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Research Papers

# Experimental Investigation of Heat Transfer Coefficient and Correlation Development for Subcooled Flow Boiling of Water–Ethanol Mixture in Conventional ChannelOPEN ACCESS

[+] Author and Article Information
B. G. Suhas

Mechanical Engineering Department,
National Institute of Technology Karnataka,
Srinivasanagara, Surathkal,
Mangalore, Karnataka 575025, India
e-mail: suhas_bg@yahoo.co.in

A. Sathyabhama

Mechanical Engineering Department,
National Institute of Technology Karnataka,
Srinivasanagara, Surathkal,
Mangalore, Karnataka 575025, India
e-mail: bhama72@gmail.com

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received April 9, 2016; final manuscript received January 21, 2017; published online April 19, 2017. Assoc. Editor: Wei Li.

J. Thermal Sci. Eng. Appl 9(4), 041003 (Apr 19, 2017) (11 pages) Paper No: TSEA-16-1089; doi: 10.1115/1.4036202 History: Received April 09, 2016; Revised January 21, 2017

## Abstract

In this present work, bubble dynamics of subcooled flow boiling in water–ethanol mixture is investigated through visualization using a high-speed camera in horizontal rectangular channels. The heat transfer coefficient of water–ethanol mixture during subcooled flow boiling is determined for various parameters like heat flux, mass flux, and channel inlet temperature. The effect of bubble departure diameter on heat transfer coefficient is discussed. A correlation is developed for subcooled flow boiling Nusselt number of water–ethanol mixture. The parameters considered for correlation are grouped as dimensionless numbers by Buckingham $π$-theorem. The present correlation is compared with the experimental data. The mean absolute error (MAE) of Nusselt number of water–ethanol mixture calculated from the experimental data and those predicted from the present correlation is 10.39%. The present correlation is also compared with the available literature correlations developed for water. The MAE of Nusselt number of water predicted from the present correlation and those predicted with Papel, Badiuzzaman, Moles–Shaw, and Baburajan correlations is 41%, 19.61%, 29.9%, and 43.1%, respectively.

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## Introduction

Boiling of binary and multicomponent mixtures is widely applicable in chemical, refrigeration, air-conditioning, and air separation industries [1,2]. Applications of flow boiling are observed in refrigeration, heat exchangers, automobile cooling, and electronic cooling systems [3]. Exact value of heat transfer coefficient of the fluids used in such applications is required for proper design of these systems. This can be determined by conducting experiments. Since experiments are expensive and tedious, alternate method is to use correlations to predict heat transfer coefficient. The two types of correlations are empirical correlation and mechanism-based correlation [4]. The empirical correlation is obtained by fitting the curves, which gives an explicit relation between several parameters [5] The mechanism-based correlation or mechanistic model tries to incorporate the thermophysical properties, thermodynamic properties, and physics involved in the boiling phenomena [6]. Few correlations are available for saturated boiling of mixtures. But the correlations are not available for subcooled flow boiling region of mixtures. Subcooled boiling heat transfer coefficient correlation for water and ethyl alcohol was developed based on experimental data obtained for diameter varying between 5 and 7 mm. It was found that the correlation predicts the experimental values with a maximum deviation of ±16% [7]. Subcooled boiling heat transfer coefficient correlation was developed by different sets of nondimensional numbers for water, hydrocarbons, cryogenic fluids, and refrigerants which compared well with the experimental data [8]. Saturated boiling heat transfer coefficient correlation was developed for water and ethylene glycol in vertical and horizontal tubes. The mean deviation between the calculated and measured boiling heat transfer coefficient was 21.4% [9].

The present work is aimed at obtaining correlation for subcooled flow boiling Nusselt number of water–ethanol mixture. The water ethanol mixture can be used in cooling of hybrid electric vehicle battery module when powered by battery and the same mixture can also be used for fumigation process when powered by fuel. The heat generation rate for these batteries during charging is at an average of 20 W per cell and may peak up to 50 W per cell [10]. This increases the temperature of the battery cells approximately to 70–80 °C. Higher temperature of the batteries will lead to chemical breakdown and eventually leads to malfunction. Hence, the cooling of the battery module is necessary. The cold plate, which acts as a conductive member, is placed above the battery module and fluid is passed through this plate. The liquid undergoes subcooled boiling when it passes through the cold plate. Therefore, to design the cold plate, knowledge of heat transfer coefficient of this mixture is essential.

The experiment is conducted to find the subcooled flow boiling heat transfer coefficient of water–ethanol mixture for various parameters such as heat fluxes (from 90.4 kW/m2 to 133.47 kW/m2), mass fluxes (from 76.67 kg/m2 s to 228.33 kg/m2 s), inlet temperatures (303 K, 313 K, and 323 K), and volume fractions of ethanol (0%, 25%, 50%, 75%, and 100%). The visualization is carried by high-speed camera and bubble departure diameter is measured. The relation between the heat transfer coefficient and bubble departure diameter is discussed. The new correlation is developed by grouping the thermophysical and thermodynamic properties of water, water–ethanol mixture, and ethanol. Input parameters such as heat flux and velocity are grouped into nondimensional numbers by Buckingham $π$-theorem. The thermodynamic and thermophysical properties correspond to the experimental fluid temperature at the channel exit. The accuracy of the correlation is tested by comparing with the experimental data.

The present section contains the literature review which provides the motivation and background for the research work followed by the objective. Section 2 addresses the experimental test facility and the procedure followed to conduct the experiment. The experimental uncertainty is also mentioned in this section. Section 3 presents the experimental results of heat transfer coefficient for various ethanol volume fractions. The effect of bubble departure diameter on heat transfer coefficient is also discussed in this section. The procedure followed to develop the new correlation and the significance of dimensionless group on heat transfer coefficient is explained. Section 4 draws the conclusion from the present work followed by references.

## Methodology

###### Experimental Setup and Procedure.

The schematic diagram of experimental test setup is shown in Fig. 1. The experimental test setup is a closed loop having rectangular aluminum block consisting of two rectangular channels, condenser coil dipped in ice water bath, reservoir, pump with variable flow rate, and preheater. The aluminum block consisting of two channels of 10 mm (width) × 10 mm (height) × 150 mm (length) is shown in Fig. 2. The two cartridge heaters are inserted inside the aluminum block. Heat loss is prevented by providing mineral wool as insulating material. The wall temperatures are measured by means of thermocouples. The inlet and outlet fluid temperatures of the channel are also measured by thermocouples. The temperature reading is obtained in the temperature indicator panel. The high-speed camera is used for flow visualization. Table 1 shows the equipments used in the present experiment.

Figure 3 shows the thermocouples arrangement in the cold plate to measure wall temperature and to calculate heat flux. The first set of five thermocouples (T11, T12, T13, T14, and T15) is placed 2 mm below the channel in a row. The second set of five thermocouples (T21, T22, T23, T24, and T25) are placed 20 mm below the first row of thermocouples. The distance between each thermocouple in a row is 25 mm. Two cylindrical cartridge heaters are placed 40 mm below the channels.

Due to the possibility of solubility of air in water and ethanol, degassing is done for around thirty minutes before commencing the experiment. The liquid is preheated and pumped through the test setup. The heat is supplied to the channel to boil the liquid. The liquid after getting cooled in the condenser coil enters the reservoir. The experiment is conducted after the degassing procedure.

The steps followed during the experiment are listed below:

1. (1)Fill the water in the reservoir.
2. (2)Set the mass flow rate of the liquid and fix the channel inlet temperature by temperature controller in the preheater.
3. (3)Set a heat input value to the channel. The heat input value must maintain the wall temperature of the channel above the inlet temperature of the liquid.
4. (4)Note down the bottom wall temperature of the channel and outlet temperature of the fluid when the bottom wall temperature of the channel reaches steady state and simultaneously capture the flow by means of high-speed camera.
5. (5)Change the volume flow rate and repeat step 4. Increase the volume flow rate so that the laminar flow is maintained.
6. (6)Change the heat input value and repeat step 5. These steps are repeated upto subcooled boiling region (before attaining saturation state).
7. (7)Repeat step 3 to step 6 for two different values of inlet temperatures of the fluid.
8. (8)Repeat step 2 to step 7 for 25%, 50%, 75%, and 100% ethanol volume fractions.

Flow visualization is carried out to understand the phenomena of heat transfer during the subcooled flow boiling of the mixture. The bubble departure diameter is measured and its relation with heat transfer coefficient is discussed. The bubble departure diameter is measured in following steps by image processing tool in lab view vision builder software.

The bubble departure diameter is expressed in the dimensionless form as given by [11,12] Display Formula

(1)$r+=rB2/A$

where $A=(bΔTfhfgρv/Tsatρl)0.5$, $b=π/7$, $B=((12/π)Ja2αl)0.5$, and r is the experimentally determined bubble departure radius.

###### Data Reduction.

Bottom wall temperature of the channel is calculated by temperature gradient between the first row and second row of aluminum block. Fourier's law of heat conduction is applied to calculate the heat flux from the measured values of temperature gradient and known value of thermal conductivity Display Formula

(2)$q″=−kdTdx$

The heat flux is calculated by substituting the values of thermal conductivity of aluminum, temperature gradient in Eq. (2) as shown by Display Formula

(3)$q″=−k(Tsr−Tfr)(Xsr−Xfr)$

The heat flux is assumed to be same for the bottom wall of the channel as the first row because it is very near to the first rows of thermocouples (i.e., 2 mm). The wall temperature is calculated by Display Formula

(4)$TW=−q″k(Xw−Xfr)+Tfr$

The heat transfer coefficient is calculated by Eq. (4) from the calculated values of heat flux, calculated values of wall temperatures, and measured values of outlet temperature. The average of five readings of wall temperatures is calculated to determine the difference between the wall and outlet fluid temperature Display Formula

(5)$h=q″(Tw−Tf)$

###### Uncertainties.

According to International Bureau of weights and measures and International organization of standards, uncertainty of measured parameters can be calculated using root-sum-square (RSS) given by Display Formula

(6)$ωmi=ωmiresolution2+ωmiconversion2+ωmicalibration2+s2σmi2$

After determining the uncertainty of measured parameters, the uncertainties of calculated parameters are determined by McClintock and Kline method [13,14] Display Formula

(7)$ωcp2=∑i=1n(∂f∂xi)2ωxi2$

Table 2 shows the uncertainties of measured and calculated parameters.

## Results and Discussions

The experiments are conducted for various values of heat flux, mass flux, inlet temperature, and ethanol volume fractions. About 478 experimental runs are carried out in the present study. These include 122 data for pure water, 288 data for three different compositions of binary mixtures, and 68 data for pure ethanol. The heat transfer coefficient is determined for various values of heat flux, mass flux, various inlet temperatures, and volume fractions of ethanol.

###### Experimental Results.

Figure 4 shows the variation of heat transfer coefficient with ethanol volume fraction for various inlet temperatures and constant heat flux of 90.4 kW/m2. This particular value of heat flux is so chosen that the subcooled boiling takes place for both water and ethanol. If the heat flux is lower than 90.4 kW/m2, subcooled boiling of water will not commence; instead, it will be in forced convective region. If the heat flux is higher than 90.4 kW/m2, saturated boiling of ethanol will be initiated.

The heat transfer coefficient decreases with increase in ethanol volume fraction except for 25% ethanol volume fraction. The heat transfer coefficient of ethanol is slightly higher than that of mixture with 75% ethanol volume fraction. Heat transfer coefficient of ethanol is lower than that of pure water [15]. This is observed in the investigated range of mass flux and inlet fluid temperature of the channel. At 25% volume fraction, maximum difference between dew point temperature and bubble point temperature is observed, and at 75% ethanol volume fraction minimum difference between dew point temperature and bubble point temperature is observed as shown in Fig. 5. The maximum difference between dew point and bubble point temperatures indicates that there is a widest range of liquid vapor coexisting region [16]. During the onset of boiling, the more volatile component of the mixture near the channel wall surface may induce concentration and temperature gradients in the microlayer region along the vapor–liquid interface. The induced gradients may cause the Marangoni force to pull the bulk liquid toward the liquid vapor interface causing microlayer agitation and thus increasing the heat transfer coefficient.

Figure 4 also depicts that an increase in channel inlet temperature decreases the heat transfer coefficient. This is attributed to (i) increase in thermal boundary layer and (ii) decrease in thermal conductivity and thermal capacity of the liquid with increase in temperature. The thermal conductivity and thermal capacity of ethanol is lower than that of water. Molar entropy of vaporization of ethanol is marginally above water. The entropy is due to the molecules that are held together in liquid by polar attractions and hydrogen bonding. Hence, more energy is required to pull these molecules of liquid. The molar latent heat of vaporization is slightly greater which actually results in higher heat transfer coefficient of ethanol [17]. But Trouton's rule states that ethanol has lower molar enthalpy of vaporization when compared to water due to lower boiling point of ethanol [18]. This decreases active nucleation sites upon heated surfaces of the channel, thus reducing the heat transfer coefficient of mixture than that of pure water. The addition of ethanol to water delays the departure of bubbles from the site causing an increase in bubble departure diameter. Delay in departure increases the time gap between the first bubble departure and next bubble nucleation resulting in decrease of active nucleation sites or bubble formation. This decreases the heat transfer coefficient of the mixture. So, when the volume fraction of the ethanol increases, the bubble departure diameter must increase and active nucleation site must decrease. But the bubble formation and bubble departure diameter size obtained in the present experiment are contrary for mixture with 25% and 75% ethanol volume fractions. Figures 6(a)6(e) show the bubble formation for pure water, water–ethanol mixture, and ethanol. The active nucleation sites are highest for 25% and least for 75% ethanol volume fraction as shown in Figs. 6(b) and 6(d). The size of the bubble departure diameter is highest for 75% ethanol volume fraction and lowest for 25% ethanol volume fraction as shown in Fig. 7. The reasons for these observations can be explained by force balance approach. For mixture with 25% ethanol volume fraction, the surface tension force between the solid–vapor phase decreases and the surface tension force between the liquid–vapor interfaces increases. The force developed due to surface tension between vapor–liquid dominates the force developed due to unsteady bubble growth and quasi-static drag force which are parallel to flow direction. The surface tension force between the liquid–vapor interfaces is larger when compared to other volume fractions, which eventually lead to faster departure of the bubble and thus increases the bubble formation on heated surface of the channel. It is observed that mixture with 75% ethanol volume fraction is having higher bubble departure and larger bubble formation when compared with that of ethanol. This may be due to the reason that the mixture has lower heat transfer coefficient than the pure component, because of the presence of local vapor of the lower boiling component in the mixture [19].

###### Correlation Development.

To arrive at a correlation for subcooled boiling heat transfer, it is reasonable to start from physical properties and parameters that characterize the heat transfer process based on some assumptions. Following are the assumptions made for developing new correlation:

• The present experiment is carried out for constant hydraulic diameter, but the hydraulic diameter is chosen as a geometric property for repeating variable.

• Effect of inlet temperature and volume fractions is considered from the thermodynamic properties and thermophysical properties, which correspond to the average of fluid temperature at the channel exit and channel wall temperature.

• The dimensionless parameters, which do not contribute for reducing mean absolute error (MAE) represented by Eq. (8) are neglected Display Formula

(8)$MAE=1n∑|theoretical values−experimental valuestheoretical values|×100$

Mixture properties like liquid density, specific heat, and thermal diffusivity are calculated by using simple mixing rule. Thermal conductivity, liquid viscosity, and surface tension are calculated by Filippov, McLaughlin equation, and Macleod–Sugden correlation [2022] represented in Eqs. (9), (10), and (11), respectively, Display Formula

(9)$km−kikj−ki=Cmfj2−mfi(1−C)$
Display Formula
(10)$ln(μm)=xilnμi+xjlnμj$
Display Formula
(11)$σm1/4=Paj(ρlmxj−ρlvyj)$

If the value of mixture constant C in Eq. (3) is not available, then C can be chosen as 0.72 [23].

The subcooled flow boiling heat transfer coefficient is a function of $ρ,v,dh,μ,k,ΔTfw,Cp,hfg,σs and q″$, i.e., h = f$(μ,ρ,v,dh,k,ΔTfw,Cp,hfg,q″,σs)$. The properties and parameters chosen are combined as dimensionless numbers by Buckingham's $π$-theorem. These dimensionless numbers are

$π1=kΔTfwρvsdh, π2=Cp ΔTfwv2, π3=σsρv2dh, π4=hfgv2, π5=q″ρvs, π6=hTΔfwρvs, and π7=μρvdh$

These dimensionless numbers can be expressed as $π6=f(π1,π2,π3,π4,π5)$. The independent dimensionless numbers ($π1,π2,π3,π4$, and $π5$), which significantly influence the dependent dimensionless number $(π6)$, are chosen. $π7$ is not considered since its value is negligible when compared to $π6$. The correlation represented by Eq. (14) is obtained by regression analysis as given in steps below.

• In the first step for each of the independent dimensionless number, an Eq. (12) is formed Display Formula

(12)$π6=a1π1b1, π6=a2π2b2, π6=a3π3b3, π6=a4π4b4, and π6=a5π5b5$

The constants ($a1,a2,a3,a4,a5$, $b1,b2,b3,b4$, and $b5$) are determined by method of ordinary least square.

• In the second step, independent dimensionless number ($π2$) is introduced in $π6=a1π1b1$ as represented by Eq. (13) and MAE is calculated Display Formula

(13)$π6=a6π1b1π2b2$

• In the third step, the MAE is reduced by introducing the next set of independent dimensionless numbers in Eq. (9), and correlation for heat transfer coefficient is represented by Eq. (10).

Figures 8(a)8(e) shows the variation of $π6$ due to addition of independent dimensionless numbers. MAE is 98.7% for $π6$ versus $π1$. MAE is 92.5% for $π6$ versus $π1π2$, 73.6% for $π6$ versus $π1π2π3$, 51.5% for $π6$ versus $π1π2π3π4$ and 9.2% for $π6$ versus $π1π2π3π4π5$. It is found that the terms $π3=σs/ρv2dh,π4=hfg/v2 and π5=q″/ρv3$ are key factors as they reduce MAE. This shows that the surface tension force, latent heat of vaporization, and heat flux are the dominating factors in the present correlation. The term $π5=q″/ρv3$ is most important because MAE reduced from 51.5% to 9.2%

Display Formula

(14)$hΔTfwρv3=1365.8(kΔTfwρv3dh)0.557(CpΔTfwv2)0.2034(σsρv2dh)0.0878(hfgv2)0.2(q″ρv3)0.4699$

$π2=CPΔTfw/v2$ is neglected because reduction in MAE is 6.2%. $π3=σs/ρv2dh$ is called $(1/channel Weber number)$. The effect of surface tension on fluid flow and heat transfer also depends upon the size of the channel [24]. When multiplied and divided by $m/2$ (where m is mass of liquid) in $π4=hfg/v2$, a nondimensional number called $(0.5/two-phase Eckert number)$ is obtained. Eckert number expresses the relation between overall heat transfer in the channel and fluid kinetic energy. Equation (15) is obtained by simplifying Eq. (14)Display Formula

(15)$hΔTfwρv3=1365.8(kΔTfwρv3dh)0.557(1Wech)0.0878(0.5Ertp)0.2(q″ρv3)0.4699$
Display Formula
(16)$hΔTfwρv3=1189(1Wech)0.0878(1Ertp)0.2(kΔTfwρv3dh)0.557(q″ρv3)0.4699$

$hΔTfw/ρv3$ and $(kΔTfw/ρv3dh)0.557$ in Eq. (14) are written as $q″/ρv3$ and $(q″/ρv3Nuscb)0.557$ where $kΔTfw/dh=hΔTfw/Nuscb=q″/Nuscb$Display Formula

(17)$q″ρv3=1189(1Wech)0.0878(1Ertp)0.2(q″ρv3Nuscb)0.557(q″ρv3)0.4699$
Display Formula
(18)$Nuscb−0.557=1189(1Wech)0.0878(1Ertp)0.2(q″ρv3)0.557(q″ρv3)0.4699(ρv3q″)$
Display Formula
(19)$Nuscb−0.557=1189(1Wech)0.0878(1Ertp)0.2(q″ρv3)0.027$
Display Formula
(20)$Nuscb=3.32(1Wech)0.105(1Ertp)0.359(q″ρv3)0.048$

$(q″/ρv3)0.048$ in Eq. (15) is written as $(hfgq″/hfgρv3)0.048=(q″hfg/ρvhfgv2)0.048=(0.5Bo/Ertp)0.048$, where $Bo=q″/ρvhfg$ is called as Boiling number.

Final form of the present correlation is expressed by Display Formula

(21)$Nuscb=3.211(1Wech)0.105(1Ertp)0.407(Bo)0.048$

###### Significance of Dimensionless Number $π3=σs/ρv2dh$.

Weber number plays an important role in flow boiling heat transfer [5]. When the bubble is formed in the active nucleation sites, it coheres at the surface of channel wall due to surface tension between the channel wall–vapor interfaces. Surface energy of channel wall tends to pull the molecules of local vapor, which is in the form of bubbles causing wetting of the channel surface known as wettability. The wetting of surface is dependent on the contact angle between the channel wall surface (solid–liquid interface) and the bubble. When contact angle increases, the wettability decreases and the bubble departs from the surface.

At higher inertial force and heat flux, the surface tension between the channel wall and the vapor decreases due to decrease in surface energy. The surface tension in the vapor–liquid interface increases in order to overcome the loss of surface tension between channel wall–vapor interfaces. This attracts the surface of the bubble toward the liquid causing an increase in vapor–liquid interface pressure and buoyancy of the bubble. The role of inertial force of the fluid is high for convective heat transfer. In subcooled boiling heat transfer, the convective heat transfer is not significant when compared to heat transfer due to agitation and evaporation [25]. Therefore, the inertial force is not significant for overall heat transfer in the subcooled boiling region and the surface tension force dominates over the inertial force of the liquid. Due to the formation of the bubbles, the overall heat transfer is reduced because of thin vapor layer of bubbles providing thermal resistance to heat transfer. Hence, the surface tension of the vapor–liquid interface must be higher than the inertial force of the liquid for bubble to depart at faster rate. Departed bubble is an energy carrier and increases the evaporative heat transfer. The adjacent layers of liquid molecules fill the site from where the bubble has departed.

###### Significance of Dimensionless Number $π4=hfg/v2$.

The dimensionless number $π4=hfg/v2$ can be represented in the form $π4=0.5/Ertp$. Eckert number is the ratio of overall heat transfer to the kinetic energy of the liquid [26]. When the wall temperature exceeds the saturation temperature of the liquid, the heat added will acquire sufficient energy to overcome the intermolecular forces of the molecules. This causes change of phase of local liquid. The clusters of molecules escape as vapor in the form of bubbles as shown in Figs. 9(a)9(d). This increases the molar latent heat of vaporization because more heat is supplied to break the intermolecular forces of liquid. Increased latent heat increases the wall temperature and thus decreases the difference between wall temperature and fluid temperature.

###### Significance of Dimensionless Number $π5=q″/ρv3$.

$q″/ρv3$ is expressed as the ratio of Boiling number to two-phase Eckert number $(0.5Bo/Ertp)$. Boiling number is defined as the ratio of heat flux to heat of evaporation. When heat flux increases, the active nucleation sites also increase. Addition of new nucleation sites influences the rate of heat transfer from the channel wall surface. In the earlier studies, it is noted that the density of active nucleation sites increases approximately as the square of the heat flux. Isolated bubbles are formed on active nucleation sites during nucleate boiling. After bubble inception, the superheated liquid layer, which is pushed outward, mixes with the subcooled liquid. The bubbles act like a pump in removing hot liquid from the surface and replacing it with subcooled adjacent liquid [27]. The heat flux is considered by combining the effect of transient conduction around nucleation sites and microlayer evaporation below the bubbles.

At higher velocity, the fluid kinetic energy increases and the active nucleation sites reduce because the heat is carried away by convection due to decrease in agitation and evaporation. This shows that increase in heat transfer is not much significant and the heat flux has a major role in heat transfer than the velocity. Hence, $π5=q″/ρv3$ is significant in heat transfer mechanism. The latent heat of vaporization and surface tension are governed by heat flux. Hence, it can be concluded that the heat flux is more significant when compared to surface tension and latent heat of vaporization.

###### Variation of Significant Dimensionless Number With Ethanol Volume Fraction.

The variation of dimensionless number $π3=σs/ρv2dh$ with ethanol volume fraction is shown in Fig. 10. It is seen that $π3$ decreases with increase in ethanol volume fraction. During subcooled flow boiling, surface tension between the local vapor and adjacent fluid molecules decreases with an increase in ethanol volume fraction. The density of ethanol is lower than that of water and the density of mixture decreases with an increase in ethanol volume concentration. It is observed that the decrease in density is negligible when compared to decrease in surface tension and hence $π3$ decreases.

The kinetic energy of the mixture decreases with increase in ethanol volume fraction due to lower values of density of the mixture. The latent heat of vaporization of ethanol is lower than that of water. Addition of ethanol to water lowers the latent heat of vaporization of the mixture than that of pure water. So, $π4=hfg/v2$ decreases when ethanol is added to water as shown in Fig. 11. The lower values of density of the mixture reduce the inertial force which increases $π5=q″/ρv3$ with ethanol volume fraction as shown in Fig. 12.

## Validation

The present correlation is validated with experimental data for water–ethanol mixture as shown in Fig. 13. The MAE of Nusselt number of water calculated from the experiment and those predicted from the present correlation is 10.39% in the investigated range of heat flux, mass flux, channel inlet temperature, and ethanol volume fractions. It can be observed that 71.69% of experimental data lies within error band of $±15%$ and 37.08% of experimental data lies within error band of $±10%$.

The present correlation is also validated with the available literature correlations for water. Papel, Badiuzzaman, Moles et al., and Shaw and Baburajan et al. developed dimensionless heat transfer coefficient correlations for water [2832]. Papel developed dimensionless subcooled boiling correlation Eq. (22) based on his experimental results. With water used as test fluid, heat fluxes were varied from 1.33 to 2.62 Mw/m2, mass fluxes were varied from 1130 to 3314 kg/m2 s and pressure were varied from 0.26 to 1.25 MPa. Display Formula

(22)$NutpNus=90BoJa−0.84(ρgρl)0.7$

Badiuzzaman modified the Papel correlation by incorporating the degree of subcooling as shown by Display Formula

(23)$NutpNus=178Bo0.75Ja−0.9(ρgρl)−0.06(ΔTsubTsat)0.45$

Moles and Shaw also modified Papel correlation by incorporating the effect of Prandtl number as shown by Display Formula

(24)$NutpNus=78.5Bo0.67Ja−0.5(ρgρl)−0.03Pr0.45$

Baburajan developed the subcooled boiling correlation for hydraulic diameters of 5.5 mm, 7.5 mm, and 9.5 mm as shown by Eq. (25). The mass fluxes were varied from 450 to 935 kg/m2 s and degree of subcooling were 29 °C, 50 °C, and 70 °C Display Formula

(25)$NutpNus=267Bo0.86Ja−0.6Pr0.23$

The single-phase term is on the right-hand side of Eqs. (22)(25). Dittus Boelter equation is chosen to solve the single-phase term in correlation and available literature correlations. Figures 14(a)14(d) show the comparison of Nusselt number of water predicted using the present correlation and those predicted with available literature correlations.

• 70.71% of predicted data lies within $±50%$ error when compared with those predicted using Papel correlation.

• 75.38% of predicted data lies within $±30%$ error when compared with those predicted using Badiuzzaman correlation.

• 67.69% of predicted data lies within $±40%$ error when compared with those predicted using Moles–Shaw correlation.

• 66.15% of predicted data lies within $±50%$ error when compared with those predicted using Baburajan correlation.

The MAE of Nusselt number for water predicted using the present correlation and those predicted with Papel, Badiuzzaman, Moles–Shaw, and Baburajan correlations are 41%, 19.61%, 29.9%, and 43.1%, respectively. The large deviation is observed because the correlations were developed for high heat fluxes and mass fluxes of water. The predictions from Badiuzzaman correlation compare well with those predicted from present correlation. This is attributed to the presence of degree of subcooling term in the Badiuzzaman correlation. At higher degree of subcooling, the local vapor causes activation of more number of nucleation sites. More number of bubbles moving at a relatively higher velocity and refilling of the sites by adjacent liquid layer create agitation in the liquid.

## Conclusions

The experiment is conducted to find the subcooled flow boiling heat transfer coefficient of water–ethanol mixture for various parameters such as heat fluxes (from 90.4 kW/m2 to 133.47 kW/m2), mass fluxes (from 76.67 kg/m2 s to 228.33 kg/m2 s), inlet temperatures (303 K, 313 K, and 323 K), and volume fractions of ethanol (0%, 25%, 50%, 75%, and 100%). Visualization is carried by using high-speed camera. Correlation is developed for subcooled flow boiling of water–ethanol mixtures based on experimental data. The following conclusions are made from the present study.

• Heat transfer coefficient decreases with increase in ethanol volume fraction. At 25% ethanol volume fraction, it is observed that the heat transfer coefficient is marginally higher than that of pure water. The heat transfer coefficient of ethanol is slightly higher than that of 75% ethanol volume fraction.

• The active nucleation sites increases for 25% ethanol volume fraction and reduces for 75% volume fraction when compared with that of pure water, ethanol, and 50% ethanol volume fraction.

• The bubble departure diameter reduces for 25% volume fraction and increases for 75% volume fraction when compared with that of pure water, ethanol, and 50% ethanol volume fraction.

• It is found that the terms $π3=σs/ρv2dh,π4=hfg/v2$, and $π5=q″ρv3$ are the key factors as they contribute to reduce MAE. The term $π5=q″/ρv3$ is most important because MAE reduced from 51.5% to 9.2%.

• The MAE of Nusselt number of water–ethanol mixture calculated from the experimental data and those predicted from the present correlation is 10.39% in the investigated range of heat flux, mass flux, channel inlet temperature, and ethanol volume fraction. It can be observed that 71.69% of experimental data lie within $±15%$ and 37.08% of experimental data lies within error band of $±10%$.

• The present correlation developed for water ethanol mixture is compared with the available literature correlations developed for water. The MAE of Nusselt number for water predicted using the present correlation and those predicted with Papel, Badiuzzaman, Moles–Shaw, and Baburajan correlations are 41%, 19.61%, 29.9%, and 43.1%, respectively.

• The Badiuzzaman correlation which consists of subcooling term agrees well with the present correlation.

## Nomenclature

• Bo =

boiling number

• Cp =

specific heat (kJ/kg K)

• Dh =

hydraulic diameter (m)

• $Ertp$ =

two-phase Eckert number

• h =

heat transfer coefficient (kW/m2 K)

• H =

channel height (m)

• hfg =

latent heat of vaporization (kJ/kg)

• Ja =

Jakob number

• $k$ =

thermal conductivity (kW/m K)

• m =

mass of the liquid

• $mf$ =

mass fraction

• n =

experimental data points

• Nu =

Nusselt number

• P =

pressure (N/m2)

• Pa =

Parachor of high boiling component

• $Pr$ =

Prandtl number

• Q =

overall heat transfer (kW)

• $q″$ =

heat flux (kW/m2)

• r =

• Re =

Reynolds number

• T =

temperature (K)

• v =

velocity (m/s)

• x =

mole fraction in liquid phase

• X =

position (m)

• y =

mole fraction in vapor phase

• $ΔT$ =

temperature difference (K)

Greek Symbols
• $μ$ =

dynamic viscosity (kg/m s)

• $ρ$ =

density (kg/m3)

• $σs$ =

surface tension (N/m)

• $ω$ =

uncertainty

Subscripts
• b =

bubble point

• Corr =

correlation

• cp =

calculated parameter

• d =

dew point

• Exp =

experimental

• fr =

first row

• fw =

wall and fluid

• i =

first component of mixture

• ip =

independent parameter

• j =

second component of mixture

• l =

liquid

• lm =

liquid mixture

• lv =

vapor mixture

• m =

mixture

• Pr corr =

present correlation

• s =

single phase

• sat =

saturated

• scb =

subcooled boiling

• sr =

second row

• sub =

subcooling

• W =

wall

• $σ$ =

standard deviation

## References

Peyghambarzadeh, S. M. , Jamialahmadi, M. , Alavi Fazel, S. A. , and Azizi, S. , 2009, “ Saturated Nucleate Boiling to Binary and Ternary Mixtures on Horizontal Cylinder,” Exp. Therm. Fluid Sci., 33(5), pp. 903–911.
Kandlikar, S. G. , 1998, “ Boiling Heat Transfer With Binary Mixture: Part-I—A Theoretical Modeling for Pool Boiling,” ASME J. Heat Transfer, 120(2), pp. 380–387.
Kouidri, A. , Madani, B. , and Roubi, B. , 2015, “ Experimental Investigation of Flow Boiling in Narrow Channel,” Int. J. Therm. Sci., 98, pp. 90–98.
Mahmouda, M. M. , and Karayiannis, T. G. , 2013, “ Heat Transfer Correlation for Flow Boiling in Small to Micro Tubes,” Int. J. Heat Mass Transfer, 66, pp. 553–574.
Kandlikar, S. G. , 2004, “ Heat Transfer Mechanisms During Flow Boiling in Microchannels,” ASME J. Heat Transfer, 126(1), pp. 8–16.
Paz, M. C. , Conde, M. , Suarez, E. , and Concheiro, M. , 2015, “ On the Effect of Surface Roughness and Material on the Subcooled Flow Boiling of Water: Experimental Study and Global Correlation,” Exp. Therm. Fluid Sci., 64, pp. 114–124.
Sarma, P. K. , Srinivas, V. , Sharmab, K. V. , Subrahmanyam, T. , and Kakac, S. , 2008, “ A Correlation to Predict Heat Transfer Coefficient in Nucleate Boiling on Cylindrical Heating Elements,” Int. J. Therm. Sci., 47(3), pp. 347–354.
Stephan, K. , and Abdelsalam, M. , 1978, “ Heat-Transfer Correlations for Natural Convection Boiling,” Int. J. Heat Mass Transfer, 23(1), pp. 73–87.
Gungor, K. E. , and Winterton, R. H. S. , 1986, “ A General Correlation for Flow Boiling in Tubes and Annuli,” Int. J. Heat Mass Transfer, 29(3), pp. 351–358.
Anthony, J. , and Li, Y. K. , 2011, “ Design Optimization of Electric Vehicle Battery Cooling Plates for Thermal Performance,” J. Power Sources, 196(23), pp. 10359–10368.
Zou, L. , 2010, “ Experimental Study on Subcooled Flow Boiling on Heating Surfaces With Different Thermal Conductivities,” Doctoral dissertation, University of Illinois at Urbana-Champaign, Champaign, IL, pp. 18–20.
Kim, M. H. , Lee, H. C. , Oh, B. D. , and Bae, S. W. , 2003, “ Single Bubble Growth in Saturated Pool Boiling on a Constant Wall Temperature Surface,” Int. J. Multiphase Flow, 29(12), pp. 1857–1874.
Kline, S. J. , and McClintock, F. A. , 1953, “ Describing Uncertainties in Single-Sample Experiments,” Mech. Eng., 75, pp. 3–8.
Callizo, C. M. , 2010, “ Flow Boiling Heat Transfer in Single Vertical Channels of Small Diameter,” Ph.D. thesis, Department of Energy Technology, Royal Institute of Technology, Stockholm, Sweden, pp. 47–49.
Sefiane, K. , Wang, Y. , and Harmand, S. , 2012, “ Flow Boiling in High-Aspect Ratio Mini- and Micro-Channels With FC-72 and Ethanol: Experimental Results and Heat Transfer Correlation Assessments,” Exp. Therm. Fluid Sci., 36, pp. 93–106.
Fu, B. R. , Tsou, M. S. , and Pan, C. , 2012, “ Boiling Heat Transfer and Critical Heat Flux of Ethanol–Water Mixtures Flowing Through a Diverging Microchannel With Artificial Cavities,” Int. J. Heat Mass Transfer, 55(5–6), pp. 1807–1814.
Green, J. A. , Irudayam, S. J. , and Henchman, R. H. , 2011, “ Molecular Interpretation of Trouton's and Hildebrand's Rules for the Entropy of Vaporization of a Liquid,” J. Chem. Thermodyn., 43(6), pp. 868–872.
Lyklema, J. , 1999, “ The Surface Tension of Pure Liquids Thermodynamic Components and Corresponding States, Colloids and Surfaces,” Physicochem. Eng. Aspects, 156(1–3), pp. 413–421.
Kandlikar, S. G. , 1998, “ Boiling Heat Transfer With Binary Mixture: Part-II—A Theoretical Modeling for Pool Boiling,” National Heat Transfer Conference, Baltimore, Maryland, Aug. 8–12.
Ratcliff, G. A. , and Khan, M. A. , 1971, “ Prediction of the Viscosities of Liquid Mixtures by a Group Solution Model,” Can. J. Chem. Eng., 49(1), pp. 125–129.
Deam, J. R. , and Mattox, R. N. , 1970, “ Interfacial Tension in Hydrocarbon Systems,” J. Chem. Eng. Data, 15(2), pp. 216–222.
Flippov, L. P. , 1968, “ Research of Liquid Thermal Conductivity at Moscow University,” Int. J. Heat Mass Transfer, 11(2), pp. 331–345.
Reid, R. C. , Prausnitz, J. M. , and Sherwood, T. K. , 1977, The Properties of Gases and Liquids, McGraw-Hill, New York, p. 533.
Peakall, J. , and Warburton, J. , 1996, “ Surface Tension in Small Hydraulic River Models—The Significance of the Weber Number,” J. Hydrol., 35(2), pp. 199–212.
Basu, N. , Vijay, K. D. , and Gopinath, R. W. , 2005, “ Wall Heat Flux Partitioning During Subcooled Flow Boiling: Part 1—Model Development,” ASME J. Heat Transfer, 127(2), pp. 131–140.
Gschwendtner, M. R. , 2004, “ The Eckert Number Phenomenon: Experimental Investigations on the Heat Transfer From a Moving Wall in the Case of a Rotating Cylinder,” Heat Mass Transfer, 40(6–7), pp. 551–559.
Kandlikar, S. G. , Shoji, M. , and Dhir, V. , 1999, Handbook of Phase Change, Taylor and Francis, New York, pp. 79–98.
Papel, S. S. , 1963, “ Subcooled Boiling Heat Transfer Under Forced Convection in a Heated Tube,” NASA Technical Report No. NASA-TN-D-1583.
Badiuzzaman, M. , 1967, “ Correlation of Subcooled Boiling Data,” Pak. Eng., 7, pp. 759–764.
Moles, F. D. , and Shaw, F. G. , 1972, “ Boiling Heat Transfer to Subcooled Liquids Under Condition of Forced Convection,” Trans. Inst. Chem. Eng., 50, pp. 76–84.
Yana, J. , Bia, Q. , Liua, Z. , Zhua, G. , and Caib, L. , 2015, “ Subcooled Flow Boiling Heat Transfer of Water in a Circular Tube Under High Heat Fluxes and High Mass Fluxes,” Fusion Eng. Des., 100, pp. 406–418.
Baburajan, P. K. , Bisht, G. S. , Gupta, S. K. , and Prabhu, S. V. , 2013, “ Measurement of Subcooled Boiling Pressure Drop and Local Heat Transfer Coefficient in Horizontal Tube Under LPLF Conditions,” Nucl. Eng. Des., 255, pp. 169–179.
View article in PDF format.

## References

Peyghambarzadeh, S. M. , Jamialahmadi, M. , Alavi Fazel, S. A. , and Azizi, S. , 2009, “ Saturated Nucleate Boiling to Binary and Ternary Mixtures on Horizontal Cylinder,” Exp. Therm. Fluid Sci., 33(5), pp. 903–911.
Kandlikar, S. G. , 1998, “ Boiling Heat Transfer With Binary Mixture: Part-I—A Theoretical Modeling for Pool Boiling,” ASME J. Heat Transfer, 120(2), pp. 380–387.
Kouidri, A. , Madani, B. , and Roubi, B. , 2015, “ Experimental Investigation of Flow Boiling in Narrow Channel,” Int. J. Therm. Sci., 98, pp. 90–98.
Mahmouda, M. M. , and Karayiannis, T. G. , 2013, “ Heat Transfer Correlation for Flow Boiling in Small to Micro Tubes,” Int. J. Heat Mass Transfer, 66, pp. 553–574.
Kandlikar, S. G. , 2004, “ Heat Transfer Mechanisms During Flow Boiling in Microchannels,” ASME J. Heat Transfer, 126(1), pp. 8–16.
Paz, M. C. , Conde, M. , Suarez, E. , and Concheiro, M. , 2015, “ On the Effect of Surface Roughness and Material on the Subcooled Flow Boiling of Water: Experimental Study and Global Correlation,” Exp. Therm. Fluid Sci., 64, pp. 114–124.
Sarma, P. K. , Srinivas, V. , Sharmab, K. V. , Subrahmanyam, T. , and Kakac, S. , 2008, “ A Correlation to Predict Heat Transfer Coefficient in Nucleate Boiling on Cylindrical Heating Elements,” Int. J. Therm. Sci., 47(3), pp. 347–354.
Stephan, K. , and Abdelsalam, M. , 1978, “ Heat-Transfer Correlations for Natural Convection Boiling,” Int. J. Heat Mass Transfer, 23(1), pp. 73–87.
Gungor, K. E. , and Winterton, R. H. S. , 1986, “ A General Correlation for Flow Boiling in Tubes and Annuli,” Int. J. Heat Mass Transfer, 29(3), pp. 351–358.
Anthony, J. , and Li, Y. K. , 2011, “ Design Optimization of Electric Vehicle Battery Cooling Plates for Thermal Performance,” J. Power Sources, 196(23), pp. 10359–10368.
Zou, L. , 2010, “ Experimental Study on Subcooled Flow Boiling on Heating Surfaces With Different Thermal Conductivities,” Doctoral dissertation, University of Illinois at Urbana-Champaign, Champaign, IL, pp. 18–20.
Kim, M. H. , Lee, H. C. , Oh, B. D. , and Bae, S. W. , 2003, “ Single Bubble Growth in Saturated Pool Boiling on a Constant Wall Temperature Surface,” Int. J. Multiphase Flow, 29(12), pp. 1857–1874.
Kline, S. J. , and McClintock, F. A. , 1953, “ Describing Uncertainties in Single-Sample Experiments,” Mech. Eng., 75, pp. 3–8.
Callizo, C. M. , 2010, “ Flow Boiling Heat Transfer in Single Vertical Channels of Small Diameter,” Ph.D. thesis, Department of Energy Technology, Royal Institute of Technology, Stockholm, Sweden, pp. 47–49.
Sefiane, K. , Wang, Y. , and Harmand, S. , 2012, “ Flow Boiling in High-Aspect Ratio Mini- and Micro-Channels With FC-72 and Ethanol: Experimental Results and Heat Transfer Correlation Assessments,” Exp. Therm. Fluid Sci., 36, pp. 93–106.
Fu, B. R. , Tsou, M. S. , and Pan, C. , 2012, “ Boiling Heat Transfer and Critical Heat Flux of Ethanol–Water Mixtures Flowing Through a Diverging Microchannel With Artificial Cavities,” Int. J. Heat Mass Transfer, 55(5–6), pp. 1807–1814.
Green, J. A. , Irudayam, S. J. , and Henchman, R. H. , 2011, “ Molecular Interpretation of Trouton's and Hildebrand's Rules for the Entropy of Vaporization of a Liquid,” J. Chem. Thermodyn., 43(6), pp. 868–872.
Lyklema, J. , 1999, “ The Surface Tension of Pure Liquids Thermodynamic Components and Corresponding States, Colloids and Surfaces,” Physicochem. Eng. Aspects, 156(1–3), pp. 413–421.
Kandlikar, S. G. , 1998, “ Boiling Heat Transfer With Binary Mixture: Part-II—A Theoretical Modeling for Pool Boiling,” National Heat Transfer Conference, Baltimore, Maryland, Aug. 8–12.
Ratcliff, G. A. , and Khan, M. A. , 1971, “ Prediction of the Viscosities of Liquid Mixtures by a Group Solution Model,” Can. J. Chem. Eng., 49(1), pp. 125–129.
Deam, J. R. , and Mattox, R. N. , 1970, “ Interfacial Tension in Hydrocarbon Systems,” J. Chem. Eng. Data, 15(2), pp. 216–222.
Flippov, L. P. , 1968, “ Research of Liquid Thermal Conductivity at Moscow University,” Int. J. Heat Mass Transfer, 11(2), pp. 331–345.
Reid, R. C. , Prausnitz, J. M. , and Sherwood, T. K. , 1977, The Properties of Gases and Liquids, McGraw-Hill, New York, p. 533.
Peakall, J. , and Warburton, J. , 1996, “ Surface Tension in Small Hydraulic River Models—The Significance of the Weber Number,” J. Hydrol., 35(2), pp. 199–212.
Basu, N. , Vijay, K. D. , and Gopinath, R. W. , 2005, “ Wall Heat Flux Partitioning During Subcooled Flow Boiling: Part 1—Model Development,” ASME J. Heat Transfer, 127(2), pp. 131–140.
Gschwendtner, M. R. , 2004, “ The Eckert Number Phenomenon: Experimental Investigations on the Heat Transfer From a Moving Wall in the Case of a Rotating Cylinder,” Heat Mass Transfer, 40(6–7), pp. 551–559.
Kandlikar, S. G. , Shoji, M. , and Dhir, V. , 1999, Handbook of Phase Change, Taylor and Francis, New York, pp. 79–98.
Papel, S. S. , 1963, “ Subcooled Boiling Heat Transfer Under Forced Convection in a Heated Tube,” NASA Technical Report No. NASA-TN-D-1583.
Badiuzzaman, M. , 1967, “ Correlation of Subcooled Boiling Data,” Pak. Eng., 7, pp. 759–764.
Moles, F. D. , and Shaw, F. G. , 1972, “ Boiling Heat Transfer to Subcooled Liquids Under Condition of Forced Convection,” Trans. Inst. Chem. Eng., 50, pp. 76–84.
Yana, J. , Bia, Q. , Liua, Z. , Zhua, G. , and Caib, L. , 2015, “ Subcooled Flow Boiling Heat Transfer of Water in a Circular Tube Under High Heat Fluxes and High Mass Fluxes,” Fusion Eng. Des., 100, pp. 406–418.
Baburajan, P. K. , Bisht, G. S. , Gupta, S. K. , and Prabhu, S. V. , 2013, “ Measurement of Subcooled Boiling Pressure Drop and Local Heat Transfer Coefficient in Horizontal Tube Under LPLF Conditions,” Nucl. Eng. Des., 255, pp. 169–179.

## Figures

Fig. 1

Schematic diagram of experimental setup: (1) Rectangular aluminum block consisting of two rectangular channels, (2) condenser coil dipped in ice water bath, (3) reservoir, (4) pump with variable flow rate, (5) preheater, (6) two cartridge heaters, (7) thermocouples to measure wall temperature, (8) thermocouple to measure channel inlet temperature, (9) thermocouple to measure channel outlet temperature, (10) temperature indicator panel, (11) high-speed camera, (12) light source, and (13) data acquisition system for flow visualization

Fig. 2

Aluminum block with rectangular channels

Fig. 3

Arrangement of thermocouples in the cold plate

Fig. 4

Variation of subcooled boiling heat transfer coefficient with ethanol volume fraction at various inlet temperatures

Fig. 5

Variation of heat transfer coefficient and (Td−Tb) with volume fraction

Fig. 6

Bubble formation for (a) water (b) 25% ethanol volume fraction (c) 50% ethanol volume fraction (d) 75% ethanol volume fraction (e) ethanol

Fig. 7

Vartiation of dimensionless bubble departure diameter with ethanol volume fraction

Fig. 8

(a) π6 versus π1 , (b) π6 versus π1π2, (c) π6 versus π1π2π3, (d) π6 versus π1π2π3π4, and (e) π6 versus π1π2π3π4π5

Fig. 9

Various stages of bubble formation and growth due to change in phase (a) bubble nucleation, (b) bubble growth, (c) bubble departure. (Pure water at heat flux of 133.47 kW/m2, mass flux = 76.67 kg/kW m2 and channel inlet temperature = 303 K.)

Fig. 10

π3 versus ethanol volume fraction

Fig. 11

π4 versus ethanol volume fraction

Fig. 12

π5 versus ethanol volume fraction

Fig. 13

Experimental data versus present correlation

Fig. 14

(a) Validation of present correlation with (a) Papel correlation, (b) Badiuzzamin correlation, (c) Moles–Shaw correlation, and (d) Baburajan correlation

## Tables

Table 1 Equipments used in the present experiment
Table 2 Uncertainties of measured and calculated parameters

## Discussions

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