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Experimental investigation of flow boiling in narrow channel
International Journal of Thermal Sciences 98 (2015) 90e98
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Experimental investigation of flow boiling in narrow channel A. Kouidri*, B. Madani, B. Roubi Laboratory of Multiphase Transport and Porous Media (LTPMP), Faculty of Mechanical and Process Engineering (FGMGP)/USTHB, BP. 32, El Alia, Algiers, Algeria
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 March 2015 Received in revised form 23 June 2015 Accepted 27 June 2015 Available online xxx
The flow boiling in narrow channel is investigated experimentally. The aim of the present work is to study the heat transfer phenomena. The working fluid is n-pentane which is chosen for its low boiling point (36 C at atmospheric pressure). The independent variables are velocity in the range from 0.015 m/s to 0.06 m/s and boiling heat flux with values between 9 and 137 kW/m2. The wall superheat and exit vapor quality are presented as dependent variables. The flow pattern was predicted based on temperature fluctuations. The experimental results are compared to those available in the literature (Shah, Gungor-Winterton and Jens correlations). A new correlation has been developed for the average heat transfer coefficient during flow boiling in a rectangular channel with validity in boiling heat flux from 9 to 137 kW/m2 and Reynolds number between 380 and 1522. © 2015 Elsevier Masson SAS. All rights reserved.
Keywords: Boiling Narrow channel Heat transfer coefficient Correlation Flow pattern
1. Introduction Many industrial processes use plate heat exchangers for applications with phase change. In these processes, the heat transfer coefficient is depending on the boiling regime (nucleate or convective); where the nucleate boiling is a type of boiling that takes place when the surface temperature is hotter than the saturated fluid temperature by a certain amount and the convective boiling refers to the convective process between the heated wall and the liquid-phase. Therefore, it is necessary to identify the basic mechanisms which occur during boiling in heat exchanger channels. There has been considerable effort to understand the boiling mechanisms and to predict the heat transfer coefficient in both tube and rectangular channel. In this paper, we try to understand the heat transfer phenomena in channel of millimetric order heat exchanger. It can be applicable in many areas: oil-cooling, heat exchanger for microcomputers. For the vertical tube, Chen [1] envisioned the local two-phase flow boiling coefficient to be the sum of the nucleate boiling and the convective boiling contributions. He proposed a correlation based on Forster-Zuber [2] and Dittus-Boelter [3] correlations with some correcting factors. Shah [4], proposed a correlation to implement his chart calculation method which consider the
* Corresponding author. E-mail address: [email protected] (A. Kouidri). http://dx.doi.org/10.1016/j.ijthermalsci.2015.06.016 1290-0729/© 2015 Elsevier Masson SAS. All rights reserved.
nucleate and convective boiling as principal heat transfer mechanisms. He proposed a method applicable to both vertical and horizontal tubes. Gungor and Winterton [5] proposed a new form of Chen [1] correlation with a large database of 3693 points from the literature for water, refrigerants and ethylene glycol, his correlation can be applicable to both up and down flow. To increase exchange surface and enhance the heat transfer coefficient, the plate heat exchangers are more and more used. Feldman [6] studied the local nucleate and convective boiling heat transfer in plate fin exchanger and the influence of fin geometry. Unfortunately, he used only two mass fluxes. Which is insufficient to mount the influence of mass flux on the heat transfer coefficient. Kim and Sohn [7] studied experimentally the flow boiling in a rectangular channel with offset stripe fins for large range of heat flux and Reynolds number. They developed a correlation for local heat transfer coefficient. This latter gives a dispersion equals to 25% compared to the experimental data. To improve the efficiency of systems using ocean thermal energy, Arima et al. [8] studied the local heat transfer coefficient in the plate heat exchangers using Ammonia and ammoniaewater as working fluid. Also, in this work a visualization of the flow patterns has been carried. In the same range of heat flux, Taboas et al. [9,10] has carried a same study but with a more important mass flux. Zakarias et al. [11] studied the boiling heat transfer in the plate generator for an absorption machine using ammoniaelithium as working fluid, he notes that the two-component mixture formed by ammonia and lithium nitrate has a lower boiling heat transfer coefficient than that of pure
A. Kouidri et al. / International Journal of Thermal Sciences 98 (2015) 90e98
Nomenclature CI Cp Dh k L m Q Re S T V z x AMV Bo F E, S N I U M G
confidence interval () specific heat (J/kg C) hydraulic diameter (m) thermal conductivity (W/m. K) channel length (m) flow rate (kg/s) heat flux (W) Reynolds number () heat exchanger surface (m2) temperature ( C) velocity (m/s) position (m) quality arithmetic mean value boiling number Shah's constant () Gungor's constant () dimensionless parameter () electric current (A) voltage (V) molar mass (kg/mol) mass velocity (kg/m2s)
ammonia. Lee et al. [12] have experimentally studied the flow boiling heat transfer in a plate heat exchanger at low mass flux condition, his study shows that the influence of the convective boiling heat transfer is suppressed under the test conditions, and the effect of boiling heat transfer was dominant. This is stating obvious from the insignificant effect of vapor quality on flow boiling heat transfer coefficient at low mass flux. Koyama et al. [13] studied the flow boiling for plate heat exchanger, heated from one side, they found that the heat transfer coefficient is governed by the nucleation and the bubble behavior driven by buoyancy rather than forced convection. Wang et al. [14] studied the boiling incipient in vertical narrow rectangular channel, he make a parametric study to evaluate the effect of pressure, inlet sub-cooling, heat flux and mass flux. His entire experimental data obtained through different determination methods indicate that inception wall superheat is dependent on the inlet sub-cooling, heat flux and mass flux, but the variation of pressure does not lead to a significant change in boiling incipience. As one can see the available studies in the literature (Table 1) focus on local heat transfer phenomena, while, for the industrials, the most important parameter in the heat exchangers is the mean heat transfer coefficient, because this is the only parameter which can give us a relevant idea about heat exchanger efficiency. The present work deals with an up-ward flow boiling in narrow rectangular heat exchanger, the effect of heat flux, velocity, wall superheated and exit vapor quality on heat transfer phenomena are experimentally investigated. These results are compared with a number of correlations available in the literature. 2. Experimental facilities A complete experimental analysis of flow boiling requires the knowledge of pressures, temperatures, and velocities in the device. The experimental test section built in-situ (Fig. 1), creates the needed conditions to conduct various tests and their reproducibility. It is equipped with pressure sensors, thermocouples and flow meters. The accuracy of the measurement is related to the
P hfg
91
pressure (Pa) latent heat (kJ/kg)
Greek symbols differential standard deviation kinematic viscosity (m2/s) density (kg/m3)
D s y r
Subscripts f fluid w wall elec electrical ther thermal Sat saturation L liquid cb convective boiling in inlet out outlet a average b boiling TP two-phase s suppression nb nucleate boiling
acquisition chain used in the present set-up. Note that the acquired measurements allow determining the spatial-temporal evolution of the transport phenomena. The Hydraulic loop (Fig. 2) is composed of several devices. A tank is designed to store up to 30l of working fluid (pentane). To set the fluid temperature at the channel inlet, this tank is equipped with an electrical resistance controlled by a thermostat. A gear pump with stainless steel volute ensures a continual feeding of the test section. The fluid velocity varies between 0.015 and 0.06 m/s. The liquid pumped from the tank is evaporated in the test channel and separated in the separator; the flow rate of the separated liquid is measured using balance at the outlet of the channel. However the condensed steam returns in the tank. The test section built in-situ (Fig. 3) is composed of two heated plates made from bronze (Fig. 3). These plates are wrapped in PTFE (PolyTetraFluorEthylene) sheets, thus ensuring both the mechanical retention and the thermal insulation of the channel. The test channel has following dimensions: 0.05 m (length) 0.005 m (width) 0.025 m (depth) [m3]. The Dh is equal to 0.0083 mm. K-type thermocouples have been used to measure the local temperature. Their diameter is equal to 0.5 mm for not disturb the flow. Locations of thermocouples are given in Fig. 3 (a). They are implanted in both wall and inside the channel along two vertical axes. Note that the fluid measurements are taken in the center of the channel. The working fluid is n-pentane which is chosen for its low boiling point (36 C at atmospheric pressure) and its small latent heat (382.450 kJ/kg) compared to water. It circulates in the upward vertical direction, between the heated plates. Four heater cartridges located vertically in the heated plates are used to heat the assembly. The heating power varies between 3.04 and 6.88 W/cm2.The channel sealing is ensured by plate gaskets made from Vitton. 3. Experimental results Fig. 4 displays fluid and wall temperature ( C) versus time (s) given by the thermocouples at z ¼ 0.035 m for Q ¼ 3.04 W/cm2,
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Table 1 State of the art on flow boiling heat transfer in plate heat exchanger. References A. Feldman et al. [6]
Flow type
Nucleate and convective boiling Kim et al. [7] Saturated flow boiling Arima et al. [8] Boiling heat transfer Taboas et al. Saturated flow [9,10] boiling Zakarias et al. Boiling heat [11] transfer Lee et al. [12] Boiling heat transfer Flow boiling Koyama et al. [12] Wang et al. Incipience [14] boiling This work Flow boiling
Thermal conditions
Type of heater
Flow direction
Flow conditions
Fluid
Wall material
Q ¼ 1e3.5 kW/m2
Uniform-both sides
Upward
G ¼ 20e45 kg/m2s
CFC114
Aluminum Exp
400*150*2.06 mm
Q ¼ 0.5e3 kW/m2 x ¼ 0 Uniform-both e0.6 sides Q ¼ 15.4e24.5 kW/m2 One side
Upward
G ¼ 17e43 kg/m2s
R 113
Stainless steel sus304
Exp
750*100*3 mm
Exp
850*380*40 mm
Exp
536*112*2 mm
Q ¼ 20e54 kW/m2 x ¼ 0e0.22 Q ¼ 1.2e4.61 kW/m2
Upward
2
G ¼ 7.5e15 kg/m s
Ammonia
G ¼ 70e140 kg/m2s
Q ¼ 0.11e0.19 kW/m xin ¼ 0.15e0.95 Q ¼ 10e20 kW/m2
Hot water
Ammoniae water Horizontal m ¼ 0.041e0.083 kg/s Ammoniae lithium Upward G ¼ 1.28e1.7 kg/m2s R134a
One side
Upward
G ¼ 5e7.5 kg/m2s
Q ¼ 20e200 kW/m2 Tin ¼ 20e74 C Q ¼ 30.4e68.8 kW/m2
Uniform-both sides Uniform-both sides
Upward
G ¼ 100e1500 kg/m2s Water
Upward
V ¼ 0.015e0.06 m/s
Water both sides Hot water 2
Upward
V ¼ 0.015 m/s and Tin ¼ 16 C. We can see that the wall temperature starts increased before that of the fluid but they reach the stationary regime at the same time. Note that for calculations, only the average values in stationary regime are considered. An axial profile of wall and bulk temperatures along the test section is drawn in Fig. 5. The test conditions were set at a velocity of 0.015 m/s and heat flux values of 12e143 kW/m2.
Ammonia
n-pentane
Approach Channel dimensions
Stainless steel Stainless steel e
Exp
576*175*2.4 mm
Exp
648*210*6 mm
Titanium
Exp
250*100*50 mm
Stainless steel Bronze
Exp
2*40*2 mm
Exp
50*25*5 mm
The boiling zone is determined using comparison between the local temperatures of fluid and the saturation temperature corresponding to the local pressures measured by pressure sensors. The fluid temperatures measured with the thermocouples are in accordance with those determined from the pressure measurement. A slight decrease of saturated fluid temperature is observed between the inlet and outlet of the test section, this is due to the
Fig. 1. Photograph of the test section and data acquisition system, 1 e Data acquisition, 2 e flowmeters, 3 e Condenser, 4 e Separator, 5 e Thermocouples, 6 e Test section, 7 e pressure sensors, 8 e variable speed drive, 9 e Electrical cabinet.
A. Kouidri et al. / International Journal of Thermal Sciences 98 (2015) 90e98
93
Fig. 2. The hydrodynamic loop.
Fig. 3. The schematic of the test section: (a) Test section detail. (b) Channel dimensions.
pressure drop along the channel. Note that the wall temperature decreases significantly at position z ¼ 0.025 m. This observation will be interesting while analyzing the evolution of local heat transfer. Subcooled boiling: (z ¼ 0 to 0.025 m) The fluid is in the liquid state and its temperature increases until it reaches the saturation temperature at position z ¼ 0.025 m in this case (Fig. 5-a). The temperature gradients in the fluid and wall are positive. Saturated boiling: (z ¼ 0.025 to 0.05 m) The temperature gradient for the fluid is constant because the boiling takes place at a constant temperature and pressure. Against
the temperature gradient of the wall is negative, it can be interpreted by the detachment of bubbles at the wall. As one can see that the evolution of the wall temperature fluctuation as well as that of the fluid are different in the three cases b, c and d. Postulate: As shown in Fig. 5 (b, c and d) the temperature uncertainties measurement in liquid phase are higher than one in saturated phase. Case 1 (Fig. 5-b): V ¼ 0.015 m/s q ¼ 29,844 W/m2. The temperature fluctuations of the fluid and the wall are constant along the boiling zone. The fluid temperature uncertainties are higher than that of the wall. On basis of postulate made above, we can say that the flow in this area can be isolate bubbles.
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The wall temperature uncertainty undergone a significant increase, it can be interpreted by the presence of a liquid film on the wall and the vapor at center of the channel, the flow in this case can be annular. Note that the prediction of flow pattern in the precedent paragraphs is only an approach.
4. The analysis of the mean heat transfer coefficients The experimental mean heat transfer coefficient for the boiling regime is calculated using Eq. (1):
ha ¼
Fig. 4. Fluid and wall temperature time histories given by thermocouples located at z ¼ 0.035 mm position.
Case 2 (Fig. 5-c): V ¼ 0.015 m/s q ¼ 73,451 W/m2. The temperature fluctuations of the fluid and the wall are interchangeable, when the fluid touches the wall, the wall temperature uncertainty is important and when it is affected by steam, the wall temperature fluctuations become less important. In this case the flow can be slug-churn. Case 3 (Fig. 5-d): V ¼ 0.015 m/s q ¼ 110,000 W/m2.
Qb ðTw Tsat Þ
(1)
where ha is the average heat transfer coefficient, Qb is the boiling heat flux (W/m2), Tw and Tsat are the mean wall and saturated temperatures, respectively, in the boiling zone. The Qb is defined as:
Qb ¼
UI Qloss m_ Cp ðTsat Tin Þ S
(2)
where U is the applied voltage (V), I is the electric current (A), m_ is the flow rate (kg/s), Cp is the specific heat (W/kg C) and Tin is the liquid temperature at the inlet. The Qloss is the loss heat flux in the test section; it is given by equation (3)
Fig. 5. (a)Temperature profiles of wall and fluid along the channel; (b) Temperature fluctuations in Bubbly regime; (c) Temperature fluctuations in slug-churn regime; (d) Temperature fluctuations in slug-annular.
A. Kouidri et al. / International Journal of Thermal Sciences 98 (2015) 90e98 Table 2 Uncertainty on measured variables.
DTl
DTw
DV
DS
DU
DI
( C)
( C)
(m/s)
(m2)
(V)
(A)
0.13
0.01
0.000
0.00003
1.0
0.02
Qloss ¼
ki Si ðTw Ta Þ ei
(3)
where ki is the insulation thermal conductivity (W/m. K), ei is the insulation thickness (m), Si is the exchange surface between the channel and the insulation (m2), Tw is the wall temperature ( C) and Ta is the ambient temperature ( C). Qloss is found between 2 and 4 %. 4.1. Uncertainties analysis The heat transfer coefficient is calculated using Eq. (4) on the basis of the Kline and McClintock [15] method.
Dh ¼ h
95
The uncertainty analysis of heat transfer coefficient was mainly attributed to the variation of power input, inlet velocity, exchange surface and different temperatures (inlet temperature, wall temperature and saturation temperature). The average results of uncertainty measured variables for all experiences are presented in Table 2. 4.2. Heat transfer results As shown in Fig 6-a, the average heat transfer coefficient increases as heat flux increase for all velocity values. This can be explained by bubble nucleation. Increment of number of nucleation sites and bubble frequency coincides with increasing heat flux, Koyama et al. [13]. Fig. 6 (b) shows the evolution of the average heat transfer coefficient versus exit vapor quality; this evolution is clearly linear, and the average heat transfer coefficient increases with increasing of exit vapor quality. As one can see, the exit vapor quality decreases with increasing of velocity because in high velocity values,
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 2 DQb 2 DV DTin 2 DTw DTsat DS þ þ þ þ þ V S Qb Tin Tw Tsat Tw Tsat
Fig. 6. Mean heat transfer coefficient for several velocity: (a) versus heat flux, (b) versus exit vapor quality and (c) versus wall superheat.
(4)
96
A. Kouidri et al. / International Journal of Thermal Sciences 98 (2015) 90e98
the fluid cannot absorb a large amount of heat flux generate by the heater Cartridge. Fig. 6 (c) gives the evolution of the mean heat transfer coefficient versus DTsat. The average heat transfer coefficient increases while wall superheat increase. For the velocity values between 0.015 m/s and 0.04 m/s, the evolution of the mean heat transfer coefficient with wall superheat has a positive gradient; above wall superheat values between DTsat ¼ 17e19 C, this gradient increases clearly. For the velocity values of 0.05 and 0.06 m/s; the gradient between average heat transfer coefficient and wall superheat is vertical, and the average heat transfer coefficient is independent of wall superheat. 5. Discussion and comparison with the literature Fig. 7 shows a comparison between the mean heat transfer coefficient obtained in the present work and those of correlations available in the literature (Table 3) versus heat flux, exit vapor quality and wall superheat. Note that these correlations were developed for the local heat transfer coefficient in a plain tube. Then we start by calculating the local heat transfer coefficient using these correlations, and then we calculate the average heat transfer coefficient based on these local heat transfer coefficients. The Gungor and Winterton [5] correlation gives a good agreement with the experimental results. This remark holds also for Jens and Lottes [16] correlation with weak superiority. Shah [4] and
Gungor and Winterton [17] correlations have largely underestimate the mean heat transfer coefficient. With a same hydraulic diameter, a rectangular channel gives a heat-exchange surface three times greater than that of a round tube. Therefore, the present results are three times greater than those obtained using Shah [4] and Gungor and Winterton [17] correlations. Fig. 8 (a) shows the experimental boiling curves for several velocities. The wall superheat increases in the same way that heat flux. For the velocity values between 0.015 m/s and 0.04 m/s, the evolution of wall superheat with heat flux tend to the critical heat flux which is the maximum heat flux. For the velocity values of 0.05 and 0.06 m/s, the gradient between wall superheat and heat flux is vertical, which means that the critical heat flux stay away. Fig. 8 (b) illustrates a comparison with Gungor and Winterton [5] and Jens and Lottes [16]. For the velocity equals to 0.04 m/s, the Jens and Lottes [16] curve gradient changes at DTsat ¼ 14 C. Whereas for Gungor and Winterton [5] the gradient remains constant. For the velocity of 0.06 m/s, both gradient of Gungor and Winterton [5] and Jens and Lottes [16] are constant. 6. Development of a new correlation to predict the mean heat transfer coefficient In flow boiling, many correlations to predict the heat transfer coefficient have been developed, especially for round tubes, but for
Fig. 7. Comparison of average heat transfer coefficient with several correlations available on the literature versus: (a) heat flux, (b) exit quality and (c) wall superheat.
A. Kouidri et al. / International Journal of Thermal Sciences 98 (2015) 90e98 Table 3 Correlation to predict the heat transfer coefficient inside plain tubes for boiling regime. Correlations
Jens and Lottes [16]
DTsat;b ¼ 25 Q 0:25 e
Shah [4]
hl ¼ 0:023
p 6:2
(5)
kl n 0:4 Vd 0:8 n d a
(6)
1 htp ¼ ðhnb Þn þ ðhcb Þn n
1:8 N
0:8
hl
N ¼ Co ¼
(7) 1 x 0:8 rv 0:8 x rl
hnb ¼ 230Bo0:5 hl N > 1 and Bo > 0:0003 hnb ¼ 1 þ 46 Bo0:5 hl N > 1 and Bo < 0:0003 hnb ¼ Fs Bo0:5 expð2:74N 0:1Þ hl 0:1 < N < 1 hnb ¼ Fs Bo0:5 expð2:74N 0:15Þ hl N < 0:1 With Fs ¼ 14:7 for Bo > 0:0011 And Fs ¼ 15:43 for Bo < 0:0011 htp ¼ E hl þ S hnb hnb ¼ 55 Pr0:12 ð 0:4343 ln Pr Þ0:55 M 0:5 q0:67 0:86 1 E ¼ 1 þ 24000Bo1:16 þ 1:37 Xtt h i1 S ¼ 1 þ 0:00000115E2 Re1:17 L Gungor and Winterton [17]
(10)
hcb ¼
Gungor and Winterton [5]
hb ¼ hl K where hl is given by Eq. (6) and K is given by Eq. (11):
Authors
Dittus and Boelter [3]
97
htp ¼ Enew hl E ¼ 1 þ 3000Bo0:86 þ 1:12
X 1X
0:75
rL rV
0:41
(8)
K ¼ 4717 Bo1:24
xexit 1 xexit
0:3 (11)
The effect of heat flux on nucleate boiling is characterized by the Boiling number, Thome [18], Bo is given by Eq. (12).
Bo ¼
Qb G hfg
(12)
In this correlation, two contributions are represented: the forced convection one by hl, and nucleate one by the coefficient K. In Fig. 9, a comparison between the present correlation and the others data is presented, as one can see that the results obtained by the established correlation fit well the experimental data with dispersion equals to ±12%. The comparison with Jens and Lottes [16] correlation gives a dispersion equals to ±25%, where, the correlation gives a good agreement with the Jens and Lottes [16] correlation for the heat transfer coefficient in the range of 2000e5000 (W/m2 C). The last comparison between the present correlation data and those given by Gungor and Winterton [5] correlation gives a dispersion equals to ±38%, as one can see that the two correlations are in agreement in the low values of heat transfer coefficient. Note that the established correlation is valid in the boiling heat flux from 9 to 137 kW/m2 and Reynolds number between 380 and 1522.
7. Conclusion (9)
the rectangular channel, the correlations are scarce. That's why we developed a new correlation to predict the mean heat transfer coefficient, which is important for industrial researchers Eq. (10) This correlation is based on the single phase heat transfer coefficient correlation developed by Dittus and Boelter [3], and the correcting factor “K”, see Eq. (11).
The plate heat exchangers have always attracted the researcher's attention, especially for their important exchangesurface. For the compactness criterion, the size of heat exchanger plays a very important role. In this sense, we have chosen to study a small heat exchanger which can be applied in specific applications, such as in oil-cooling circuits or micro-processor computers. A large database was constructed by varying several parameters (velocity and heat flux). The results of mean heat transfer coefficient were compared with those available in the literature. The experimental mean heat transfer coefficients were found between those of Gungor and Winterton [5] and Jens and Lottes
Fig. 8. Experimental boiling curves: (a) influence of velocity on boiling curve, (b) comparison of boiling curve with results given by Gungor and Winterton [5] and Jens and Lottes [16].
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Fig. 9. Comparison of the present correlation with others data: (a) versus present data, (b) Jens and Lottes [16] correlation, and (c) Gungor and Winterton [5] correlation.
[16]. The comparison with correlations of Gungor and Winterton [17] and Shah [4] showed that the experimental results are three times larger than the latter. That is logical, because the exchangesurface of the present rectangle channel is approximately three times greater than that of round tube for the same hydraulic diameter. To facilitate the prediction of the mean heat transfer coefficient in plate heat exchangers, a new correlation has been developed; it is based on the correlation of Dittus and Boelter [3] which represents the convective boiling contribution. This correlation is multiplied by a coefficient “K” which represents the nucleate boiling part, where, this last is based on the Bo number and exit vapor quality. This correlation gives a dispersion equals to 12% compared to experimental data, while, his validity varied between boiling heat flux from 9 to 137 kW/m2 and Reynolds number between 380 and 1522. Acknowledgment This work was supported by the General Directorate for Scientific Research and Technological Development of Algeria (PNR 08/ U160/658), for which the authors are very thankful. References [1] J.C. Chen, Correlation for boiling heat transfer to saturated fluids in convective flow, Ind. Eng. Chem. Process Des. Dev. 5 (1966) 322e329. [2] H. Forster, N. Zuber, Dynamics of vapor bubbles and boiling heat transfer, AIChE J. 1 (1955) 531e535. [3] F. Dittus, L. Boelter, University of California publications on engineering, Univ. Calif. Publ. Eng. 2 (1930) 371.
[4] M. Shah, Chart correlation for saturated boiling heat transfer: equations and further study, ASHRAE Trans.; (United States) 88 (1982). [5] K. Gungor, R. Winterton, A general correlation for flow boiling in tubes and annuli, Int. J. Heat Mass Transf. 29 (1986) 351e358. [6] A. Feldman, C. Marvillet, M. Lebouche, Nucleate and convective boiling in plate fin heat exchangers, Int. J. Heat Mass Transf. 43 (2000) 3433e3442. [7] B. Kim, B. Sohn, An experimental study of flow boiling in a rectangular channel with offset strip fins, Int. J. Heat Fluid Flow 27 (2006) 514e521. [8] H. Arima, J. Kim, A. Okamoto, Y. Ikegami, Local boiling heat transfer characteristics of ammonia in a vertical plate evaporator, Int. J. Refrig. 33 (2010) 359e370. s, M. Bourouis, A. Coronas, Flow boiling heat transfer of [9] F. T aboas, M. Valle ammonia/water mixture in a plate heat exchanger, Int. J. Refrig. 33 (2010) 695e705. boas, M. Valle s, M. Bourouis, A. Coronas, Assessment of boiling heat [10] F. Ta transfer and pressure drop correlations of ammonia/water mixture in a plate heat exchanger, Int. J. Refrig. 35 (2012) 633e644. [11] A. Zacarías, R. Ventas, M. Venegas, A. Lecuona, Boiling heat transfer and pressure drop of ammonia-lithium nitrate solution in a plate generator, Int. J. Heat Mass Transf. 53 (2010) 4768e4779. [12] H. Lee, S. Li, Y. Hwang, R. Radermacher, H.-H. Chun, Experimental investigations on flow boiling heat transfer in plate heat exchanger at low mass flux condition, Appl. Therm. Eng. 61 (2013) 408e415. [13] K. Koyama, H. Chiyoda, H. Arima, Y. Ikegami, Experimental study on thermal characteristics of ammonia flow boiling in a plate evaporator at low mass flux, Int. J. Refrig. 38 (2014) 227e235. [14] C. Wang, H. Wang, S. Wang, P. Gao, Experimental study of boiling incipience in vertical narrow rectangular channel, Ann. Nucl. Energy 66 (2014) 152e160. [15] S.J. Kline, F.A. McClintock, Describing Uncertainties in Single Sample Experiments, 1953. [16] W. Jens, P. Lottes, Analysis of Heat Transfer, Burnout, Pressure Drop and Density Date for High-pressure Water, Argonne National Lab, 1951. [17] K. Gungor, R. Winterton, Simplified general correlation for saturated flow boiling and comparisons of correlations with data, Chem. Eng. Res. Des. 65 (1987) 148e156. [18] J.R. Thome, Engineering Data Book III, Wolverine Tube Inc, 2004.
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Experimental investigation of flow boiling in narrow channel A. Kouidri*, B. Madani, B. Roubi Laboratory of Multiphase Transport and Porous Media (LTPMP), Faculty of Mechanical and Process Engineering (FGMGP)/USTHB, BP. 32, El Alia, Algiers, Algeria
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 March 2015 Received in revised form 23 June 2015 Accepted 27 June 2015 Available online xxx
The flow boiling in narrow channel is investigated experimentally. The aim of the present work is to study the heat transfer phenomena. The working fluid is n-pentane which is chosen for its low boiling point (36 C at atmospheric pressure). The independent variables are velocity in the range from 0.015 m/s to 0.06 m/s and boiling heat flux with values between 9 and 137 kW/m2. The wall superheat and exit vapor quality are presented as dependent variables. The flow pattern was predicted based on temperature fluctuations. The experimental results are compared to those available in the literature (Shah, Gungor-Winterton and Jens correlations). A new correlation has been developed for the average heat transfer coefficient during flow boiling in a rectangular channel with validity in boiling heat flux from 9 to 137 kW/m2 and Reynolds number between 380 and 1522. © 2015 Elsevier Masson SAS. All rights reserved.
Keywords: Boiling Narrow channel Heat transfer coefficient Correlation Flow pattern
1. Introduction Many industrial processes use plate heat exchangers for applications with phase change. In these processes, the heat transfer coefficient is depending on the boiling regime (nucleate or convective); where the nucleate boiling is a type of boiling that takes place when the surface temperature is hotter than the saturated fluid temperature by a certain amount and the convective boiling refers to the convective process between the heated wall and the liquid-phase. Therefore, it is necessary to identify the basic mechanisms which occur during boiling in heat exchanger channels. There has been considerable effort to understand the boiling mechanisms and to predict the heat transfer coefficient in both tube and rectangular channel. In this paper, we try to understand the heat transfer phenomena in channel of millimetric order heat exchanger. It can be applicable in many areas: oil-cooling, heat exchanger for microcomputers. For the vertical tube, Chen [1] envisioned the local two-phase flow boiling coefficient to be the sum of the nucleate boiling and the convective boiling contributions. He proposed a correlation based on Forster-Zuber [2] and Dittus-Boelter [3] correlations with some correcting factors. Shah [4], proposed a correlation to implement his chart calculation method which consider the
* Corresponding author. E-mail address: [email protected] (A. Kouidri). http://dx.doi.org/10.1016/j.ijthermalsci.2015.06.016 1290-0729/© 2015 Elsevier Masson SAS. All rights reserved.
nucleate and convective boiling as principal heat transfer mechanisms. He proposed a method applicable to both vertical and horizontal tubes. Gungor and Winterton [5] proposed a new form of Chen [1] correlation with a large database of 3693 points from the literature for water, refrigerants and ethylene glycol, his correlation can be applicable to both up and down flow. To increase exchange surface and enhance the heat transfer coefficient, the plate heat exchangers are more and more used. Feldman [6] studied the local nucleate and convective boiling heat transfer in plate fin exchanger and the influence of fin geometry. Unfortunately, he used only two mass fluxes. Which is insufficient to mount the influence of mass flux on the heat transfer coefficient. Kim and Sohn [7] studied experimentally the flow boiling in a rectangular channel with offset stripe fins for large range of heat flux and Reynolds number. They developed a correlation for local heat transfer coefficient. This latter gives a dispersion equals to 25% compared to the experimental data. To improve the efficiency of systems using ocean thermal energy, Arima et al. [8] studied the local heat transfer coefficient in the plate heat exchangers using Ammonia and ammoniaewater as working fluid. Also, in this work a visualization of the flow patterns has been carried. In the same range of heat flux, Taboas et al. [9,10] has carried a same study but with a more important mass flux. Zakarias et al. [11] studied the boiling heat transfer in the plate generator for an absorption machine using ammoniaelithium as working fluid, he notes that the two-component mixture formed by ammonia and lithium nitrate has a lower boiling heat transfer coefficient than that of pure
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Nomenclature CI Cp Dh k L m Q Re S T V z x AMV Bo F E, S N I U M G
confidence interval () specific heat (J/kg C) hydraulic diameter (m) thermal conductivity (W/m. K) channel length (m) flow rate (kg/s) heat flux (W) Reynolds number () heat exchanger surface (m2) temperature ( C) velocity (m/s) position (m) quality arithmetic mean value boiling number Shah's constant () Gungor's constant () dimensionless parameter () electric current (A) voltage (V) molar mass (kg/mol) mass velocity (kg/m2s)
ammonia. Lee et al. [12] have experimentally studied the flow boiling heat transfer in a plate heat exchanger at low mass flux condition, his study shows that the influence of the convective boiling heat transfer is suppressed under the test conditions, and the effect of boiling heat transfer was dominant. This is stating obvious from the insignificant effect of vapor quality on flow boiling heat transfer coefficient at low mass flux. Koyama et al. [13] studied the flow boiling for plate heat exchanger, heated from one side, they found that the heat transfer coefficient is governed by the nucleation and the bubble behavior driven by buoyancy rather than forced convection. Wang et al. [14] studied the boiling incipient in vertical narrow rectangular channel, he make a parametric study to evaluate the effect of pressure, inlet sub-cooling, heat flux and mass flux. His entire experimental data obtained through different determination methods indicate that inception wall superheat is dependent on the inlet sub-cooling, heat flux and mass flux, but the variation of pressure does not lead to a significant change in boiling incipience. As one can see the available studies in the literature (Table 1) focus on local heat transfer phenomena, while, for the industrials, the most important parameter in the heat exchangers is the mean heat transfer coefficient, because this is the only parameter which can give us a relevant idea about heat exchanger efficiency. The present work deals with an up-ward flow boiling in narrow rectangular heat exchanger, the effect of heat flux, velocity, wall superheated and exit vapor quality on heat transfer phenomena are experimentally investigated. These results are compared with a number of correlations available in the literature. 2. Experimental facilities A complete experimental analysis of flow boiling requires the knowledge of pressures, temperatures, and velocities in the device. The experimental test section built in-situ (Fig. 1), creates the needed conditions to conduct various tests and their reproducibility. It is equipped with pressure sensors, thermocouples and flow meters. The accuracy of the measurement is related to the
P hfg
91
pressure (Pa) latent heat (kJ/kg)
Greek symbols differential standard deviation kinematic viscosity (m2/s) density (kg/m3)
D s y r
Subscripts f fluid w wall elec electrical ther thermal Sat saturation L liquid cb convective boiling in inlet out outlet a average b boiling TP two-phase s suppression nb nucleate boiling
acquisition chain used in the present set-up. Note that the acquired measurements allow determining the spatial-temporal evolution of the transport phenomena. The Hydraulic loop (Fig. 2) is composed of several devices. A tank is designed to store up to 30l of working fluid (pentane). To set the fluid temperature at the channel inlet, this tank is equipped with an electrical resistance controlled by a thermostat. A gear pump with stainless steel volute ensures a continual feeding of the test section. The fluid velocity varies between 0.015 and 0.06 m/s. The liquid pumped from the tank is evaporated in the test channel and separated in the separator; the flow rate of the separated liquid is measured using balance at the outlet of the channel. However the condensed steam returns in the tank. The test section built in-situ (Fig. 3) is composed of two heated plates made from bronze (Fig. 3). These plates are wrapped in PTFE (PolyTetraFluorEthylene) sheets, thus ensuring both the mechanical retention and the thermal insulation of the channel. The test channel has following dimensions: 0.05 m (length) 0.005 m (width) 0.025 m (depth) [m3]. The Dh is equal to 0.0083 mm. K-type thermocouples have been used to measure the local temperature. Their diameter is equal to 0.5 mm for not disturb the flow. Locations of thermocouples are given in Fig. 3 (a). They are implanted in both wall and inside the channel along two vertical axes. Note that the fluid measurements are taken in the center of the channel. The working fluid is n-pentane which is chosen for its low boiling point (36 C at atmospheric pressure) and its small latent heat (382.450 kJ/kg) compared to water. It circulates in the upward vertical direction, between the heated plates. Four heater cartridges located vertically in the heated plates are used to heat the assembly. The heating power varies between 3.04 and 6.88 W/cm2.The channel sealing is ensured by plate gaskets made from Vitton. 3. Experimental results Fig. 4 displays fluid and wall temperature ( C) versus time (s) given by the thermocouples at z ¼ 0.035 m for Q ¼ 3.04 W/cm2,
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Table 1 State of the art on flow boiling heat transfer in plate heat exchanger. References A. Feldman et al. [6]
Flow type
Nucleate and convective boiling Kim et al. [7] Saturated flow boiling Arima et al. [8] Boiling heat transfer Taboas et al. Saturated flow [9,10] boiling Zakarias et al. Boiling heat [11] transfer Lee et al. [12] Boiling heat transfer Flow boiling Koyama et al. [12] Wang et al. Incipience [14] boiling This work Flow boiling
Thermal conditions
Type of heater
Flow direction
Flow conditions
Fluid
Wall material
Q ¼ 1e3.5 kW/m2
Uniform-both sides
Upward
G ¼ 20e45 kg/m2s
CFC114
Aluminum Exp
400*150*2.06 mm
Q ¼ 0.5e3 kW/m2 x ¼ 0 Uniform-both e0.6 sides Q ¼ 15.4e24.5 kW/m2 One side
Upward
G ¼ 17e43 kg/m2s
R 113
Stainless steel sus304
Exp
750*100*3 mm
Exp
850*380*40 mm
Exp
536*112*2 mm
Q ¼ 20e54 kW/m2 x ¼ 0e0.22 Q ¼ 1.2e4.61 kW/m2
Upward
2
G ¼ 7.5e15 kg/m s
Ammonia
G ¼ 70e140 kg/m2s
Q ¼ 0.11e0.19 kW/m xin ¼ 0.15e0.95 Q ¼ 10e20 kW/m2
Hot water
Ammoniae water Horizontal m ¼ 0.041e0.083 kg/s Ammoniae lithium Upward G ¼ 1.28e1.7 kg/m2s R134a
One side
Upward
G ¼ 5e7.5 kg/m2s
Q ¼ 20e200 kW/m2 Tin ¼ 20e74 C Q ¼ 30.4e68.8 kW/m2
Uniform-both sides Uniform-both sides
Upward
G ¼ 100e1500 kg/m2s Water
Upward
V ¼ 0.015e0.06 m/s
Water both sides Hot water 2
Upward
V ¼ 0.015 m/s and Tin ¼ 16 C. We can see that the wall temperature starts increased before that of the fluid but they reach the stationary regime at the same time. Note that for calculations, only the average values in stationary regime are considered. An axial profile of wall and bulk temperatures along the test section is drawn in Fig. 5. The test conditions were set at a velocity of 0.015 m/s and heat flux values of 12e143 kW/m2.
Ammonia
n-pentane
Approach Channel dimensions
Stainless steel Stainless steel e
Exp
576*175*2.4 mm
Exp
648*210*6 mm
Titanium
Exp
250*100*50 mm
Stainless steel Bronze
Exp
2*40*2 mm
Exp
50*25*5 mm
The boiling zone is determined using comparison between the local temperatures of fluid and the saturation temperature corresponding to the local pressures measured by pressure sensors. The fluid temperatures measured with the thermocouples are in accordance with those determined from the pressure measurement. A slight decrease of saturated fluid temperature is observed between the inlet and outlet of the test section, this is due to the
Fig. 1. Photograph of the test section and data acquisition system, 1 e Data acquisition, 2 e flowmeters, 3 e Condenser, 4 e Separator, 5 e Thermocouples, 6 e Test section, 7 e pressure sensors, 8 e variable speed drive, 9 e Electrical cabinet.
A. Kouidri et al. / International Journal of Thermal Sciences 98 (2015) 90e98
93
Fig. 2. The hydrodynamic loop.
Fig. 3. The schematic of the test section: (a) Test section detail. (b) Channel dimensions.
pressure drop along the channel. Note that the wall temperature decreases significantly at position z ¼ 0.025 m. This observation will be interesting while analyzing the evolution of local heat transfer. Subcooled boiling: (z ¼ 0 to 0.025 m) The fluid is in the liquid state and its temperature increases until it reaches the saturation temperature at position z ¼ 0.025 m in this case (Fig. 5-a). The temperature gradients in the fluid and wall are positive. Saturated boiling: (z ¼ 0.025 to 0.05 m) The temperature gradient for the fluid is constant because the boiling takes place at a constant temperature and pressure. Against
the temperature gradient of the wall is negative, it can be interpreted by the detachment of bubbles at the wall. As one can see that the evolution of the wall temperature fluctuation as well as that of the fluid are different in the three cases b, c and d. Postulate: As shown in Fig. 5 (b, c and d) the temperature uncertainties measurement in liquid phase are higher than one in saturated phase. Case 1 (Fig. 5-b): V ¼ 0.015 m/s q ¼ 29,844 W/m2. The temperature fluctuations of the fluid and the wall are constant along the boiling zone. The fluid temperature uncertainties are higher than that of the wall. On basis of postulate made above, we can say that the flow in this area can be isolate bubbles.
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The wall temperature uncertainty undergone a significant increase, it can be interpreted by the presence of a liquid film on the wall and the vapor at center of the channel, the flow in this case can be annular. Note that the prediction of flow pattern in the precedent paragraphs is only an approach.
4. The analysis of the mean heat transfer coefficients The experimental mean heat transfer coefficient for the boiling regime is calculated using Eq. (1):
ha ¼
Fig. 4. Fluid and wall temperature time histories given by thermocouples located at z ¼ 0.035 mm position.
Case 2 (Fig. 5-c): V ¼ 0.015 m/s q ¼ 73,451 W/m2. The temperature fluctuations of the fluid and the wall are interchangeable, when the fluid touches the wall, the wall temperature uncertainty is important and when it is affected by steam, the wall temperature fluctuations become less important. In this case the flow can be slug-churn. Case 3 (Fig. 5-d): V ¼ 0.015 m/s q ¼ 110,000 W/m2.
Qb ðTw Tsat Þ
(1)
where ha is the average heat transfer coefficient, Qb is the boiling heat flux (W/m2), Tw and Tsat are the mean wall and saturated temperatures, respectively, in the boiling zone. The Qb is defined as:
Qb ¼
UI Qloss m_ Cp ðTsat Tin Þ S
(2)
where U is the applied voltage (V), I is the electric current (A), m_ is the flow rate (kg/s), Cp is the specific heat (W/kg C) and Tin is the liquid temperature at the inlet. The Qloss is the loss heat flux in the test section; it is given by equation (3)
Fig. 5. (a)Temperature profiles of wall and fluid along the channel; (b) Temperature fluctuations in Bubbly regime; (c) Temperature fluctuations in slug-churn regime; (d) Temperature fluctuations in slug-annular.
A. Kouidri et al. / International Journal of Thermal Sciences 98 (2015) 90e98 Table 2 Uncertainty on measured variables.
DTl
DTw
DV
DS
DU
DI
( C)
( C)
(m/s)
(m2)
(V)
(A)
0.13
0.01
0.000
0.00003
1.0
0.02
Qloss ¼
ki Si ðTw Ta Þ ei
(3)
where ki is the insulation thermal conductivity (W/m. K), ei is the insulation thickness (m), Si is the exchange surface between the channel and the insulation (m2), Tw is the wall temperature ( C) and Ta is the ambient temperature ( C). Qloss is found between 2 and 4 %. 4.1. Uncertainties analysis The heat transfer coefficient is calculated using Eq. (4) on the basis of the Kline and McClintock [15] method.
Dh ¼ h
95
The uncertainty analysis of heat transfer coefficient was mainly attributed to the variation of power input, inlet velocity, exchange surface and different temperatures (inlet temperature, wall temperature and saturation temperature). The average results of uncertainty measured variables for all experiences are presented in Table 2. 4.2. Heat transfer results As shown in Fig 6-a, the average heat transfer coefficient increases as heat flux increase for all velocity values. This can be explained by bubble nucleation. Increment of number of nucleation sites and bubble frequency coincides with increasing heat flux, Koyama et al. [13]. Fig. 6 (b) shows the evolution of the average heat transfer coefficient versus exit vapor quality; this evolution is clearly linear, and the average heat transfer coefficient increases with increasing of exit vapor quality. As one can see, the exit vapor quality decreases with increasing of velocity because in high velocity values,
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 2 DQb 2 DV DTin 2 DTw DTsat DS þ þ þ þ þ V S Qb Tin Tw Tsat Tw Tsat
Fig. 6. Mean heat transfer coefficient for several velocity: (a) versus heat flux, (b) versus exit vapor quality and (c) versus wall superheat.
(4)
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A. Kouidri et al. / International Journal of Thermal Sciences 98 (2015) 90e98
the fluid cannot absorb a large amount of heat flux generate by the heater Cartridge. Fig. 6 (c) gives the evolution of the mean heat transfer coefficient versus DTsat. The average heat transfer coefficient increases while wall superheat increase. For the velocity values between 0.015 m/s and 0.04 m/s, the evolution of the mean heat transfer coefficient with wall superheat has a positive gradient; above wall superheat values between DTsat ¼ 17e19 C, this gradient increases clearly. For the velocity values of 0.05 and 0.06 m/s; the gradient between average heat transfer coefficient and wall superheat is vertical, and the average heat transfer coefficient is independent of wall superheat. 5. Discussion and comparison with the literature Fig. 7 shows a comparison between the mean heat transfer coefficient obtained in the present work and those of correlations available in the literature (Table 3) versus heat flux, exit vapor quality and wall superheat. Note that these correlations were developed for the local heat transfer coefficient in a plain tube. Then we start by calculating the local heat transfer coefficient using these correlations, and then we calculate the average heat transfer coefficient based on these local heat transfer coefficients. The Gungor and Winterton [5] correlation gives a good agreement with the experimental results. This remark holds also for Jens and Lottes [16] correlation with weak superiority. Shah [4] and
Gungor and Winterton [17] correlations have largely underestimate the mean heat transfer coefficient. With a same hydraulic diameter, a rectangular channel gives a heat-exchange surface three times greater than that of a round tube. Therefore, the present results are three times greater than those obtained using Shah [4] and Gungor and Winterton [17] correlations. Fig. 8 (a) shows the experimental boiling curves for several velocities. The wall superheat increases in the same way that heat flux. For the velocity values between 0.015 m/s and 0.04 m/s, the evolution of wall superheat with heat flux tend to the critical heat flux which is the maximum heat flux. For the velocity values of 0.05 and 0.06 m/s, the gradient between wall superheat and heat flux is vertical, which means that the critical heat flux stay away. Fig. 8 (b) illustrates a comparison with Gungor and Winterton [5] and Jens and Lottes [16]. For the velocity equals to 0.04 m/s, the Jens and Lottes [16] curve gradient changes at DTsat ¼ 14 C. Whereas for Gungor and Winterton [5] the gradient remains constant. For the velocity of 0.06 m/s, both gradient of Gungor and Winterton [5] and Jens and Lottes [16] are constant. 6. Development of a new correlation to predict the mean heat transfer coefficient In flow boiling, many correlations to predict the heat transfer coefficient have been developed, especially for round tubes, but for
Fig. 7. Comparison of average heat transfer coefficient with several correlations available on the literature versus: (a) heat flux, (b) exit quality and (c) wall superheat.
A. Kouidri et al. / International Journal of Thermal Sciences 98 (2015) 90e98 Table 3 Correlation to predict the heat transfer coefficient inside plain tubes for boiling regime. Correlations
Jens and Lottes [16]
DTsat;b ¼ 25 Q 0:25 e
Shah [4]
hl ¼ 0:023
p 6:2
(5)
kl n 0:4 Vd 0:8 n d a
(6)
1 htp ¼ ðhnb Þn þ ðhcb Þn n
1:8 N
0:8
hl
N ¼ Co ¼
(7) 1 x 0:8 rv 0:8 x rl
hnb ¼ 230Bo0:5 hl N > 1 and Bo > 0:0003 hnb ¼ 1 þ 46 Bo0:5 hl N > 1 and Bo < 0:0003 hnb ¼ Fs Bo0:5 expð2:74N 0:1Þ hl 0:1 < N < 1 hnb ¼ Fs Bo0:5 expð2:74N 0:15Þ hl N < 0:1 With Fs ¼ 14:7 for Bo > 0:0011 And Fs ¼ 15:43 for Bo < 0:0011 htp ¼ E hl þ S hnb hnb ¼ 55 Pr0:12 ð 0:4343 ln Pr Þ0:55 M 0:5 q0:67 0:86 1 E ¼ 1 þ 24000Bo1:16 þ 1:37 Xtt h i1 S ¼ 1 þ 0:00000115E2 Re1:17 L Gungor and Winterton [17]
(10)
hcb ¼
Gungor and Winterton [5]
hb ¼ hl K where hl is given by Eq. (6) and K is given by Eq. (11):
Authors
Dittus and Boelter [3]
97
htp ¼ Enew hl E ¼ 1 þ 3000Bo0:86 þ 1:12
X 1X
0:75
rL rV
0:41
(8)
K ¼ 4717 Bo1:24
xexit 1 xexit
0:3 (11)
The effect of heat flux on nucleate boiling is characterized by the Boiling number, Thome [18], Bo is given by Eq. (12).
Bo ¼
Qb G hfg
(12)
In this correlation, two contributions are represented: the forced convection one by hl, and nucleate one by the coefficient K. In Fig. 9, a comparison between the present correlation and the others data is presented, as one can see that the results obtained by the established correlation fit well the experimental data with dispersion equals to ±12%. The comparison with Jens and Lottes [16] correlation gives a dispersion equals to ±25%, where, the correlation gives a good agreement with the Jens and Lottes [16] correlation for the heat transfer coefficient in the range of 2000e5000 (W/m2 C). The last comparison between the present correlation data and those given by Gungor and Winterton [5] correlation gives a dispersion equals to ±38%, as one can see that the two correlations are in agreement in the low values of heat transfer coefficient. Note that the established correlation is valid in the boiling heat flux from 9 to 137 kW/m2 and Reynolds number between 380 and 1522.
7. Conclusion (9)
the rectangular channel, the correlations are scarce. That's why we developed a new correlation to predict the mean heat transfer coefficient, which is important for industrial researchers Eq. (10) This correlation is based on the single phase heat transfer coefficient correlation developed by Dittus and Boelter [3], and the correcting factor “K”, see Eq. (11).
The plate heat exchangers have always attracted the researcher's attention, especially for their important exchangesurface. For the compactness criterion, the size of heat exchanger plays a very important role. In this sense, we have chosen to study a small heat exchanger which can be applied in specific applications, such as in oil-cooling circuits or micro-processor computers. A large database was constructed by varying several parameters (velocity and heat flux). The results of mean heat transfer coefficient were compared with those available in the literature. The experimental mean heat transfer coefficients were found between those of Gungor and Winterton [5] and Jens and Lottes
Fig. 8. Experimental boiling curves: (a) influence of velocity on boiling curve, (b) comparison of boiling curve with results given by Gungor and Winterton [5] and Jens and Lottes [16].
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Fig. 9. Comparison of the present correlation with others data: (a) versus present data, (b) Jens and Lottes [16] correlation, and (c) Gungor and Winterton [5] correlation.
[16]. The comparison with correlations of Gungor and Winterton [17] and Shah [4] showed that the experimental results are three times larger than the latter. That is logical, because the exchangesurface of the present rectangle channel is approximately three times greater than that of round tube for the same hydraulic diameter. To facilitate the prediction of the mean heat transfer coefficient in plate heat exchangers, a new correlation has been developed; it is based on the correlation of Dittus and Boelter [3] which represents the convective boiling contribution. This correlation is multiplied by a coefficient “K” which represents the nucleate boiling part, where, this last is based on the Bo number and exit vapor quality. This correlation gives a dispersion equals to 12% compared to experimental data, while, his validity varied between boiling heat flux from 9 to 137 kW/m2 and Reynolds number between 380 and 1522. Acknowledgment This work was supported by the General Directorate for Scientific Research and Technological Development of Algeria (PNR 08/ U160/658), for which the authors are very thankful. References [1] J.C. Chen, Correlation for boiling heat transfer to saturated fluids in convective flow, Ind. Eng. Chem. Process Des. Dev. 5 (1966) 322e329. [2] H. Forster, N. Zuber, Dynamics of vapor bubbles and boiling heat transfer, AIChE J. 1 (1955) 531e535. [3] F. Dittus, L. Boelter, University of California publications on engineering, Univ. Calif. Publ. Eng. 2 (1930) 371.
[4] M. Shah, Chart correlation for saturated boiling heat transfer: equations and further study, ASHRAE Trans.; (United States) 88 (1982). [5] K. Gungor, R. Winterton, A general correlation for flow boiling in tubes and annuli, Int. J. Heat Mass Transf. 29 (1986) 351e358. [6] A. Feldman, C. Marvillet, M. Lebouche, Nucleate and convective boiling in plate fin heat exchangers, Int. J. Heat Mass Transf. 43 (2000) 3433e3442. [7] B. Kim, B. Sohn, An experimental study of flow boiling in a rectangular channel with offset strip fins, Int. J. Heat Fluid Flow 27 (2006) 514e521. [8] H. Arima, J. Kim, A. Okamoto, Y. Ikegami, Local boiling heat transfer characteristics of ammonia in a vertical plate evaporator, Int. J. Refrig. 33 (2010) 359e370. s, M. Bourouis, A. Coronas, Flow boiling heat transfer of [9] F. T aboas, M. Valle ammonia/water mixture in a plate heat exchanger, Int. J. Refrig. 33 (2010) 695e705. boas, M. Valle s, M. Bourouis, A. Coronas, Assessment of boiling heat [10] F. Ta transfer and pressure drop correlations of ammonia/water mixture in a plate heat exchanger, Int. J. Refrig. 35 (2012) 633e644. [11] A. Zacarías, R. Ventas, M. Venegas, A. Lecuona, Boiling heat transfer and pressure drop of ammonia-lithium nitrate solution in a plate generator, Int. J. Heat Mass Transf. 53 (2010) 4768e4779. [12] H. Lee, S. Li, Y. Hwang, R. Radermacher, H.-H. Chun, Experimental investigations on flow boiling heat transfer in plate heat exchanger at low mass flux condition, Appl. Therm. Eng. 61 (2013) 408e415. [13] K. Koyama, H. Chiyoda, H. Arima, Y. Ikegami, Experimental study on thermal characteristics of ammonia flow boiling in a plate evaporator at low mass flux, Int. J. Refrig. 38 (2014) 227e235. [14] C. Wang, H. Wang, S. Wang, P. Gao, Experimental study of boiling incipience in vertical narrow rectangular channel, Ann. Nucl. Energy 66 (2014) 152e160. [15] S.J. Kline, F.A. McClintock, Describing Uncertainties in Single Sample Experiments, 1953. [16] W. Jens, P. Lottes, Analysis of Heat Transfer, Burnout, Pressure Drop and Density Date for High-pressure Water, Argonne National Lab, 1951. [17] K. Gungor, R. Winterton, Simplified general correlation for saturated flow boiling and comparisons of correlations with data, Chem. Eng. Res. Des. 65 (1987) 148e156. [18] J.R. Thome, Engineering Data Book III, Wolverine Tube Inc, 2004.