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Recommended Citation
Thakur, Bhabesh K., "A **new** **correlation** for **heat** **transfer** **during** **flow** **boiling**" (1981). Thesis. Rochester Institute of Technology.

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compared to the other models we examined and can be used in a lot of cases due its ease of application. The performance of most correlations changed with the change of diameter and heated length. This may be due to the fact that most microscale correla- tions were developed based on channels of short lengths. If the length is too short, the applied **heat** ﬂux must be much higher for the same exit quality compared to long channels. Accordingly, there is a possibility for the nucleate **boiling** mechanism to domi- nate, i.e. the local **heat** **transfer** coefﬁcient does not vary with local quality. Therefore, it is expected that these correlations perform poorly as the heated length increases, i.e. as h increases with x to- wards the channel exit. A **new** **correlation** of the Chen type was proposed in this paper, which is more general especially for refrig- erants and can predict local and hence average **heat** **transfer** coef- ﬁcient values. The **new** **correlation** predicts the increasing trend of h vs. x that was observed in micro tubes. The **correlation** predicted 92% of all data within the ±30% error bands at a MAE value of 14.3%. The **new** **correlation** predicted satisfactorily the data for the three different lengths available for the 1.1 mm dia. tube. How- ever, the effect of heated length need to be examined further and included in a future version probably as a non-dimensional term (L/D).

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N.B.: This is the PREPRINT (submitted) version of this article. The final, published version of the article can be found at: https://doi.org/10.1016/j.expthermflusci.2019.04.006
Abstract
This paper presents an experimental investigation on two-phase **heat** **transfer** and dry-out occurrence for refrigerant R452A in a single horizontal circular stainless-steel tube having an internal diameter of 6.0 mm. The effects of mass flux (from 150 to 600 kg/m 2 s), saturation (bubble) temperature (from 23 to 55 °C) and **heat** flux (from 10 to 65 kW/m 2 ) are investigated and discussed. **Heat** **transfer** coefficient and dry-out vapor quality data are then compared to R404A results in the same operating conditions, observing that the nucleate **boiling** contribution of the **new** blend is penalized by its very high glide temperature **during** evaporation. The assessment of some dry-out and **flow** **boiling** **heat** **transfer** coefficient prediction methods is finally carried-out and a correction factor on the nucleate **boiling** term is proposed to take into account the negative effect of the glide temperature difference on the mass diffusion in the liquid. By implementing this modification on two chosen asymptotic models, the statistical error analysis is considerably improved.

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12 1.2 Objectives
From a review of literature, although some effort has been made in pool conditions, few studies have systematically analyzed the effect of wettability on **heat** **transfer** and CHF in **flow** **boiling**. The objectives of this thesis are to meet the data needs for improved understanding of the influence of surface wettability on **heat** **transfer** and CHF in **flow** **boiling**, and evaluate the prediction capability of existing CHF models. This is accomplished by characterizing the effect of various system parameters on the **boiling** properties and CHF values for a hydrophilic surface and comparing them to the effects on a hydrophobic surface. The hydrophilic surface is a polished copper surface studied over a range of pressure, mass flux, and inlet subcooling values up to CHF.

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Saisorn et al. (2010) p erformed **flow** visualization study for R- 134a refrigerant **during** **flow** **boiling** in a circular channel having a diameter of 1.75 mm. Slug **flow**, throat-annular **flow**, churn **flow**, annular **flow** and annular-rivulet **flow** were observed and found t o influence the **flow** **boiling** **heat** **transfer** process as seen in Fig. 2. Slug **flow** appeared with the lowest **heat** **transfer** coefficient in comparison to the other **flow** regimes. Annular-rivulet **flow** showed a relatively high **heat** **transfer** coefficient but a local dry-out region was observed at high vapour qualities, which has been undesirable for a thermal design approach dealing with a cooling system implemented with small channels. Moderate values of he at **transfer** coefficient were given by throat-annular **flow**, churn **flow** and annular **flow** which might be good choices for t he development of t he micro-scale devices. Besides, their **flow** pattern data were compared with the transition lines by Triplett et al. (1999) for t wo-phase air-water **flow** through a 1.45 mm diameter channel. In general, the comparisons showed inconsistencies between the **flow** pattern map established from two-phase gas-liquid **flow** and that from phase-change process. Such inconsistencies were also reported by Yang and Shieh (2001) and Martin-Callizo et al. (2010). Yang and Shieh (2001) performed **flow** visualization with air-water mixture and refrigerant R-134a, and the comparison between such two cases were discussed. Martin- Callizo et al. (2010) c onducted the visualization of R -134a **during** **flow** **boiling** in a tube with a diameter of 1.33 m m. Their test section was made from a quartz glass tube coated externally by Indium Tin Oxide (ITO) which was served as the resistive coating over which a potential difference generated by a DC power supply was applied. Their **flow** pattern data were also compared with the transition lines by Triplett et al. (1999), i ndicating that the agreement was not satisfactory. However, two-phase gas-liquid **flow** phenomena tend to be compatible with **flow** mechanisms based on phase-change process in different aspects. In m icro-channels, for instance, Saisorn and Wongwises (2010) re ported the fair agreement between their gas- liquid **flow** pattern data and the transition lines of G arimella et al. (2002) for condensation **flow**.

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Considering the data reduction, in the case of flow boiling heat transfer measurements, the vapour quality at the inlet of the test section depends on the refrigerant conditions at the i[r]

In the present paper, one- and two-dimensional mathematical models are proposed to describe the stationary **heat** **transfer** in **flow** **boiling** of cooling liquid in the cylindrical annular gap. A set of experimental data governs the form of energy equations in the cylindrical coordinates and the boundary conditions. The two- dimensional model is formulated to minimize the number of experimentally determined constants. In addition to the fixed thermal-**flow** parameters, this model uses two quantities determined experimentally: the surface temperature of the thermal conductive filler layer and void fraction. The method for determining the fluid temperature distribution depends on the **flow** type. The

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ing in a horizontal small circular pipe of 2.0 mm inside diameter. They noted that the **boiling** **heat** **transfer** coefficient was higher at a higher imposed wall **heat** flux except in the high vapour quality region, and also, the **boiling** **heat** **transfer** coefficient was higher at a higher mass flux and saturation temperature when the imposed **heat** flux was low. Vertical **flow** **boiling** of R134a in small multi-channels was investigated by Agostini and Bontemps (2004). Their experimental results indicated that **heat** **transfer** rates were greater than that reported in the previous litera- ture for conventional tubes, while dry-out occurred at low qualities. However, from their results, it was very difficult to conclude which regime was dominant, nucleation or forced con- vection.

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The effect of pressure drop elements (PDEs) on **flow** **boiling** **heat** **transfer** is also presented in this section. All tests in this section are conducted with microchannels in the horizontal orientation with water as the working liquid.
The results from the case without PDEs are compared to those with 6.1% PDEs at the inlet of each channel. The latter case uses manifold which incorporates inlet openings of 127 microns diameter at the inlet to each channel, giving an open area that is 6.1% of the cross sectional area of a 1054 x 197 µm 2 microchannel. These pressure restrictors are expected to reduce the backflow by forcing an expanding vapor bubble in the downstream direction and not allowing the liquid-vapor mixture to enter the inlet manifold. One example of **flow** reversal using a constant mass flux of 212.8 kg/m 2 s is depicted in Fig. 10.2. Using water as the working liquid, the sequence of frames in Fig.

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Abstract. This paper reports an impact of selected thermal and **flow** parameters i.e., mass flux and inlet pressure on **flow** **boiling** **heat** **transfer** in a minichannel. Research was carried out on the experimental set up with the test section fitted with a single, rectangular and vertically oriented minichannel 1.7 mm deep.
Infrared thermography was used to determine changes in the temperature on the outer side of the heated minichannel wall in the central part of the minichannel. The heated element for HFE-649 flowing in the minichannel was a thin alloy plate, made of Haynes-230. Local values of **heat** **transfer** coefficient for stationary state conditions were calculated using a simple one-dimensional method. Analysis of the results was based on experimental series obtained for the same **heat** flux, various mass fluxes and average inlet pressures. The experimental results are presented as the relationship between the **heat** **transfer** coefficient and the distance along the minichannel length and **boiling** curves. The highest local **heat** **transfer** coefficients were obtained for the lower average inlet pressure and for the highest mass flux at lower **heat** flux.

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183 3.2.2 Effect of **heat** flux on **heat** **transfer**
In both micro and macro scale, the impact of **heat** flux represents an essential part in treating the case of representing predominant **flow** **boiling** **heat** **transfer** mechanism(s). The nucleate **boiling** mechanism is assumed to be predominant when the **heat** **transfer** coefficient does not vary with vapor quality and mass flux and increases with increasing **heat** flux. Also, convective **boiling** is considered to be the dominant **heat** **transfer** mechanism when the **heat** **transfer** coefficient does not depend on **heat** flux and increases with increasing mass flux and vapor quality. To determine the impact of the **heat** flux upon the local **heat** **transfer** coefficient, obviously for the test section, the **heat** fluxes are divided into two groups the first group with low **heat** flux values. In contrast, the others are considered as moderate to high **heat** fluxes. Figs. 9 and 10 show the variation of the low **heat** flux and high **heat** flux on local two-phase **heat** **transfer** coefficient, respectively, at 1700 kg /m 2 s mass flux and subcooled inlet fluid temperature is 31 ˚C. In Fig.9, the **heat** **transfer** coefficient remains in a single-phase region and it increases with increasing **heat** flux. The reason for that is the thermal boundary layer was not fully developed. Also, Fig.9 shows that the **heat** **transfer** coefficient increased along the microchannel test part length for the fixed **heat** flux because of the effect wall temperature of microchannel increase in the axial direction due to the axial **heat** conduction effect.

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Abstract In this paper we present experimental data on **heat** **transfer** and pressure drop characteristics at **flow** **boiling** of refrigerant R-134a in a horizontal microchannel **heat** sink. The primary objective of this study is to establish experimentally how the local **heat** **transfer** coefficient and pressure drop correlate with the **heat** flux, mass flux and vapor quality. The copper plate of microchannel **heat** sink contains 21 microchannels with 335x930 m 2 cross-section. The microchannel plate and heating block were divided by the partition wall for the local **heat** flux measurements. Distribution of local **heat** **transfer** coefficients along the length and width of the microchannel plate were measured in the range of external **heat** fluxes from 50 to 500 kW/m 2 ; the mass flux was varied within 200-600 kg/m 2 s, and pressure was varied within 6-16 bar. The obvious impact of **heat** flux on the magnitude of **heat** **transfer** coefficient was observed. It shows that nucleate **boiling** is the dominant mechanism for **heat** **transfer**. The **new** model of **flow** **boiling** **heat** **transfer**, which accounts nucleate **boiling** suppression and liquid film evaporation, was proposed and verified experimentally in this paper.

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Abstract. The paper presents mathematical modelling of **flow** **boiling** **heat** **transfer** in a rectangular minichannel asymmetrically heated by a thin and one-sided enhanced foil. Both surfaces are available for observations due to the openings covered with glass sheets. Thus, changes in the colour of the plain foil surface can be registered and then processed. Plain side of the heating foil is covered with a base coat and liquid crystal paint. Observation of the opposite, enhanced surface of the minichannel allows for identification of the gas- liquid two-phase **flow** patterns and vapour quality. A two-dimensional mathematical model of **heat** **transfer** in three subsequent layers (sheet glass, heating foil, liquid) was proposed. **Heat** **transfer** in all these layers was described with the respective equations: Laplace equation, Poisson equation and energy equation, subject to boundary conditions corresponding to the observed physical process. The solutions (temperature distributions) in all three layers were obtained by Trefftz method. Additionally, the temperature of the **boiling** liquid was obtained by homotopy perturbation method (HPM) combined with Trefftz method. The **heat** **transfer** coefficient, derived from Robin boundary condition, was estimated in both approaches. In comparison, the results by both methods show very good agreement especially when restricted to the thermal sublayer.

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1 Introduction
**Boiling** is an extremely efficient **heat** **transfer** process used in power generation, chemical industry and nuclear engineering. One of the relevant **boiling** features is the high value of the **heat** **transfer** coefficient, due to which large **heat** fluxes can be transported. Miniheat exchangers are used to provide higher cooling capability for **new** technologies. Owing to the change of state, which accompanies **flow** **boiling** in minichannels, it is possible to meet contradictory demands simultaneously, i.e. to obtain a **heat** flux as large as possible at small temperature difference between the heating surface and the saturated liquid and, at the same time, retain small dimensions of **heat** **transfer** systems. Review of relevant literature and the selected publications covering **flow** **boiling** **heat** **transfer** in minichannels is presented in [1,2], and having enhanced surfaces - in [3-5]. It leads to the conclusion that although much has been written recently on **flow** **boiling** **heat** **transfer** in minichannels, the observations related to the effects of various factors on **boiling** **heat** **transfer** in minichannels are diverse and frequently conflicting. They are usually verified experimentally for channel systems heated by smooth heating surfaces.

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18
Chapter 2: Literature Review
2.1 Previous Work
Microchannel two-phase cooling is accomplished with the help of a **heat** sink that consists of a high conductivity material containing parallel, small diameter channels. The simplicity and ease of fabrication of the design are the key reasons behind its unprecedented popularity in the industry. Most microchannel geometries of interest possess diameters in the range of 0.1–0.6 mm. These microchannel devices are therefore very compact and lightweight, and provide high **heat** **transfer** coefficients by capitalizing upon the coolant’s latent **heat** content rather than the sensible **heat** alone (seen in single phase liquid cooling). This greatly reduces the **flow** rate required to dissipate the same amount of **heat** compared to single-phase cooling, which also helps reduce coolant inventory for the entire cooling system. **Flow** **boiling** with microchannels also provides better temperature uniformity by maintaining surface temperatures close to the coolant’s saturation temperature. However, two-phase microchannel cooling is not without shortcomings, and their implementation is hindered by the relatively limited understanding of two-phase **flow** in microchannels.

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18
Chapter 2: Literature Review
2.1 Previous Work
Microchannel two-phase cooling is accomplished with the help of a **heat** sink that consists of a high conductivity material containing parallel, small diameter channels. The simplicity and ease of fabrication of the design are the key reasons behind its unprecedented popularity in the industry. Most microchannel geometries of interest possess diameters in the range of 0.1–0.6 mm. These microchannel devices are therefore very compact and lightweight, and provide high **heat** **transfer** coefficients by capitalizing upon the coolant’s latent **heat** content rather than the sensible **heat** alone (seen in single phase liquid cooling). This greatly reduces the **flow** rate required to dissipate the same amount of **heat** compared to single-phase cooling, which also helps reduce coolant inventory for the entire cooling system. **Flow** **boiling** with microchannels also provides better temperature uniformity by maintaining surface temperatures close to the coolant’s saturation temperature. However, two-phase microchannel cooling is not without shortcomings, and their implementation is hindered by the relatively limited understanding of two-phase **flow** in microchannels.

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A 2 4
(2.1)
where, H is the height of microchannel; W is the width of microchannel; L is the length of microchannel; D h is the hydraulic diameter of microchannel. A large ratio of surface area to volume is achieved by reducing the hydraulic diameter to micro-scale. This assists in developing a compact and efficient design of **heat** exchanger. These types of systems are quiet and can be accommodated in the restricted space inside the equipment. The advantage of cooling the electronic chips by dissipating **heat** through the liquid flowing in the microchannels is that the **heat** **transfer** coefficient is high as it is inversely proportional to the hydraulic diameter of the channel. It is to be noted that the coolant temperature rise along the channel is very high in case of single-phase **flow** because all the **heat** generated by the electronic device is carried away by relatively small amount of liquid. Therefore, it is preferred to have a two-phase **flow** cooling system. **Flow** **boiling** in microchannel **heat** sinks offers those same attributes while providing the following important advantages over their single-phase counterparts: much higher convective **heat** **transfer** coefficients due to large latent **heat** **during** **boiling**; better temperature uniformity;

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Abstract This study moves from the need to study **flow** **boiling** of zeotropic mixture in microchannels. In the recent years much attention has been paid to the possible use of fluorinated propene isomers for the substitution of high-GWP refrigerants. The available HFOs (hydrofluoroolefins) cannot cover all the air- conditioning, **heat** pump, and refrigeration systems when used as pure fluids because their thermodynamic properties are not suitable for all operating conditions and therefore some solutions may be found using blends of refrigerants, to satisfy the demand for a wide range of working conditions. In the present paper a mixture of R1234ze(E) and R32 (0.5/0.5 by mass) has been studied. The local **heat** **transfer** coefficient **during** **flow** **boiling** of this mixture in a single microchannel with 0.96 mm diameter is measured at a pressure of 14 bar, which corresponds to a bubble temperature of 26.3°C. The **flow** **boiling** data taken in the present test section are discussed, with particular regard to the effect of **heat** flux, mass velocity and vapor quality. The **heat** **transfer** coefficients are compared against some predicting models available in the literature.

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saturation temperatures, mass fluxes, **heat** fluxes and working fluids etc. Therefore, the extrapolation of the available prediction methods to other fluids and channels do not work properly. It must be stressed here that big discrepancies among the experimental data from different independent laboratories may be caused due to different surface roughness of the test channels, channel dimension uncertainties, improper data reduction methods, **flow** **boiling** instabilities, improper designed test facility, test sections and experimental procedures. In some cases, the published results are unreasonable such as too big or too small **heat** **transfer** coefficients, some or complete wrong **heat** **transfer** behaviours and trends and correlations of various parameters and physical properties even if they have been published in journals. For instance, quite anomaly **heat** **transfer** trends are presented but they cannot be explained according to the corresponding **flow** **boiling** mechanisms in some papers although it is said that such mechanisms account for the **heat** **transfer** behaviours as detailed in a recent analysis in a comprehensive review by Ribatski et al. [7]. Furthermore, some **flow** **boiling** **heat** **transfer** correlations and models were proposed by simply regressing limited experimental data at limited test parameter ranges without considering the **heat** **transfer** mechanisms. Therefore, it is necessary to evaluate these correlations to validate their applicability before using these correlations. In fact, in most cases, such correlations do not work properly for other fluids and conditions. Therefore, it is essential to analyse and evaluate these correlations to identify further research needs in this important field.

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