) by purely excreted magnetic pressure at the test section. As a challenging thermal application of this set-up (to be extended to realize a practical cooling device) in comparison with heat pipe, some discussions are given in the proceeding sections for a possibility of achieving long distance heat transport.
2. Experimental apparatus and procedure 2.1. Test fluids TSMF used in the present study is commercially supplied magnetic fluid, which is composed of the low-Curie temperature
Table 1 Physical properties of TSMF, n-Hexane and binary temperature-sensitive magnetic fluid at 1 atm, 293 K. TSMF
Binary TSMF
n-Hexane
Density ρ [kg/m3] Viscosity η [Pa s] Specific heat cp [J/(kg K)]
1.401 103 1.72 10 2 1387
1.143 103 2.35 10 3 1564
6.540 102 2.96 10 4 2249
Thermal conductivity λ [W/(m K)] Thermal expansion β [1/K] Curie temperature TC [K]
0.175 6.4 10 4 526
0.160 8.9 10 4 526
0.126 1.36 10 3 –
Saturated temperature TS [K]
377–523
358
342
40
Magnetization M [kA/m]
230
796 [kA/m] 1592 [kA/m] 2388 [kA/m] 3184 [kA/m] 3980 [kA/m]
30
20
10 Room Temperature 0
300
350 400 Temperature T [K]
450
Fig. 1. TSMF, magnetization relation versus temperature.
magnetic nanoparticles of Mn–Zn ferrite dispersed in carrier liquid of Kerosene. The magnetization of TSMF is sensible with temperature in a room temperature range. The proposed binary TSMF used, as a reference in the present study, is a mixture of TSMF with a low-boiling-saturation-temperature organic solution of n-Hexane (with 20 wt% concentration). The physical thermal properties of TSMF, the binary TSMF and n-Hexane at 1 atm and 293 K are listed in Table 1. In Fig. 1, the magnetization of TSMF is plotted versus temperature. It is seen from Fig. 1 that the magnetization of TSMF decreases substantially as temperature being increased, where almost maximum 67% reduction is evident within the room temperature (300 K–400 K) range. 2.2. Experimental set-up In view of constructing a practical cooling device in competition with heat pipe (considering long distance heat transport device), the experimental set-up is manufactured as 5 m loop length (with connection pipe of 10 mm diameter). Angle dependence of core heating section with electric magnetic coil (named test section), where the binary TSMF is driven by magnetic pressure, is examined in order to verify the fact whether if the system may circulate (and transport heat) with its own magnetic driving pressure at different setting angle. The schematic diagram of the experimental set-up with the closed loop structure is shown in Fig. 2(a). The apparatus is mainly composed of the test section (heating and imposing magnetic field section), radiator, pre-heater and mass flow meter. The above mentioned components are connected by copper pipes of diameter 10 mm with 5 m total
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231
Fig. 2. (a): Schematic diagram of experimental set-up. (b): Schematic diagram of test section. (c): Angle θ dependence testing.
length, in which the working fluid of the binary TSMF is full-filled in the closed loop. The detailed test section is schematically depicted in Fig. 2(b). The test section is mainly composed of a solenoidal electromagnet (coil), two heaters and a heated body. With supplying DC power (0–60 V, 10–10 A) to the solenoid coil, the
solenoidal magnetic field is induced with maximum magnetic field strength of Hx, max ¼155 kA/m. A typical magnetic field distribution (solenoidal field) imposing to the binary TSMF is displayed in Fig. 3, noting that the directional magnetic field Hx( x ) is the actually measured magnetic field, Hx( x ) is used to estimate the
232
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reading. The temperatures in the test section are measured by thermocouples installed at the inlet, the outlet and representative points at inner wall of the heated part. 2.3. Evaluation parameters and experimental conditions The heat transfer characteristics of the binary TSMF under nonuniform magnetic field (Fig. 3) are evaluated by the local Nusselt ¯ . As number Nu( x ) together with the averaged Nusselt number Nu shown in Fig. 2(b), four inner wall temperatures at A2, B2, C2, D2 positions are measured by thermocouples, where the heat transfer coefficient are evaluated at each representing point x . With the assumption of a constant heat flux along the channel axis of the test section, the local heat transfer coefficient at position x is defined as
h( x) =
q( x) Tiw( x) − Tm( x)
(1)
where Tiw is the inner wall temperature and q is the heat flux. The liquid bulk temperature Tm is calculated by Fig. 3. Axial magnetic field distribution Hx( x ) .
Tm( x) = Tin + magnetic (driving) pressure lately in the following sections. A Coriolis-type flow meter is used to measure the mass flow rate. To control the temperature at the inlet of the test section, a pre-heater is installed so that precise local heat transfer along the test section can be measured at controlled conditions (by controlling inlet temperature to the test section). In order to obtain consistent data (with rigorous precision in data acquisition) of the heat transfer coefficient, an inverter controlled circulation pump (with volumetric flow control function) is installed as shown in Fig. 2(a). By controlling the circulation pump (controlling the flow rate), the circulating flow Reynolds number at the test section can be fixed during the heat transfer (temperature) measurements (by fixing electric power heater input). Applying magnetic field will cause the driving pressure rise of circulating working fluid (the binary TSMF); the test section does act alike a line pump while by the circulation pump the flow rate is controlled to be constant. In the present study, as mentioned before, the circulating flow rate is originally controlled to obtain unified heat transfer coefficient (for fixed Reynolds number). The inclination angle of the test section, in consideration whether if the closed loop (system) can transport heat at various angle position under effect of the gravity, is made variable as indicated in Fig. 2(c). In the present study, θ ¼0° (horizontal position), 30°, 60° and 90° (vertical position) are examined representatively. The self-circulating performances are then recorded with each angle position, taking heat transfer (energy transport) measurements as well as magnetic driving pressure data at the same time. In the test section (Fig. 2(b)), the test fluid is heated, while passing through the point ( x ¼0) of the maximum magnetic field strength toward the downstream side region ( x > 0). After the test section, the heated magnetic fluid is cooled and the generated gasbubbles in the test section are condensed in the cooling unit, which is installed in the closed loop (as shown Fig. 2(a)). In the test section, as shown in Fig. 2(b), the heated part (at the test section as indicated in Fig. 2(b)) is made of brass metal and has the following dimensions; 10.0 mm inner diameter, 5.0 mm wall thickness and 100.0 mm length. AC power supplies are connected to inside and outside heaters to provide the necessary heat flux to the working fluids. Two thermocouples are installed between the inside and the outside heaters. In order to minimize heat loss to the surroundings, the outside heater is controlled to make both measured temperatures the same value by monitoring thermocouple
πD ∫ q( x)dx cpG
(2)
where Tin is the temperature at the inlet of the heated body (position I1 in Fig. 2(b)), D is the inner diameter of the heated body, cp is the specific heat and G is the mass flow rate measured by the mass flow meter. The local Nusselt number Nu( x )and the averaged ¯ can be defined as Nusselt number Nu
h( x)D λ
Nu( x) =
¯ = 1 Nu L
∫ Nu( x)dx
(3)
(4)
where λ is the thermal conductivity and L is the length of the heated body. To characterize the measured data, the Reynolds number Re and the magnetic pressure number Rp are defined as follows
Re =
Rp =
ρUD η
(5)
μ 0 χ0 Hx2, max ρU2
(6)
where g is the gravitational acceleration, ρ is the density, β is the thermal expansion coefficient, U is the averaged velocity, η is the viscosity, ΔT is the reference temperature under constant heat flux which is express as follow
ΔT =
qD λ
(7)
3. Results and discussion 3.1. Basic feature in heat transfer characteristics – influence of boiling heat transfer at the presence of magnetic field Although utilization of TSMF as well as the binary TSMF for heat transport (cooling) device without mechanical pump has been found to be feasible [4–8], the basic feature with respect to the heat transfer of the binary TSMF has not been fully examined
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233
Inner wall temperature [K]
66 36
64 36
62 36
60 36 0
500
1000 Time [s]]
1500
Fig. 4. Inner wall temperature T of heating body with Hx, max ¼ 28.0 kA/m; Re ¼ 100 and heat flux of q ¼18.7 W/m2.
2000 elapsed
time;
yet. Before designing in a practical magnetically-driven heat transport device with the binary TSMF, it is essential to give substantial discussion on basic heat transfer characteristics (presented ¯ ) as well as magnetic driving pressure (presented as Nu( x ) and Nu as Δp and self-circulating flow Reynolds number Re ). Before discussing the basic heat transfer (and heat transport) characteristics, examining primitive temperature information is helpful to understand the flow state inside of the test section, in which no flow visualization is possible. The primary experiment was conducted with the binary TSMF at a representative experimental condition, in which the test fluid (binary TSMF) was driven by the mechanical pump; where Reynolds number was fixed to 100 and the device was horizontally placed, i.e. θ ¼0°. Fig. 4 shows the inner wall temperature variation measured at position T2 (in Fig. 2(b)) with time elapse after relatively weak magnetic field of 28.0 kA/m being imposed. The heat flux input was set as 18.7 kW/m2. From the figure, it is clearly observed that the inner wall temperature rapidly drops from 366.1 K to 359.9 K, dropping 6.2 K after imposing the weak magnetic field. The data indicates that the test fluid is accelerated by the magnetic (driving) pressure
Δp =
∫1
2
MdH
(8)
where 1 and 2 in the integration is the reference position as indicated in Fig. 3. Thus, it is confirmed that the flow of test fluid cools the test section (and transport the heat energy toward the direction to the cooling unit, circulating in the closed loop). Furthermore in order to see the influence of the magnetic field on the temperature drop ΔT as well as associated average Nusselt num¯ , Fig. 5 shows a typical trend of ΔT and Nu ¯ when imposing ber Nu the magnetic field by varying the strength from 0 to 155 kA/m. As shown in the figure, the inner wall temperature is found to decrease largely (plotted as increasing order) with the increase of the magnetic field intensity. Owing to the temperature drop, the average Nusselt number increases with the increase of the magnetic field strength. When the magnetic field of 155 kA/m as the maximum value is imposed, the temperature drop ΔT and the ¯ are observed to become maximum as averaged Nusselt number Nu 20.1 K and 38.8, respectively. This result reveals that imposing magnetic field greatly enhances the heat transfer and effectively cools the heating part. The important information that is con¯ in Fig. 5, is that the order of Nu ¯ is in the range of heat tained in Nu
Fig. 5. The magnitude of temperature drop and average Nusselt number by imposing magnetic field Hx, max ; Reynolds number of Re ¼ 100 and heat flux of q ¼18.7 kW/m2.
transfer with phase change, i.e. in the case of present set-up condition this is in the subcooled boiling region. It is mentioned that Fig. 5 indicates the magnetic driving pressure does effect the heat transfer (vice versa) allowing the test fluid to boil. Retailed discussion for the magnetic (driving) pressure Δp will be given in later section. The influence of the magnetic field on the flow behavior of the binary TSMF is evident and the boiling occurrence does drive the fluid and transports the thermal energy. In order to discuss the effect of the boiling occurrence and the heat transfer enhancement, the local Nusselt numbers at the presence of magnetic field is investigated for representative conditions, where the test fluid is also circulated by the circulation pump at Reynolds number of Re ¼100. Fig. 6 shows the local Nusselt number Nu( x+) by varying the magnetic field strength (represented as magnetic pressure number Rp ) for the binary TSMF. The horizontal axis is the nondimensional length from the inlet of the test section, defined as
x+ =
x 1 D RePr
(
(9)
)
where Pr =ηcp/λ is Prandtl number. The solid line indicates an approximate expression on a reference local Nusselt number for single-phase laminar flow given by Shah and London [22], 3
Nu( x+)
10 ⎫ 10 ⎧ ⎛ 220x+ ⎞− 9 ⎪ ⎪ = 5.364⎨ 1 + ⎜ ⎟ ⎬ − 1.0 ⎝ π ⎠ ⎪ ⎪ ⎩ ⎭
(10)
As shown in Fig. 6(a), it is mentioned that the experimental results and the approximation (10) quantitatively agree with each other at the absence of the magnetic fluid, i.e. Rp ¼0. It is observed, however, that there are quantitative differences between the experimental results and the approximation as data being larger (along tube length). The reason can be speculated from the effect of natural convection on the heat transfer, since the flow speed of the test fluids is low enough, Re ¼ 100, that there may be quite effect from natural connection taking place, while the approximation formula does not consider the effect of natural convection in heat transfer. However for Rp ¼ 0 in Fig. 6(b) when sub-cooled liquid enters the heated tube, the heat transfer coefficient dramatically increases along the tube length, when the first bubbles appear on the wall in sub-cooled flow boiling process [23]. In order to verify quantitative trend to verify the contribution
234
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80
80
70
approximation formula Rp = 0 [-] Rp =1598 [-] Rp =4066 [-] Rp =7022 [-]
50
60 Nu (x+) [-]
Nu (x+) [-]
60
40 30
approximation formula Rp = 0 [-] Rp =1598 [-] Rp =4066 [-] Rp =7022 [-]
40
20
20 10 0
0.001
0.002 0.003 + x [-]
0.004
0
0.001
0.002
0.003
0.004
+
x [-]
Fig. 6. Local Nusselt number at heat fluxes of (a) 6.6 kW/m2 and (b) 34.2 kW/m2 with variation of magnetic pressure number Rp ; Reynolds number Re ¼ 100. Solid line represent the calculated local Nusselt number from approximation formula given by formula (10) [22].
of the magnetic field to the heat transfer characteristics, Fig. 6 further presents the experiment results of local Nusselt at (a) 6.6 kW/m2 (liquid single-phase flow) and (b) 34.2 kW/m2 (boiling gas-liquid two-phase flow). As shown in Fig. 6(a), the local Nusselt numbers at every temperature measuring points are increased by imposing the magnetic field. Our previous numerical investigation of the thermal flow behavior of single-phase TSMF under a non-uniform magnetic field revealed that the flow is accelerated near the heating wall and is decelerated close to the center of the heating tube due to the effect of the temperaturedependent magnetization in TSMF [24]. Therefore, in the present experiment, it can be easily speculated that the flow is accelerated (as the magnetic field strength presented by Rp is increased) near the heating wall under the non-uniform magnetic field, enhancing the heat transfer. When the flow regime is in the boiling twophase flow (Fig. 6(b)), the local Nusselt number substantially increases with increase of the magnetic field strength (presented by Rp). It is further noted that in addition to the effect of the temperature-dependent magnetization as likely observed in the liquid single-phase flow in Fig. 6(a), the effect of the magnetic buoyancy force (repelling force for bubbles in magnetic field) acting on the boiling gas-bubbles would pay dominant role when strong magnetic field gradients is affected. Due to the above mentioned heat transfer characteristic and driving flow mechanism along with the change of the magnetic field strength, the binary TSMF transports a large amount of latent heat by boiling the organic binary-mixture at heating section. The fundamental test carried out in the present investigation revealed that the configuration of the device, including the configuration of the magnetic field imposition, is effective as the heat transports device, and resultantly heat flux of 34.2 kW/m2 (total energy input of 107 W) can be transported by magnetic driving pressure (the test section acts as a linepump boosting pressure against the circulation pump). To the next step of experiment in the present study, the circulation pump is by-passed (shut down the circulation pump) and the set-up is operated by setting the angle position of the test section for given magnetic field strength ( Hx, max ¼0, 51, 102, 123 and 155 kA/m). Mass flow rate (presented as Re ) is measured for each experimental condition, when self-circulation by its own
magnetic driving pressure is identified. Though the direct measurement of Δp (the magnetic driving pressure) was partly carried out, due to small range of pressure difference Δp"311 Pa, Δp can be estimated from Re and from known associated parameters. 3.2. Influence of inclination angle on the flow rate and the heat transfer in the magnetically-driven self-circulation loop One of the most interesting feature of utilization of the binary TSMF as the working fluid in the heat transport (cooling) device is that the device can be magnetically driven without any mechanical work input (without the circulation pump) by absorbing and transporting thermal energy. When establishing the automatic heat transport device (self-circulation loop), identifying the selfcirculating mass flow rate (presented as Reynolds number at the test section), the effect of the gravity (inclination angle of the test section) on the heat transfer characteristics should be discussed. Fig. 7(a) and (b) show respectively resultant Reynolds number and average Nusselt number with varying the inclination angle ( θ ¼0°, 30°, 60°, and 90°) of the test section under various magnetic field strength. As shown in Fig. 7(a), even when relatively weak magnetic field ( Hx, max ¼51 kA/m) is imposed, the device can be operated evidently at the inclination angle after θ ¼ 30°. Reynolds number (derived from the circulation volumetric flow rate) increases with increase of the inclination angle. This is due to the buoyancy force acting on the rising boiling gas bubble, which facilitates to drive the working fluid upward against gravity. This effect is observed for all the cases on the inclination angle as it is increased to the vertical position θ ¼90°. It is noted that no selfcirculation is observed, when the heat transport device is horizontally placed at weakly imposing magnetic field strength of 0 and 51 kA/m. On the other hand, when relatively strong magnetic field (above 122 kA/m) is imposed, it is evident that the device can be operated even when the test section is placed horizontally, i.e. θ ¼0°. Reynolds number is increased with increasing magnetic field strength up to Reynolds number of 22.0 at θ ¼0°. This result implies that the proposed magnetically-driven heat transport (cooling) device is feasible and is able to transport the heat energy with the long-distance of 5 m with the magnetic driving force. The maximum Reynolds number was measured as
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235
Fig. 7. (a) Variation of Reynolds number and (b) average Nusselt number with variation of inclination angle of and magnetic field intensity; heat flux, 11.4 kW/m2.
40.1, when the device was vertically placed with the magnetic field intensity of 155 kA/m. Similarly, Fig. 7(b) shows the average Nusselt number as the function of the inclination angle of the test section with varying the strength of the imposed magnetic field. Owing to the fact that the flow rate depends on the strength of the magnetic field and the inclination angle, the heat transfer is strongly related with the flow rate; the value of the average Nusselt number tends to decrease at around 20–40 in a range of 30° ≤ θ ≤ 90°and 102 kA/ m o Hx, max o155 kA/m as the inclination angle is increased. While the device is horizontally placed, Nusselt number dramatically increases. This is because of the large latent heat from active boiling process (nucleate boiling phenomena) taking place, enhancing the heat transfer due to the low flow rate at θ ¼ 0°. As mentioned previously, when θ is increased, the average Nusselt ¯ decreases (for a given heat flux, q ¼34.2 kW/m2; heat number Nu flux controlled experiment). This is entirely due to increasing flow rate (as observed in Fig. 7(a)), shifting the two-phase heat transfer mode (i.e. boiling heat transfer) to sub-cooled heat transfer and further toward single-phase heat transfer mode as clearly observed in Fig. 7(b). Similar trend of the heat transport of the device is observed and with the maximum magnetic field intensity of Hx, max ¼155 kA/m, the maximum heat flux q ¼34.2 kW/m2 (the thermal energy of 107 W) can be transported with distance of 5 m when the set-up (device) is placed horizontally, θ ¼0°. It is easily speculated from the results displaced in Fig. 7(a) and (b), that when heat flux at the test section is increased, the trend of heat transport capability can become substantially strong, increasing the magnetic driving pressure (promising further long distant heat transport capability) at any inclination angle setting.
applied magnetic field strength is increased. Also as mentioned earlier, it was quite difficult to measure the precise pressure rise Δp, due to small magnetic pressure (measurement Δp is too small with some degree of fluctuation) that conventional pressure transducer could not yield precision measurement. In the present study, however, Δp can be estimated with reasonable degree of accuracy by employing the formulation (8), knowing M = M ( T , H ; x ) as T = T ( x ) and H = H ( x ). Fig. 8 is a simple schematic of the magnetic field Hx( x ) derived from the present solenoid coil used in the set-up. Thus, from the formula (9), the integration Δp =
2
∫1 MdH can be sub-divided into 1-2-3
to yield the Δp ;
Δp =
∫1
2
MdH −
∫2
3
MdH
where the position 1-2 (at the test section) implies the section of non-heating region, while the position 2-3 is the heating section, where at the position 2 the peak value of the magnetic field strength exists. Assuming H1≈0 kA/m and H3≈0 kA/m (assuming H1 and H3 are far apart from the effective magnetic field), formula (12) gives Δpcal. ¼188 Pa in the case of θ ¼0° with Hx, max ¼102 kA/m. The direct measurement of Δpexp. for the experimental condition was approximately Δpexp. ¼242 Pa, resulting in reasonable account of formula (11). Though as mentioned previously, the direct
3.3. Discussion of long distance heat transport of magnetically-driven heat transport device using binary temperature-sensitive magnetic fluid In competing with an advance heat pipe [3], it is worthy discussing the feasibility of the present heat transport device (if this set-up is manufactured as actual practical device) based on the experimental results gained in the previous sections. As observed in Fig. 7(a), the device does work as (self-circulating) heat transport device, knowing that flow rate (presented as Re ) increases as
(11)
Fig. 8. Schematic diagram of simplify solenoidal magnetic field.
236
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measurement of Δp is difficult, the preliminary measurement of Δp yielded for the case of θ ¼0°, as Δpexp. ¼ 271 Pa and Δpexp. ¼311 Pa with Hx, max ¼123 kA/m and Hx, max ¼155 kA/m respectively, while the estimated magnetic driving pressure calculated from formula (11)) are Δpcal. ¼279 Pa and Δpcal. ¼ 420 Pa, respectively. Similarly reasonable estimation of formula (11) is evident. 2
L=
ΔpD 32μ 0 u¯
(12)
Using representative value of Δpcal. ¼188 Pa (above mentioned value) at θ ¼0°and Hx, max ¼102 kA/m, the ideal heat transport distance L (based on Newtonian pipe flow, the diameter D ¼ 0.01 m and Newtonian viscosity and μ0 ¼2.35 10 3 Pa s u¯ ¼3.71 10 3 m/s as average flow speed obtained from measured Re) can be calculated by formula (12) to give L ¼40.7 m, meaning that the device based on this set-up can carry heat as far as 40.7 m long distance at ideal condition. In comparison with advanced heat pipe (in competing heat pipe), whose limitation of heat transport distance is approximately 10 m for conditions of volumetric was flow rate of carrier fluid as 1.32 kg/min [25]. Using this value for an estimation of the heat transport distance L of the present device (based on the present set-up), it will be L ¼12.2 m when Hx, max ¼ 400 kA/m is assumed, indicating that the device should be feasible and competitive against the heat pipe in consideration of the long distance heat transport.
4. Conclusions An experimental investigation of the heat transfer characteristic of the binary TSMF is performed. The main results obtained here are summarized as follows. 1. Inner wall temperature of test section rapidly decreases when an external non-uniform magnetic field is applied, indicating that the working fluid is driven by the magnetic driving pressure. This implies that the constructed device (the set-up) does perform and has a potential as a heat transport device (cooling device). 2. Averaged Nusselt number increases with increase of the magnetic field strength. Particularly, averaged Nusselt number dramatically increase when subcooled boiling occurs in the test section, boosting the magnetic driving pressure to circulate in the closed loop. 3. The evaluation of the long distance heat transport on the present set-up yields that the set-up is feasible to design an actual heat transport device in competition with heat pipe.
Acknowledgment The work was supported by a grant-in-aid for Scientific
Research (c) from the Ministry of Education, Culture, Sports, Science and Technology (Grant No. 26420126), Japan.
References [1] A. Danowitz, K. Kelley, J. Mao, J.P. Stevenson, M. Horowitz, CPU DB: Recording Microporocessor Histroy, Queen-Processors, Vol. 10, 2012, pp. 1–18. [2] A. Faghri, Review and advances in heat pipe science and technology, J. Heat. Transf. 134 (2012) 123001. [3] M. Mitomi, H. Nagano, Long-distance loop heat pipe for effective utilization of energy, Int. J. Heat. Mass Transf. 77 (2014) 777–784. [4] S. Shuchi, T. Mori, H. Yamaguchi, Flow boiling heat transfer of binary mixed magnetic fluid, IEEE Trans. Magn. 38 (2002) 3234–3236. [5] S. Shuchi, K. Sakatani, H. Yamaguchi, Boiling heat transfer characteristics of binary magnetic fluid flow in a vertical circular pipe with a partly heated region, Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 218 (2004) 223–232. [6] Y. Iwamoto, H. Yamaguchi, X.D. Niu, Magnetically-driven heat transport device using a binary temperature-sensitive magnetic fluid, J. Magn. Magn. Mater. 323 (2011) 1378–1383. [7] Y. Iwamoto, Y. Fuji, K. Takeda, X.-D. Niu, H. Yamaguchi, Application of a binarysensitive magnetic fluid for a mini magnetically-driven heat transport device, J. Jpn. Soc. Exp. Mech. 13 (2013) s18–s23. [8] H. Yamaguchi, Y. Iwamoto, Heat transport with temperature-sensitive magnetic fluid for application to micro-cooling device, Magnetohydrodynamics 49 (2013) 448–453. [9] E.L. Resler, R.E. Rosensweig, Magnetocaloric Power, AIAA J. 2 (1964) 1418–1422. [10] E.L. Resler, R.E. Rosensweig, Regenerative thermomagnetic power, J. Eng. Power 89 (1967) 399–406. [11] H. Yamaguchi, A. Sumiji, S. Shiuchi, T. Yonemura, Characteristics of thermomagnetic driven motor using magnetic fluid, J. Magn. Magn. Mater. 272–276 (2004) 2362–2364. [12] K. Fumoto, H. Yamagishi, M. Ikegawa, A mini heat transport device based on thermo-sensitive magnetic fluid, Nano. Micro. Therm. Eng. 11 (2007) 201–210. [13] K. Fumoto, M. Ikegawa, T. Kawanami, Heat transfer characteristics of a thermosensitive magnetic fluid in micro-channel, J. Therm. Sci. Technol. 4 (2009) 332–339. [14] Y. Xuan, W. Lian, Electric cooling using an automatic energy transport device based on themomagnetic effect, Appl. Therm. Eng. 31 (2011) 1487–1494. [15] W. Lina, Y. Xuan, Q. Li, Characterization of miniature automatic energy transport devices based on the thermomagnetic effect, Energy Convers. Manag. 50 (2009) 35–42. [16] W. Lian, Y. Xuan, Q. Li, Design method of automatic energy transport devices based on the thermomagnetic effect of magnetic fluids, Int. J. Heat Mass Transf. 52 (2009) 5451–5458. [17] Y. Mitamura, E. Okamoto, Numerical analysis of the effects of a high gradient magnetic field on flowing erythrocytes in a membrane oxygenator, J. Magn. Magn. Mater. 380 (2015) 54–60. [18] A.N. Afifah, S. Syahrullail, NAC Sidik, Magnetoviscous effect and thermomagnetic convection of magnetic fluid: a review, Renew. Sustain. Energy Rev. 55 (2016) 1030–1040. [19] J. Ishimoto, M. Okubo, S. Kamiyama, M. Higashitani, Bubble behaviour in magnetic fluid under a nonuniform magnetic field, Jpn. Soc. Mech. Eng. Int. J. Ser. B 38 (1995) 382–387. [20] S. Kamiyama, J. Ishimoto, Boiling two-phase flows of magnetic fluid in a nonuniform magnetic field, J. Magn. Magn. Mater. 149 (1995) 125–131. [21] E. Aursand, M.A. Gjennestad, K.Y. Levag, H. Lund, A multi-phase flow model with equation of state for thermomagnetic pumping and heat transfer, J. Magn. Magn. Mater. 402 (2016) 8–19. [22] R.K. Shah, A.L. London, Laminar Flow Forced Convection in Ducts, Academic Press, New York, 1978. [23] C.T. Crowe, Multiphase Flow Handbook, CRC Press, Boca Raton, 2006. [24] Y. Iwamoto, H. Ishizuka, X.-D. Niu, H. Yamaguchi, T. Kuwahara, Active Flow Control of Ferrofluids using External Magnetic Fields, in: Proceedings of the 20th MAGDA Conference in Pacific Asia, 2011, pp. 309–314. [25] N.A. Avgerions, D.P. Margaris, D.T. Tsahalis, Effect of the working liquid to the capillary pumped loop performance, Int. J. Low.-Carbon Technol. 0 (2013) 1–7.