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Marangoni effect on microbubbles emission boiling generation during pool boiling of self-rewetting fluid
International Journal of Heat and Mass Transfer 134 (2019) 10–16
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Marangoni effect on microbubbles emission boiling generation during pool boiling of self-rewetting fluid Yanxin Hu a,b, Hai Wang a, Mengjie Song b, Jin Huang a,⇑ a b
School of Materials and Energy, Guangdong University of Technology, 510006 Guangzhou, People’s Republic of China Department of Human and Engineered Environmental Studies, The University of Tokyo, 277-8563 Kashiwa, Chiba, Japan
a r t i c l e
i n f o
Article history: Received 17 September 2018 Received in revised form 30 December 2018 Accepted 2 January 2019
Keywords: Self-rewetting fluid Marangoni effect Marangoni number Microbubble emission boiling Pool boiling
a b s t r a c t In order to clarify the Marangoni effect on microbubbles emission boiling (MEB) generation during the pool boiling of self-rewetting fluid (SRWF), a plenty of boiling experiments were carried out, which used heptanol aqueous solution as SRWF. A horizontal platinum wire was used as heated surface during the pool boiling experiments. Additionally, a high speed video camera was used to record the nucleation boiling process. The experimental results show that, the MEB phenomenon only appeared in the heptanol aqueous solution case. Due to the occurrence of MEB phenomenon, the 0.1 wt% heptanol aqueous solution shows much better critical heat flux (CHF) and heat transfer coefficient. Furthermore, the Marangoni effect was quantitatively analyzed combining dimensionless parameters of the thermal Marangoni number (MaT) and solutal Marangoni number (MaS). The results show that, the Marangoni convection along the vapor/liquid interface is the key factor to induce the MEB. Since the Marangoni number reaches about 3 106 when the MEB appeared, the Marangoni number of 3 106 should be the critical magnitude that induces the MEB phenomenon for 0.1 wt% heptanol aqueous solution in this case. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Required for high heat transfer ability, nucleate boiling has been widely used in many industrial fields such as microelectronic devices, nuclear power plant and refrigeration. Due to the limitation of critical heat flux (CHF), the common nucleate boiling process may not meet the heat transfer requirements with the miniaturization and increasing power density of electronic equipment. Subcooled boiling is recommended for efficient cooling or temperature systems because of its high heat transfer rate. [1] Inada et al. [2] carried out pool boiling experiments on the heated copper cylinder tip submerged in water under subcooling condition of 30 K. They discovered that the bubbles appeared on the heated surface with high heat flux, and collapsed into many microbubbles when they contacted with the surrounding subcooled liquid. The microbubbles emitted into the bulk liquid and aroused strong disturbance which enhances the heat transfer process. The boiling mode is so called microbubbles emission boiling (MEB). Due to the great potential in solving the thermal problems, many researchers focus on investigating the MEB phenomenon.
⇑ Corresponding author. E-mail address: [email protected] (J. Huang). https://doi.org/10.1016/j.ijheatmasstransfer.2019.01.011 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
Many experiments on its characteristics and mechanism have been conducted. Inada et al. [3] carried out pool boiling experiments on the copper heated surface in water at the subcooling of 30 K. Massive microbubbles were found emitting rapidly from the collapsing bubbles with noisy sound, and the MEB occurred. Wang et al. [4] measured the maximum heat flux of subcooled pool boiling of water with a thin platinum wire. They observed that nucleation jet flows from the wire were formed and some jets evolved to miniature bubbles when the subcooling exceeds 40 K. Tange et al. [5] also conducted subcooled pool boiling of water with platinum wires. The result showed that the incipient subcooling of MEB was 30–40 K. Under the different thermal capacity heating surfaces and heating methods, a serial of pool boiling experiments with water were conducted by Furuya [6] for investigating the occurring conditions of MEB. With the subcooling of 50 K, the experimental results showed that when the time required for bubble condensation is less than the time constant determined by heating method and heat capacity, the MEB can occur stably. Ueno et al. [7,8] proposed a simplified approach to study water bubble collapse process by injecting vapor bubbles into a subcooled pool, and it was found that effective condensation was also a key factor to trigger MEB. They concluded that the necessary condition for triggering MEB in pool boiling is that the subcooling should exceed 35–40 K. Recently, Tang et al. [9–11] carried out experiments of subcooled pool boiling at subcooling of 0–60 K to study the phe-
Y. Hu et al. / International Journal of Heat and Mass Transfer 134 (2019) 10–16
nomenon of MEB. They found that the minimum subcooling of the water that triggered the MEB at atmospheric pressure was 20 K, and the wall superheat and vapor generation rate raise with the increase of liquid subcooling, which is beneficial for forming MEB. However, since the liquid temperature is easily heated up in small passages due to the small heat capacity of the flow, it is difficult to maintain a high subcooled temperature. Thus, other effective ways to trigger MEB should be investigated. In order to accelerate the formation of MEB, efforts were made to investigate the effects of pressure [12], gravity [13], ultrasonic vibration [14], channel geometry [15,16], heating surface [17] and working fluids [18–22] on heat transfer performance in MEB. Among the mentioned researches, applying new and efficient working fluids should be one of the most direct choices for accelerating MEB formation. Suzuki et al. [19] carried out numbers of boiling experiments for alcohol-water mixtures and compared with the boiling characteristics of water. They found that alcohol-water mixtures accelerate MEB generation and increase the heat fluxes by Marangoni effect in the interface of vapor and liquid. Hu et al. [20] carried out boiling experiments with dilute heptanol aqueous solution, and the results showed that the Marangoni flow induced by the temperature gradient and concentration gradient of SRWF is probably one of the key factors triggering the MEB phenomenon. Zhou et al. [21] conducted nucleate boiling on a thin wire with the aqueous n-butanol solution. They found that the thermocapillary convection can induce bubble emission at the superheated thin liquid layer for the n-butanol solution, and the similar phenomenon has also been reported by Wang et al. [22] when they conducted pool boiling in a surfactant solution. Concluded from what mentioned above, MEB seems easier to be triggered in aqueous alcohol solution, which is so-called self-rewetting fluid (SRWF). Due to the Marangoni effect caused by the temperature gradient and concentration gradient, SRWFs are believed to be promising working fluids for the enhancement of heat transfer. However, these experiments did not quantitatively analyze the Marangoni effect with dimensionless analysis, and there are still limited studies on the inducement mechanism of MEB with self-rewetting fluids. To sum up, although the MEB phenomenon has been investigated decades, the inducement mechanism of MEB is still not totally understood. Therefore, boiling experiments of selfrewetting fluid (heptanol aqueous solution) on horizontal heated wires under different input powers were experimentally investigated. To clarify the Marangoni effect on MEB generation of SRWF, the nucleate boiling processes have been recorded using a highspeed CCD. In order to better understand the heat transfer characteristics of MEB, the critical heat flux (CHF) and heat transfer coefficient have been analyzed in detail. Combining the experimental results with dimensionless parameters of thermal Marangoni number (MaT) and solutal Marangoni number (MaS), the effect of Marangoni convection on MEB generation of SRWF have been quantitatively analyzed.
2. Experimental details The experiments were conducted in a Pyrex glass water vessel under atmospheric pressure. The dilute heptanol aqueous solutions were chosen as the test fluid because of the apparent surface tension gradient. Fig. 1 is the schematic diagram of the experimental setup, and the test fluid was heated on the horizontal platinum wire. The apparatus consists of a Pyrex glass water vessel, an optical observation system, an electronic data acquisition system and a liquid temperature controlling unit. The size of the water vessel is 250 mm 250 mm 300 mm. The length and the diameter of platinum wire were fixed to be 20 mm and 0.2 mm, respectively.
11
Fig. 1. The experimental apparatus.
In addition, the working fluid in the container was heated to boil for at least one hours before each experiment to ensure degassing. To avoid the concentration change of SRWF during degassing, the pure water was heated to boil first, and the heptanol was added according to the corresponding weight ratio 0.1 wt% after degassing. After that, ultrasonic agitator was used to ensure the dispersion of the solution. The platinum wire and the water vessel were carefully cleaned with acetone before each experiment, and the platinum wire was heated through the electrical bars with DC power supply (MCH 1550). To degrade the effect of the subcooling and avoid the perturbation of the boiling liquid, an electrical heater and a thermostatic bath cooler were applied to keep the temperature of the bulk liquid 1 °C lower than the boiling point. The bulk liquid temperature was monitored with a thermocouple, and the temperature fluctuated within ±0.5 °C during the boiling experiments. By mixing water and heptanol with the corresponding weight ratio, the concentration of the working fluid (heptanol aqueous solution) was fixed to be a prescribed value, and the concentration was 0.1 wt% (0.1 wt% is the saturated concentration of heptanol aqueous solution at 18 °C). The heat flux of the platinum wire is adjusted by changing the electric power from low heat flux to critical heat flux (CHF), and the experiments were stopped when the heat flux reached the CHF. Since the heat flux was stepwise increased with an increment of 5%, the heat flux values were measured with an accuracy of 5%. The temperature of platinum wire was determined by the temperature dependence of the electric resistance of platinum, and the temperature-electric resistance relationship of platinum can be referred in [23]. The electric resistance can be obtained through the electronic multimeter, so the heated surface temperature can be obtained. During the experiment, the observation system was used to capture the boiling behavior near the heated wire. The high-speed video (American Fastec Corporation, model Troubleshooter HR) was used to observe the overall aspects of boiling and the behaviors of bubbles. The images were stored in the connected computer. Experimental errors were considered during the experimental process. According to the Evaluation and Expression of Uncertainty in Measurement JJF1059-1999 standard, for directly measured values, such as the temperature, the uncertainty can be defined as
U Tj ¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Xm Xn 1 T T ij j j¼1 i¼1 mðn 1Þ
ð1Þ
here m is the number of test iterations and n is the number of variables. Therefore, because the accuracy of the thermocouple is ±0.5 °C, the maximum uncertainty for the temperature values
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Y. Hu et al. / International Journal of Heat and Mass Transfer 134 (2019) 10–16
was calculated to be 1.77 °C. The nominal uncertainty in the output voltage from the DC stabilized power supply is ±1.57%. Therefore, based on the principle of error propagation, the uncertainty of the heat flux
U ðQ in Þ ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðI uðV ÞÞ2 þ ðV uðIÞÞ2 V I
¼ 2:22%
ð2Þ
Similarly, the uncertainty of the heat transfer coefficient was calculated as
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 Dq 1 U ðhÞ ¼ þ DT 2f þ DT 2w ¼ 7:8% q Tw Tf
ð3Þ
Fig. 3 shows the boiling feature of 0.1 wt% heptanol solution at different heat flux, and the pictures were taken at the subcooled temperature of 1 K. The early boiling feature of 0.1 wt% heptanol solution is similar to that of water. As shown in the figure, the bubble number increases with the increase of heat flux. When the heat flux reached a certain value about 1.00 MW/m2, the micro-bubble emission boiling appeared, which was very different from the boiling feature of water. It can be seen from the Fig. 3(b), the bubbles collapsed on the heated wire, and many microbubbles emitted from collapsed bubbles jetted into the liquid. With the increase of heat flux, the MEB feature became more and more frequent as shown in Fig. 3(c). Eventually, when the heat flux reached 2.08 MW/m2, bubbles are formed so rapidly that bubbles coalesce and form a vapor film that covers the heated surface, which indicates the boiling system has reached the critical heat flux.
3. Results and discussion 3.1. Boiling process
3.2. Heat transfer performance
The nucleation boiling process of water and self-wetting fluids should be understood before clarifying the Marangoni effect on MEB generation. Fig. 2 shows the boiling process of water at the subcooled temperature of 1 K, and the pictures were taken at different heat flux. As shown in the figure, when the heat flux is 0.10 MW/m2, the bubbles begin to generate on the heated wire. The bubbles adhere to the wire and hardly detach from the contact area. As the heat flux increases, the number of bubbles increases apparently, and bubbles begin to fall off the heating wire. When the heat flux reaches 0.69 MW/m2, more and more bubbles generate around the heated wire and coalesce into a bigger bubble. The boiling feature becomes more and more intense. Furthermore, when the heat flux reaches 0.85 MW/m2, the bubbles around the heated wire combine together completely. There exists vapor film covering on the heated wire, which indicates that the boiling system reaches the critical heat flux. The experiment will be stopped when the phenomenon appears.
The critical heat fluxes and heat transfer coefficients of water and self-wetting solution (0.1 wt% heptanol aqueous solution) were compared to highlight the enhancement of heat transfer caused by the micro bubble emission boiling.
3.2.1. Critical heat flux Fig. 4 shows the boiling curve of pure water and SRWF. The results show that the CHF of water reaches 0.85 MW/m2, and the CHF of 0.1 wt% heptanol solution is 2.08 MW/m2. The CHF of 0.1 wt% heptanol solution is 2.45 times that of water, which indicates much better heat transfer performance. Taking the boiling feature into consideration, the micro-bubble emission boiling (MEB) appeared only in the 0.1 wt% heptanol solution case. The MEB mode should be responsible for the improvement of CHF. Since the vapor film on heated surface broke up during the MEB mode, the bulk liquid rushed into the heated surface, and it is ben-
Fig. 2. The boiling feature of pure water at different heat flux. (a) 0.10 MW/m2, (b) 0.36 MW/m2, (c) 0.69 MW/m2, (d) 0.85 MW/m2.
Y. Hu et al. / International Journal of Heat and Mass Transfer 134 (2019) 10–16
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Fig. 3. The boiling feature of the 0.1 wt% heptanol solution at different heat flux. (a) 0.35 MW/m2, (b) 1.00 MW/m2, (c) 1.50 MW/m2, (d) 2.08 MW/m2.
Fig. 5. The heat transfer coefficients of the working fluids at different heat fluxes. Fig. 4. The boiling curves of the working fluids.
eficial for promoting the heat convection between the cold liquid and the dry out patch. Thus, the CHF was increased significantly.
3.2.2. Heat transfer coefficient Fig. 5 shows the heat transfer coefficients (HTCs) of the working fluids at different heat fluxes. For the water boiling curve, it can be divided into two regions. The region 1 is the natural convection region. The liquid near the heated surface was superheated slightly, and pure heat transfer convection between the superheated liquid and bulk liquid dominated throughout the region. Thus, the heat transfer coefficient increased with the heat flux gently. Furthermore, bubbles began to form on the surface of the wire. Region 2 indicated the beginning of nucleate boiling, and the heat transfer coefficient increased with the heat flux rapidly. As for the 0.1 wt% heptanol solution curve, due to Marangoni convection induced by the self-rewetting behavior of SRWF, the heat transfer coefficient was higher than that of water during the whole
boiling process. To explain the increment of HTC, for the 0.1 wt% heptanol solution, since the 0.1 wt% heptanol solution contain two kinds of non-azeotropic compositions, the preferential evaporation of more volatile component takes place, which results in a concentration gradient around the liquid/vapor interface. The concentration gradient induces solutal Marangoni flow, and the bulk liquid will be driven towards the bottom liquid due to the solutal Marangoni flow. Furthermore, the non-linear thermal surface tension behavior of 0.1 wt% heptanol aqueous solutions leads to a positive thermal Marangoni flow that drives the bulk liquid transferring towards the bottom liquid, then the flow behavior will strengthen the heat transfer process, and the HTC of the SRWF is greatly increased during the whole boiling process. Furthermore, the curve can be divided into three regions, and the first two regions of the 0.1 wt% heptanol solution curve is similar to that of water. However, when the heat flux reached about 1.00 MW/ m2, the micro-bubble emission boiling (MEB) phenomenon appeared. During the MEB process, the breakdown of the vapor
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Y. Hu et al. / International Journal of Heat and Mass Transfer 134 (2019) 10–16
film is conducive to promoting the heat convection between cold liquid and hot heated surface. Meanwhile, the generated microbubbles caused intense turbulence, which can also improve the heat transfer coefficient. Thus, the heat transfer coefficient increased with the heat flux more rapidly than that of region 2. 3.3. Marangoni numbers Considering the MEB phenomenon only appear in the 0.1 wt% heptanol solution case, the Marangoni convection caused by the surface tension gradient of SRWF should be a key factor to induce the MEB phenomenon. As we know, the Marangoni effect takes place when there is a gradient of surface tension at the interface between two phases, and the surface tension typically changes due to variations in temperature and solute concentration along the interface. Since the surface tension gradient along the vapor/ liquid interface of SRWF is much more obvious, the Marangoni convection around the bubble of SRWF will be more intense. To quantitatively analyze the Marangoni effect with dimensionless number, the thermal Marangoni number (MaT) and solutal Marangoni number (MaS) are presented comparatively. The MaT and MaS can be obtained using the following equations
MaT ¼
@ rm L DT @T gm am
ð4Þ
MaS ¼
@ rm L DC @C gm Dm
ð5Þ
rm rm here @@T is the thermal surface tension gradient of mixture, and @@C is the solutal surface tension gradient of the mixture. DT is the temperature difference between the bulk fluid temperature and the superheated liquid temperature which is close to the heating surface temperature. DC is the concentration difference between bulk liquid and superheated liquid. The thermal surface tension gradients and the solutal surface tension gradient of mixture are obtained from the previous work [24], and the thermal surface tension gradient of water is 0.16 mN/(mK). For the case of 0.1 wt% heptanol aqueous solutions, the empirical equations for calculating the thermal and solutal surface tension gradients can be fitted as:
rT ¼ 0:0053T 2 3:3241T þ 556:91
ð6Þ
rC ¼ 1059:8C 2 188:49C þ 59:17
ð7Þ
For the 0.1 wt% heptanol aqueous solutions with the bulk liquid temperature of 372.15 K, the thermal surface tension gradient is 0.62 mN/(mK). To calculate the solutal Marangoni number, it is assumed that the concentration of superheated liquid is 10% lower than that of bulk liquid. Then Eq. (5) can turn into
MaS ¼ DrS
L
ð8Þ
gm Dm
here DrS is the solutal surface tension difference between bulk liquid and superheated liquid. L is the characteristic length which is
the radius of adherent bubble here. According to the views of the adherent bubbles of working fluids on the platinum wire, the mean radius of the bubbles is about 0.55 mm. gm is the viscosity of mixture. Since the mass fraction difference between the components of the 0.1 wt% heptanol solution is so large that the viscosity of mixture approaches that of pure water, then gm can be obtained. am is the thermal diffusivity of mixture which can be obtained by
am ¼
km
ð9Þ
qm cpm
here cpm is the specific heat capacity of mixture, qm is the density of mixture, and km is the thermal conductivity of mixture. The above parameters can be obtained on the basis of the liquid component fractions. Dm is the diffusion coefficient, and it can be obtained based on the equation [25]
Dm ¼
7:4 108 ð/M 2 Þ0:5 T
ð10Þ
g2 V 0:6 1
here / is the dimensionless correlation factor of solvent 2, and it is valued as 2.6 when the solvent is water. M2 is the molecular weight of water, and T is the temperature of mixture. g2 is the viscosity of water, and V1 is the molar volume of heptanol at its normal boiling temperature in this case. Tables 1 and 2 shows the involved parameters with different input power, and Table 3 shows the thermal Marangoni number and solutal Marangoni number for comparison. The thermal Marangoni number of working fluids are shown in Table 3. As demonstrated in the table, the thermal Marangoni numbers of water are negative values due to the negative thermal surface tension gradient of water, while the thermal Marangoni numbers of 0.1 wt% heptanol solution are positive values. The minus sign before the Marangoni number of water indicates the inverse flow direction compared with the flow direction of 0.1 wt % heptanol solution. Furthermore, the thermal Marangoni numbers of water range from 2.65 104 to 8.32 104, while the thermal Marangoni numbers of 0.1 wt% heptanol solution range from 5.29 104 to 2.76 105. Since larger Marangoni number leads to stronger Marangoni convection, the thermal Marangoni convection of 0.1 wt% heptanol solution is more intense than that of water. Moreover, the MEB phenomenon did not show up in the case of water, so the thermal Marangoni number is not large enough to induce MEB. Furthermore, the solutal Marangoni numbers of 0.1 wt% heptanol solution exceed a magnitude of 106. Larkin [26] addressed that when the Marangoni number exceeds a value of 105, the Marangoni convection become a significant heat transfer mechanism. Therefore, very strong solutal Marangoni convection generates along the vapor/liquid interface, which results in the collapse of the bubble. Subsequently, the boiling mode transforms into MEB. Compared the thermal Marangoni number with the solutal Marangoni number, the solutal Marangoni number is significantly larger than the thermal Marangoni number, which indicates that the solutal Marangoni effect is the main factor to trigger MEB. Since the MEB appeared when the heat flux reached a certain value
Table 1 The related parameters for water with different input power. Input power (W)
Heat flux (Wm2)
Heated surface temperature Tw/(K)
Bulk liquid temperature T/(K)
Thermal surface tension
0.5 2 4 6 8 10
3.98 104 1.59 105 3.18 105 4.77 105 6.37 105 7.95 105
384.20 392.48 398.13 403.69 407.41 410.00
372.15 372.15 372.15 372.15 372.15 372.15
0.16 0.16 0.16 0.16 0.16 0.16
rw /(mNm1K1) gradient @@T
Characteristic length Lw/(mm)
Viscosity gw/(lPas)
Thermal diffusivity aw/(m2s1)
0.55 0.55 0.55 0.55 0.55 0.55
282.21 282.21 282.21 282.21 282.21 282.21
1.68 107 1.68 107 1.68 107 1.68 107 1.68 107 1.68 107
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Y. Hu et al. / International Journal of Heat and Mass Transfer 134 (2019) 10–16 Table 2 The related parameters for 0.1 wt% heptanol solution with different input power. Input power (W)
Heat flux (Wm2)
Heated surface temperature Tw/ (K)
Bulk liquid temperature T/ (K)
Thermal surface tension rm / gradient @@T (mNm1K1)
Solutal surface tension difference DrS/ (mNm1)
Characteristic length Lw/ (mm)
Viscosity gw/ (lPas)
Thermal diffusivity aw/ (m2s1)
0.5 2 4 6 8 10 12 16 20 24
3.98 104 1.59 105 3.18 105 4.77 105 6.37 105 7.95 105 9.55 105 1.27 106 1.59 106 1.91 106
379.49 386.97 394.30 398.93 401.67 403.80 406.64 408.50 409.79 410.40
372.15 372.15 372.15 372.15 372.15 372.15 372.15 372.15 372.15 372.15
0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62
0.31 0.63 0.95 1.15 1.26 1.36 1.48 1.56 1.61 1.64
0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55
282.21 282.21 282.21 282.21 282.21 282.21 282.21 282.21 282.21 282.21
1.68 107 1.68 107 1.68 107 1.68 107 1.68 107 1.68 107 1.68 107 1.68 107 1.68 107 1.68 107
Table 3 Thermal and solutal Marangoni numbers of the working fluids with different input power. Input power (W)
Heat flux (Wm2)
Thermal Marangoni number/MaT Water
0.5 2 4 6 8 10 12 16 20 24
4
3.98 10 1.59 105 3.18 105 4.77 105 6.37 105 7.95 105 9.55 105 1.27 106 1.59 106 1.91 106
Solutal Marangoni number/MaS
0.1 wt% heptanol solution 4
2.65 10 4.47 104 5.71 104 6.93 104 7.75 104 8.32 104 – – – –
about 1.00 MW/m2 and the corresponding solutal Marangoni number is about 3 106, it can be concluded that the MEB would appear for 0.1 wt% heptanol aqueous solution only if the Marangoni convection reach the Marangoni number of 3 106 in this case.
4. Conclusions In order to clarify the Marangoni effect on microbubbles emission boiling (MEB) generation during pool boiling of selfrewetting fluid (SRWF), a plenty of boiling experiments were carried out. The Marangoni effect was quantitatively analyzed by using dimensionless parameters of the thermal Marangoni number (MaT) and the solutal Marangoni number (MaS). The results can be concluded as follows: 1. Compared with the thermal Marangoni number, the solutal Marangoni number is significantly larger. The very strong solutal Marangoni convection generates along the vapor/liquid interface and results in the collapse of the bubble, which indicates that the solutal Marangoni effect is the main factor to induce MEB. 2. Since the MEB appeared when the Marangoni number reaches about 3 106, the Marangoni number of 3 106 should be the critical magnitude that induces the MEB phenomenon for 0.1 wt% heptanol aqueous solution in this case. 3. During the MEB process, due to the collapse of the vapor film and the intense turbulence caused by the generated microbubbles, the critical heat flux and the heat transfer coefficient were improved significantly. Conflict of interest The authors declared that there is no conflict of interest.
4
5.29 10 1.07 105 1.60 105 1.93 105 2.13 105 2.28 105 2.49 105 2.62 105 2.71 105 2.76 105
Water
0.1 wt% heptanol solution
– – – – – – – – – –
6.33 105 1.28 106 1.91 106 2.31 106 2.55 106 2.73 106 2.97 106 3.14 106 3.25 106 3.30 106
Acknowledgements This work was supported by the National Natural Science Foundation of China (Granted Nos. 51476038 and 51876044), the Natural Science Foundation of Guangdong Province (No. 2018A030310515) and Science and Technology Plan Industry University Research Collaborative Innovation Major Project of Guangzhou city (No. 201704030009).
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[19] K. Suzuki, Microbubble emission boiling of alcohol-water mixtures, in: Proceedings of the 3rd IASME/WSEAS Int. Conf. on Heat Transfer, Thermal Engineering and Environment, Greece, 2005, pp. 91–96. [20] Y. Hu, S. Zhang, X. Li, S. Wang, Heat transfer enhancement mechanism of pool boiling with self-rewetting fluid, Int. J. Heat Mass Transfer 79 (2014) 309–313. [21] L. Zhou, Y. Li, L. Wei, X. Du, Y. Yang, P. Jiang, B. Wang, Multi-jet flows and bubble emission during subcooled nucleate boiling of aqueous n-butanol solution on thin wire, Exp. Therm. Fluid Sci. 58 (2014) 1–8. [22] J. Wang, F. Li, X. Li, Bubble explosion in pool boiling around a heated wire in surfactant solution, Int. J. Heat Mass Transfer 99 (2016) 569–575. [23] R.F. Vines, M. Wise, The Platinum Metals and Their Alloys, McGraw-Hill Book Co., Inc., New York, 1941. [24] Y. Hu, S. Zhang, X. Li, S. Wang, Heat transfer enhancement of subcooled pool boiling with self-rewetting fluid, Int. J. Heat Mass Transfer 83 (2015) 64–68. [25] R.C. Reid, J.M. Prausnitz, T.K. Sherwood, The Properties of Gases and Liquids, third ed., McGraw-Hill, New York, 1977. [26] B.K. Larkin, Thermocapillary flow around a hemispherical bubble, AIChEJ 16 (1970) 101–107.
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Marangoni effect on microbubbles emission boiling generation during pool boiling of self-rewetting fluid Yanxin Hu a,b, Hai Wang a, Mengjie Song b, Jin Huang a,⇑ a b
School of Materials and Energy, Guangdong University of Technology, 510006 Guangzhou, People’s Republic of China Department of Human and Engineered Environmental Studies, The University of Tokyo, 277-8563 Kashiwa, Chiba, Japan
a r t i c l e
i n f o
Article history: Received 17 September 2018 Received in revised form 30 December 2018 Accepted 2 January 2019
Keywords: Self-rewetting fluid Marangoni effect Marangoni number Microbubble emission boiling Pool boiling
a b s t r a c t In order to clarify the Marangoni effect on microbubbles emission boiling (MEB) generation during the pool boiling of self-rewetting fluid (SRWF), a plenty of boiling experiments were carried out, which used heptanol aqueous solution as SRWF. A horizontal platinum wire was used as heated surface during the pool boiling experiments. Additionally, a high speed video camera was used to record the nucleation boiling process. The experimental results show that, the MEB phenomenon only appeared in the heptanol aqueous solution case. Due to the occurrence of MEB phenomenon, the 0.1 wt% heptanol aqueous solution shows much better critical heat flux (CHF) and heat transfer coefficient. Furthermore, the Marangoni effect was quantitatively analyzed combining dimensionless parameters of the thermal Marangoni number (MaT) and solutal Marangoni number (MaS). The results show that, the Marangoni convection along the vapor/liquid interface is the key factor to induce the MEB. Since the Marangoni number reaches about 3 106 when the MEB appeared, the Marangoni number of 3 106 should be the critical magnitude that induces the MEB phenomenon for 0.1 wt% heptanol aqueous solution in this case. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Required for high heat transfer ability, nucleate boiling has been widely used in many industrial fields such as microelectronic devices, nuclear power plant and refrigeration. Due to the limitation of critical heat flux (CHF), the common nucleate boiling process may not meet the heat transfer requirements with the miniaturization and increasing power density of electronic equipment. Subcooled boiling is recommended for efficient cooling or temperature systems because of its high heat transfer rate. [1] Inada et al. [2] carried out pool boiling experiments on the heated copper cylinder tip submerged in water under subcooling condition of 30 K. They discovered that the bubbles appeared on the heated surface with high heat flux, and collapsed into many microbubbles when they contacted with the surrounding subcooled liquid. The microbubbles emitted into the bulk liquid and aroused strong disturbance which enhances the heat transfer process. The boiling mode is so called microbubbles emission boiling (MEB). Due to the great potential in solving the thermal problems, many researchers focus on investigating the MEB phenomenon.
⇑ Corresponding author. E-mail address: [email protected] (J. Huang). https://doi.org/10.1016/j.ijheatmasstransfer.2019.01.011 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
Many experiments on its characteristics and mechanism have been conducted. Inada et al. [3] carried out pool boiling experiments on the copper heated surface in water at the subcooling of 30 K. Massive microbubbles were found emitting rapidly from the collapsing bubbles with noisy sound, and the MEB occurred. Wang et al. [4] measured the maximum heat flux of subcooled pool boiling of water with a thin platinum wire. They observed that nucleation jet flows from the wire were formed and some jets evolved to miniature bubbles when the subcooling exceeds 40 K. Tange et al. [5] also conducted subcooled pool boiling of water with platinum wires. The result showed that the incipient subcooling of MEB was 30–40 K. Under the different thermal capacity heating surfaces and heating methods, a serial of pool boiling experiments with water were conducted by Furuya [6] for investigating the occurring conditions of MEB. With the subcooling of 50 K, the experimental results showed that when the time required for bubble condensation is less than the time constant determined by heating method and heat capacity, the MEB can occur stably. Ueno et al. [7,8] proposed a simplified approach to study water bubble collapse process by injecting vapor bubbles into a subcooled pool, and it was found that effective condensation was also a key factor to trigger MEB. They concluded that the necessary condition for triggering MEB in pool boiling is that the subcooling should exceed 35–40 K. Recently, Tang et al. [9–11] carried out experiments of subcooled pool boiling at subcooling of 0–60 K to study the phe-
Y. Hu et al. / International Journal of Heat and Mass Transfer 134 (2019) 10–16
nomenon of MEB. They found that the minimum subcooling of the water that triggered the MEB at atmospheric pressure was 20 K, and the wall superheat and vapor generation rate raise with the increase of liquid subcooling, which is beneficial for forming MEB. However, since the liquid temperature is easily heated up in small passages due to the small heat capacity of the flow, it is difficult to maintain a high subcooled temperature. Thus, other effective ways to trigger MEB should be investigated. In order to accelerate the formation of MEB, efforts were made to investigate the effects of pressure [12], gravity [13], ultrasonic vibration [14], channel geometry [15,16], heating surface [17] and working fluids [18–22] on heat transfer performance in MEB. Among the mentioned researches, applying new and efficient working fluids should be one of the most direct choices for accelerating MEB formation. Suzuki et al. [19] carried out numbers of boiling experiments for alcohol-water mixtures and compared with the boiling characteristics of water. They found that alcohol-water mixtures accelerate MEB generation and increase the heat fluxes by Marangoni effect in the interface of vapor and liquid. Hu et al. [20] carried out boiling experiments with dilute heptanol aqueous solution, and the results showed that the Marangoni flow induced by the temperature gradient and concentration gradient of SRWF is probably one of the key factors triggering the MEB phenomenon. Zhou et al. [21] conducted nucleate boiling on a thin wire with the aqueous n-butanol solution. They found that the thermocapillary convection can induce bubble emission at the superheated thin liquid layer for the n-butanol solution, and the similar phenomenon has also been reported by Wang et al. [22] when they conducted pool boiling in a surfactant solution. Concluded from what mentioned above, MEB seems easier to be triggered in aqueous alcohol solution, which is so-called self-rewetting fluid (SRWF). Due to the Marangoni effect caused by the temperature gradient and concentration gradient, SRWFs are believed to be promising working fluids for the enhancement of heat transfer. However, these experiments did not quantitatively analyze the Marangoni effect with dimensionless analysis, and there are still limited studies on the inducement mechanism of MEB with self-rewetting fluids. To sum up, although the MEB phenomenon has been investigated decades, the inducement mechanism of MEB is still not totally understood. Therefore, boiling experiments of selfrewetting fluid (heptanol aqueous solution) on horizontal heated wires under different input powers were experimentally investigated. To clarify the Marangoni effect on MEB generation of SRWF, the nucleate boiling processes have been recorded using a highspeed CCD. In order to better understand the heat transfer characteristics of MEB, the critical heat flux (CHF) and heat transfer coefficient have been analyzed in detail. Combining the experimental results with dimensionless parameters of thermal Marangoni number (MaT) and solutal Marangoni number (MaS), the effect of Marangoni convection on MEB generation of SRWF have been quantitatively analyzed.
2. Experimental details The experiments were conducted in a Pyrex glass water vessel under atmospheric pressure. The dilute heptanol aqueous solutions were chosen as the test fluid because of the apparent surface tension gradient. Fig. 1 is the schematic diagram of the experimental setup, and the test fluid was heated on the horizontal platinum wire. The apparatus consists of a Pyrex glass water vessel, an optical observation system, an electronic data acquisition system and a liquid temperature controlling unit. The size of the water vessel is 250 mm 250 mm 300 mm. The length and the diameter of platinum wire were fixed to be 20 mm and 0.2 mm, respectively.
11
Fig. 1. The experimental apparatus.
In addition, the working fluid in the container was heated to boil for at least one hours before each experiment to ensure degassing. To avoid the concentration change of SRWF during degassing, the pure water was heated to boil first, and the heptanol was added according to the corresponding weight ratio 0.1 wt% after degassing. After that, ultrasonic agitator was used to ensure the dispersion of the solution. The platinum wire and the water vessel were carefully cleaned with acetone before each experiment, and the platinum wire was heated through the electrical bars with DC power supply (MCH 1550). To degrade the effect of the subcooling and avoid the perturbation of the boiling liquid, an electrical heater and a thermostatic bath cooler were applied to keep the temperature of the bulk liquid 1 °C lower than the boiling point. The bulk liquid temperature was monitored with a thermocouple, and the temperature fluctuated within ±0.5 °C during the boiling experiments. By mixing water and heptanol with the corresponding weight ratio, the concentration of the working fluid (heptanol aqueous solution) was fixed to be a prescribed value, and the concentration was 0.1 wt% (0.1 wt% is the saturated concentration of heptanol aqueous solution at 18 °C). The heat flux of the platinum wire is adjusted by changing the electric power from low heat flux to critical heat flux (CHF), and the experiments were stopped when the heat flux reached the CHF. Since the heat flux was stepwise increased with an increment of 5%, the heat flux values were measured with an accuracy of 5%. The temperature of platinum wire was determined by the temperature dependence of the electric resistance of platinum, and the temperature-electric resistance relationship of platinum can be referred in [23]. The electric resistance can be obtained through the electronic multimeter, so the heated surface temperature can be obtained. During the experiment, the observation system was used to capture the boiling behavior near the heated wire. The high-speed video (American Fastec Corporation, model Troubleshooter HR) was used to observe the overall aspects of boiling and the behaviors of bubbles. The images were stored in the connected computer. Experimental errors were considered during the experimental process. According to the Evaluation and Expression of Uncertainty in Measurement JJF1059-1999 standard, for directly measured values, such as the temperature, the uncertainty can be defined as
U Tj ¼
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Xm Xn 1 T T ij j j¼1 i¼1 mðn 1Þ
ð1Þ
here m is the number of test iterations and n is the number of variables. Therefore, because the accuracy of the thermocouple is ±0.5 °C, the maximum uncertainty for the temperature values
12
Y. Hu et al. / International Journal of Heat and Mass Transfer 134 (2019) 10–16
was calculated to be 1.77 °C. The nominal uncertainty in the output voltage from the DC stabilized power supply is ±1.57%. Therefore, based on the principle of error propagation, the uncertainty of the heat flux
U ðQ in Þ ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðI uðV ÞÞ2 þ ðV uðIÞÞ2 V I
¼ 2:22%
ð2Þ
Similarly, the uncertainty of the heat transfer coefficient was calculated as
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 Dq 1 U ðhÞ ¼ þ DT 2f þ DT 2w ¼ 7:8% q Tw Tf
ð3Þ
Fig. 3 shows the boiling feature of 0.1 wt% heptanol solution at different heat flux, and the pictures were taken at the subcooled temperature of 1 K. The early boiling feature of 0.1 wt% heptanol solution is similar to that of water. As shown in the figure, the bubble number increases with the increase of heat flux. When the heat flux reached a certain value about 1.00 MW/m2, the micro-bubble emission boiling appeared, which was very different from the boiling feature of water. It can be seen from the Fig. 3(b), the bubbles collapsed on the heated wire, and many microbubbles emitted from collapsed bubbles jetted into the liquid. With the increase of heat flux, the MEB feature became more and more frequent as shown in Fig. 3(c). Eventually, when the heat flux reached 2.08 MW/m2, bubbles are formed so rapidly that bubbles coalesce and form a vapor film that covers the heated surface, which indicates the boiling system has reached the critical heat flux.
3. Results and discussion 3.1. Boiling process
3.2. Heat transfer performance
The nucleation boiling process of water and self-wetting fluids should be understood before clarifying the Marangoni effect on MEB generation. Fig. 2 shows the boiling process of water at the subcooled temperature of 1 K, and the pictures were taken at different heat flux. As shown in the figure, when the heat flux is 0.10 MW/m2, the bubbles begin to generate on the heated wire. The bubbles adhere to the wire and hardly detach from the contact area. As the heat flux increases, the number of bubbles increases apparently, and bubbles begin to fall off the heating wire. When the heat flux reaches 0.69 MW/m2, more and more bubbles generate around the heated wire and coalesce into a bigger bubble. The boiling feature becomes more and more intense. Furthermore, when the heat flux reaches 0.85 MW/m2, the bubbles around the heated wire combine together completely. There exists vapor film covering on the heated wire, which indicates that the boiling system reaches the critical heat flux. The experiment will be stopped when the phenomenon appears.
The critical heat fluxes and heat transfer coefficients of water and self-wetting solution (0.1 wt% heptanol aqueous solution) were compared to highlight the enhancement of heat transfer caused by the micro bubble emission boiling.
3.2.1. Critical heat flux Fig. 4 shows the boiling curve of pure water and SRWF. The results show that the CHF of water reaches 0.85 MW/m2, and the CHF of 0.1 wt% heptanol solution is 2.08 MW/m2. The CHF of 0.1 wt% heptanol solution is 2.45 times that of water, which indicates much better heat transfer performance. Taking the boiling feature into consideration, the micro-bubble emission boiling (MEB) appeared only in the 0.1 wt% heptanol solution case. The MEB mode should be responsible for the improvement of CHF. Since the vapor film on heated surface broke up during the MEB mode, the bulk liquid rushed into the heated surface, and it is ben-
Fig. 2. The boiling feature of pure water at different heat flux. (a) 0.10 MW/m2, (b) 0.36 MW/m2, (c) 0.69 MW/m2, (d) 0.85 MW/m2.
Y. Hu et al. / International Journal of Heat and Mass Transfer 134 (2019) 10–16
13
Fig. 3. The boiling feature of the 0.1 wt% heptanol solution at different heat flux. (a) 0.35 MW/m2, (b) 1.00 MW/m2, (c) 1.50 MW/m2, (d) 2.08 MW/m2.
Fig. 5. The heat transfer coefficients of the working fluids at different heat fluxes. Fig. 4. The boiling curves of the working fluids.
eficial for promoting the heat convection between the cold liquid and the dry out patch. Thus, the CHF was increased significantly.
3.2.2. Heat transfer coefficient Fig. 5 shows the heat transfer coefficients (HTCs) of the working fluids at different heat fluxes. For the water boiling curve, it can be divided into two regions. The region 1 is the natural convection region. The liquid near the heated surface was superheated slightly, and pure heat transfer convection between the superheated liquid and bulk liquid dominated throughout the region. Thus, the heat transfer coefficient increased with the heat flux gently. Furthermore, bubbles began to form on the surface of the wire. Region 2 indicated the beginning of nucleate boiling, and the heat transfer coefficient increased with the heat flux rapidly. As for the 0.1 wt% heptanol solution curve, due to Marangoni convection induced by the self-rewetting behavior of SRWF, the heat transfer coefficient was higher than that of water during the whole
boiling process. To explain the increment of HTC, for the 0.1 wt% heptanol solution, since the 0.1 wt% heptanol solution contain two kinds of non-azeotropic compositions, the preferential evaporation of more volatile component takes place, which results in a concentration gradient around the liquid/vapor interface. The concentration gradient induces solutal Marangoni flow, and the bulk liquid will be driven towards the bottom liquid due to the solutal Marangoni flow. Furthermore, the non-linear thermal surface tension behavior of 0.1 wt% heptanol aqueous solutions leads to a positive thermal Marangoni flow that drives the bulk liquid transferring towards the bottom liquid, then the flow behavior will strengthen the heat transfer process, and the HTC of the SRWF is greatly increased during the whole boiling process. Furthermore, the curve can be divided into three regions, and the first two regions of the 0.1 wt% heptanol solution curve is similar to that of water. However, when the heat flux reached about 1.00 MW/ m2, the micro-bubble emission boiling (MEB) phenomenon appeared. During the MEB process, the breakdown of the vapor
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Y. Hu et al. / International Journal of Heat and Mass Transfer 134 (2019) 10–16
film is conducive to promoting the heat convection between cold liquid and hot heated surface. Meanwhile, the generated microbubbles caused intense turbulence, which can also improve the heat transfer coefficient. Thus, the heat transfer coefficient increased with the heat flux more rapidly than that of region 2. 3.3. Marangoni numbers Considering the MEB phenomenon only appear in the 0.1 wt% heptanol solution case, the Marangoni convection caused by the surface tension gradient of SRWF should be a key factor to induce the MEB phenomenon. As we know, the Marangoni effect takes place when there is a gradient of surface tension at the interface between two phases, and the surface tension typically changes due to variations in temperature and solute concentration along the interface. Since the surface tension gradient along the vapor/ liquid interface of SRWF is much more obvious, the Marangoni convection around the bubble of SRWF will be more intense. To quantitatively analyze the Marangoni effect with dimensionless number, the thermal Marangoni number (MaT) and solutal Marangoni number (MaS) are presented comparatively. The MaT and MaS can be obtained using the following equations
MaT ¼
@ rm L DT @T gm am
ð4Þ
MaS ¼
@ rm L DC @C gm Dm
ð5Þ
rm rm here @@T is the thermal surface tension gradient of mixture, and @@C is the solutal surface tension gradient of the mixture. DT is the temperature difference between the bulk fluid temperature and the superheated liquid temperature which is close to the heating surface temperature. DC is the concentration difference between bulk liquid and superheated liquid. The thermal surface tension gradients and the solutal surface tension gradient of mixture are obtained from the previous work [24], and the thermal surface tension gradient of water is 0.16 mN/(mK). For the case of 0.1 wt% heptanol aqueous solutions, the empirical equations for calculating the thermal and solutal surface tension gradients can be fitted as:
rT ¼ 0:0053T 2 3:3241T þ 556:91
ð6Þ
rC ¼ 1059:8C 2 188:49C þ 59:17
ð7Þ
For the 0.1 wt% heptanol aqueous solutions with the bulk liquid temperature of 372.15 K, the thermal surface tension gradient is 0.62 mN/(mK). To calculate the solutal Marangoni number, it is assumed that the concentration of superheated liquid is 10% lower than that of bulk liquid. Then Eq. (5) can turn into
MaS ¼ DrS
L
ð8Þ
gm Dm
here DrS is the solutal surface tension difference between bulk liquid and superheated liquid. L is the characteristic length which is
the radius of adherent bubble here. According to the views of the adherent bubbles of working fluids on the platinum wire, the mean radius of the bubbles is about 0.55 mm. gm is the viscosity of mixture. Since the mass fraction difference between the components of the 0.1 wt% heptanol solution is so large that the viscosity of mixture approaches that of pure water, then gm can be obtained. am is the thermal diffusivity of mixture which can be obtained by
am ¼
km
ð9Þ
qm cpm
here cpm is the specific heat capacity of mixture, qm is the density of mixture, and km is the thermal conductivity of mixture. The above parameters can be obtained on the basis of the liquid component fractions. Dm is the diffusion coefficient, and it can be obtained based on the equation [25]
Dm ¼
7:4 108 ð/M 2 Þ0:5 T
ð10Þ
g2 V 0:6 1
here / is the dimensionless correlation factor of solvent 2, and it is valued as 2.6 when the solvent is water. M2 is the molecular weight of water, and T is the temperature of mixture. g2 is the viscosity of water, and V1 is the molar volume of heptanol at its normal boiling temperature in this case. Tables 1 and 2 shows the involved parameters with different input power, and Table 3 shows the thermal Marangoni number and solutal Marangoni number for comparison. The thermal Marangoni number of working fluids are shown in Table 3. As demonstrated in the table, the thermal Marangoni numbers of water are negative values due to the negative thermal surface tension gradient of water, while the thermal Marangoni numbers of 0.1 wt% heptanol solution are positive values. The minus sign before the Marangoni number of water indicates the inverse flow direction compared with the flow direction of 0.1 wt % heptanol solution. Furthermore, the thermal Marangoni numbers of water range from 2.65 104 to 8.32 104, while the thermal Marangoni numbers of 0.1 wt% heptanol solution range from 5.29 104 to 2.76 105. Since larger Marangoni number leads to stronger Marangoni convection, the thermal Marangoni convection of 0.1 wt% heptanol solution is more intense than that of water. Moreover, the MEB phenomenon did not show up in the case of water, so the thermal Marangoni number is not large enough to induce MEB. Furthermore, the solutal Marangoni numbers of 0.1 wt% heptanol solution exceed a magnitude of 106. Larkin [26] addressed that when the Marangoni number exceeds a value of 105, the Marangoni convection become a significant heat transfer mechanism. Therefore, very strong solutal Marangoni convection generates along the vapor/liquid interface, which results in the collapse of the bubble. Subsequently, the boiling mode transforms into MEB. Compared the thermal Marangoni number with the solutal Marangoni number, the solutal Marangoni number is significantly larger than the thermal Marangoni number, which indicates that the solutal Marangoni effect is the main factor to trigger MEB. Since the MEB appeared when the heat flux reached a certain value
Table 1 The related parameters for water with different input power. Input power (W)
Heat flux (Wm2)
Heated surface temperature Tw/(K)
Bulk liquid temperature T/(K)
Thermal surface tension
0.5 2 4 6 8 10
3.98 104 1.59 105 3.18 105 4.77 105 6.37 105 7.95 105
384.20 392.48 398.13 403.69 407.41 410.00
372.15 372.15 372.15 372.15 372.15 372.15
0.16 0.16 0.16 0.16 0.16 0.16
rw /(mNm1K1) gradient @@T
Characteristic length Lw/(mm)
Viscosity gw/(lPas)
Thermal diffusivity aw/(m2s1)
0.55 0.55 0.55 0.55 0.55 0.55
282.21 282.21 282.21 282.21 282.21 282.21
1.68 107 1.68 107 1.68 107 1.68 107 1.68 107 1.68 107
15
Y. Hu et al. / International Journal of Heat and Mass Transfer 134 (2019) 10–16 Table 2 The related parameters for 0.1 wt% heptanol solution with different input power. Input power (W)
Heat flux (Wm2)
Heated surface temperature Tw/ (K)
Bulk liquid temperature T/ (K)
Thermal surface tension rm / gradient @@T (mNm1K1)
Solutal surface tension difference DrS/ (mNm1)
Characteristic length Lw/ (mm)
Viscosity gw/ (lPas)
Thermal diffusivity aw/ (m2s1)
0.5 2 4 6 8 10 12 16 20 24
3.98 104 1.59 105 3.18 105 4.77 105 6.37 105 7.95 105 9.55 105 1.27 106 1.59 106 1.91 106
379.49 386.97 394.30 398.93 401.67 403.80 406.64 408.50 409.79 410.40
372.15 372.15 372.15 372.15 372.15 372.15 372.15 372.15 372.15 372.15
0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62 0.62
0.31 0.63 0.95 1.15 1.26 1.36 1.48 1.56 1.61 1.64
0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55
282.21 282.21 282.21 282.21 282.21 282.21 282.21 282.21 282.21 282.21
1.68 107 1.68 107 1.68 107 1.68 107 1.68 107 1.68 107 1.68 107 1.68 107 1.68 107 1.68 107
Table 3 Thermal and solutal Marangoni numbers of the working fluids with different input power. Input power (W)
Heat flux (Wm2)
Thermal Marangoni number/MaT Water
0.5 2 4 6 8 10 12 16 20 24
4
3.98 10 1.59 105 3.18 105 4.77 105 6.37 105 7.95 105 9.55 105 1.27 106 1.59 106 1.91 106
Solutal Marangoni number/MaS
0.1 wt% heptanol solution 4
2.65 10 4.47 104 5.71 104 6.93 104 7.75 104 8.32 104 – – – –
about 1.00 MW/m2 and the corresponding solutal Marangoni number is about 3 106, it can be concluded that the MEB would appear for 0.1 wt% heptanol aqueous solution only if the Marangoni convection reach the Marangoni number of 3 106 in this case.
4. Conclusions In order to clarify the Marangoni effect on microbubbles emission boiling (MEB) generation during pool boiling of selfrewetting fluid (SRWF), a plenty of boiling experiments were carried out. The Marangoni effect was quantitatively analyzed by using dimensionless parameters of the thermal Marangoni number (MaT) and the solutal Marangoni number (MaS). The results can be concluded as follows: 1. Compared with the thermal Marangoni number, the solutal Marangoni number is significantly larger. The very strong solutal Marangoni convection generates along the vapor/liquid interface and results in the collapse of the bubble, which indicates that the solutal Marangoni effect is the main factor to induce MEB. 2. Since the MEB appeared when the Marangoni number reaches about 3 106, the Marangoni number of 3 106 should be the critical magnitude that induces the MEB phenomenon for 0.1 wt% heptanol aqueous solution in this case. 3. During the MEB process, due to the collapse of the vapor film and the intense turbulence caused by the generated microbubbles, the critical heat flux and the heat transfer coefficient were improved significantly. Conflict of interest The authors declared that there is no conflict of interest.
4
5.29 10 1.07 105 1.60 105 1.93 105 2.13 105 2.28 105 2.49 105 2.62 105 2.71 105 2.76 105
Water
0.1 wt% heptanol solution
– – – – – – – – – –
6.33 105 1.28 106 1.91 106 2.31 106 2.55 106 2.73 106 2.97 106 3.14 106 3.25 106 3.30 106
Acknowledgements This work was supported by the National Natural Science Foundation of China (Granted Nos. 51476038 and 51876044), the Natural Science Foundation of Guangdong Province (No. 2018A030310515) and Science and Technology Plan Industry University Research Collaborative Innovation Major Project of Guangzhou city (No. 201704030009).
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