2.1 Critical Heat Flux in Flow Boiling in Microchannels

The critical heat flux (CHF) condition is characterized by a sharp reduction of the local heat transfer coefficient as a result of the replacement of liquid by vapor adjacent to the heat transfer surface [1]. The CHF condition in flow boiling can be of different nature [1–5]. At low vapor quality, it is associated with subcooled boiling or saturated boiling and high heat. However, at medium or high quality, it is the dryout and there is no liquid film on the tube wall. Usually this is in case of annular flow and due to surface wave instabilities or entrainment and vaporization.

Critical heat flux can be understood by fluid dynamics, thermodynamics and heat transfer. It is influenced by a large number of process and system variables [6–8]. The scenario during CHF has been studied in [4]. Understanding of CHF mechanisms needs hydrodynamic instability theory [4]. Figure 2.1 [9] shows the variations of the evaporation heat transfer coefficient with the imposed wall heat flux at different mean vapor quality.

Fig. 2.1
figure 1

Variations of the evaporation heat transfer coefficient with the imposed wall heat flux at different mean vapor quality [9]

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Near wall fluid behaves as if a growing bubble is fed by the vapor evaporated from a thin microlayer at its bottom and CHF occurs due to the dryout of the microlayer [10]. Effects of the refrigerant saturated temperature on the evaporation heat transfer coefficient at two different wall heat fluxes are shown in Fig. 2.2 [9].

Fig. 2.2
figure 2

Effects of the refrigerant saturated temperature on the evaporation heat transfer coefficient at two different wall heat fluxes [9]

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There is a thermal boundary layer adjacent to the heater surface during nucleate and transition boiling. Depending on the wettability and the temperature of the surface, the vapor stems undergo changes and the merging of the vapor stems triggers CHF [11, 12].

At CHF, there is instability of velocity boundary layer and dryout of microlayer adjacent to the surface seem. Bergles [13] and Kandlikar [14] studied the effects of contact angle, surface orientation and subcooling.

In the microlayer evaporation based model for CHF [15, 16], it is assumed that a dry spot is formed when there are a critical number of bubbles surrounding a single bubble and the liquid supply to the microlayer of the central bubble is restricted. Bulk fluid movement and the lateral movement of the bubbles in subcooled boiling are very important [17, 18]. Thin film dryout and receding contact angle during evaporation in a moving fluid should be considered as a mechanistic representation for CHF in flow boiling in microchannels.

2.2 Investigations of CHF

Many experimental investigations have been carried out [19–23]. There is a strong influence of flow regimes on CHF. Experiments on microchannels cover a wide range of geometry, physical dimensions, working fluids and operating parameters. There is a wide range of parameters [24, 25]. Very recent and important experimental investigations are given in Table 2.1 [26].

Table 2.1 Some typical investigations CHF during flow boiling through micro channels [26]
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In case of microtubes; both single and multiple tubes have been used [27–31]. On the other hand, microchannels are studied in multiple. Parallel microchannel heat sinks are made of silicon, copper and stainless steel. Working fluids are water, refrigerants (R134a, R245fa, R236fa, R123, R32, R113 etc.), CO2, nitrogen, helium, ethanol etc. CHF depends on type of fluid [32, 33]. However, CHF is a weak function of saturation.

CHF depends on the hydraulic diameter and length to diameter. For subcooled boiling, CHF increases with the decrease in channel diameter due to decrease in the departure diameter of the vapor bubbles, increase in bubble velocity relative to liquid and strong condensation at the tip of bubble [34, 35]. On the other hand for x eq  > 0, CHF decreases with decrease in d. CHF increases monotonically with the increase in mass flux and linearly with the increase in subcooling [36].

2.3 Prediction of CHF

The previous section discussed some important experimental investigations on flow boiling through microchannels. Some trends of the variation of CHF have already emerged. This has encouraged the researchers to try for the prediction of CHF as a function of geometric and operational parameters as well as fluid properties. Such predictions can be made through correlations or modeling. In this section, the correlations for the CHF in microchannels have been examined. Table 2.2 provides a compilation of correlations relevant for the CHF in microchannel [26]. Critical heat flux varies proportionally with the mass velocity and the enthalpy needed for vaporization [37–40].

Table 2.2 Correlations used for the prediction of CHF in microchannels [26]
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Katto [37] predicted the correlation for uniformly heated vertical channels. Wu et al. [41] used the Katto [37] correlation for a large number of refrigerants, water and nitrogen, and obtained a reasonable prediction. The correlation by Katto and Ohno [42] has been used for predicting saturated CHF in a single channel.

There are fewer correlations for horizontal flow than those for vertical flow at low mass fluxes. Groeneveld [43] has suggested a simple method of prediction for CHF in horizontal channel by multiplying the corresponding value in vertical tubes with a constant. According to Yu et al. [44] this gives the correct trend of CHF in small tubes. Shah [45] has proposed a widely applicable correlation for CHF in uniformly heated vertical channel. Tong [46] derived a CHF correlation by applying boundary layer; one parameter was given as a function of quality. Nariai et al. [47] studied CHF of subcooled flow boiling in narrow tubes. Celata et al. [48] also modified Tong’s correlation. Hall and Mudawar [49] derived a statistical five-parameter correlation.

Qu and Mudawar [38] compared the Katto-Ohno [42] correlation and found vapor backflow in the upstream plenum as a result of flow instabilities and CHF was independent of inlet subcooling. Wojtan et al. [40] developed a correlation from R-134a and R-245fa data. Ong and Thome [50] and Zhang et al. [51] used an extensive to develop the correlations.

Kosar and Peles [52] concluded that CHF decreased with exit quality. A similar trend was also observed by Qi et al. [53]. However, the Kosar and Peles [52] correlation has poor predictive ability. Qi et al. [53] proposed a correlation that has been verified for aqueous data only. Wu et al. [41] developed a complicated correlation.

An excellent survey for predictive correlations for CHF has been done by Revellin et al. [54]. For saturated boiling CHF increases with mass flux with hydraulic diameter, heated length, subcooling and saturation pressure.

2.4 Models

Our knowledge of the nature of CHF is still not complete [55, 56]. An important aspect of multi-microchannel block is the conjugate effect. A multiple microchannel system is often considered as a single heat sink. Such channels at relatively high mass flux have been studied [43, 57, 58]. Though, most of the microchannel applications are limited to not-very-high mass flux, care must be taken in their design and operation as the CHF behavior can deviate substantially from the usual trend. There could be a number of flow regimes. A unique phenomenon related to microchannel flow boiling is the rapidly expanding vapor bubbles. Also, there may be a reverse flow of the liquid in the direction of the inlet manifold.

2.5 Boiling and CHF studies

CHF studies can be grouped into studies in single and parallel microchannels. Jiang et al. [59] investigated phase-change in multiple microchannel heat sink systems. Yen et al. [60] used single circular tubes and observed that the exit quality at CHF was approximately 1.0.

Bowers and Mudawar [61] used R-113 in circular mini-channel and 510 μm diameter copper micro-channel heat sinks. They concluded that the CHF was not a function of inlet subcooling. CHF increased with mass velocity.

Qu and Mudawar [38] measured the CHF for a water-cooled microchannel heat sink that contained 21 parallel microchannels. They observed back flow, Fig. 2.3 [38]. The CHF condition advanced with an increase in mass velocity and it was independent of inlet temperature. They proposed a new correlation for CHF.

Fig. 2.3
figure 3

Vapor back flow in the experiments of Qu and Mudawar [38]

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Three major flow instabilities affect CHF in microchannel heat exchangers—the upstream compressible volume instability, the excursive instability, and the parallel channel instability. The upstream compressible volume instability causes severe pressure drop oscillation leading to a premature CHF [62]. Upstream throttling in [38] took care of the compressible volume instability, but it was subject to excursive instability. This can be avoided by increasing the available pressure drop. In the case of parallel microchannels, improved fabrication techniques can be used to employ flow restrictions at the inlet of each channel to accomplish the pressure drop needed [63]. This technique was used by Kosar et al. [64]. The value of CHF increased with an increase in restrictor length. Using the same device as in [64], Koşar and Peles [65] studied the CHF condition of R-123 at exit pressures ranging from 227 to 520 kPa. CHF data were obtained over wide heat flux and mass flux range. Dryout was the leading CHF mechanism. CHF increased fairly linearly with mass flux. Kuan and Kandlikar [66] studied the effect of flow boiling stability on CHF with R-123 in six parallel microchannels. They studied the effect of using pressure drop elements to restrict the flow and reduce vapor backflow. There is decrease in the CHF value with the use of restrictors.

Conjugate heat transfer effects may become important in microchannels since the channel wall thickness becomes comparable to the microchannel size. For microchannels fabricated on large blocks, it is possible that there is significant axial and longitudinal conduction through the substrate. This results in redistribution of heat flux away from those locations where the CHF condition typically initiates i.e., at the exit and eventually leads to the CHF condition occurring at the hottest surface. Higher values of the apparent CHF could be obtained due to these conjugate effects. Conjugate heat transfer with single-phase flow in microchannels has been studied [67] numerically, but such studies for two-phase flow and the effects on CHF have not been reported. There are very few CHF investigations in small circular tubes [34, 68–70]. Bergles and Rohsenow [70] studied CHF with de-ionized. At high subcooling CHF decreased monotonically with increases in quality and then increased in the bulk boiling region following a minimum.

Roach et al. [71] studied the CHF associated with flow boiling of subcooled water in circular tubes. Oh and Englert [72] conducted sub-atmospheric CHF experiments with water in a single rectangular aluminum channel heated on one side with electric strip heaters. CHF experiments were performed by Lazarek and Black [73] with R-113 in a stainless steel. CHF occurred because of the dryout of the liquid and always at the exit of the heated test section length. Yu et al. [74] carried out CHF experiments with water in a stainless steel channel. The relative size of the channel compared to the wall thickness played a role in the CHF condition.

Lezzi et al. [75] reported experimental results on CHF in forced convection boiling of water in a horizontal tube and the critical heat flux was reached due to dryout. They claimed that no oscillations affected the CHF condition. Wojtan et al. [40] investigated saturated critical heat flux in single uniformly heated microchannels with R-134a and R-245fa. They presented a new correlation to predict CHF in circular uniformly heated microchannel. Harirchian and Garimella [76, 77] reported five major flow regimes; bubbly, slug, churn, wispy annular, annular and a post dryout regime of inverted annular flow. The observed flow regimes were not much different from those observed in large size conduits.

A scale analysis based theoretical model for CHF was proposed by Kandlikar [78]. He considered evaporation momentum, surface tension, inertia and viscous forces and the constants were extracted from the available experimental data. Dryout during flow boiling has been associated with the elongated bubbles, [79] or annular flow regime. Kandilkar [80] observed the local dry-patch in elongated bubbles, micro-layer evaporation and the meniscus of an expanding bubble.

Revellin and Thome [81] suggested a mechanistic mode of CHF for flow boiling through heated microchannels. Revellin and Thome [24] extended the film dryout model. They argued that even though water had higher CHF compared to all other fluids, it is not good for electronic component cooling due to its very low saturation pressure at 30–40 °C. Revellin et al. [82] have done optimization analysis using CHF model on a constructal based tree shaped microchannel network in a disc shaped heat sink.

Kosar [83] constructed a simple model of CHF for saturated flow boiling. Kuan and Kandlikar [84] proposed another mechanistic model of critical heat flux based on force balance at the interface of a vapor plug in a microchannel. Yen et al. [85] studied convective flow boiling in a circular Pyrex glass microtube and a square Pyrex glass microchannel. Higher heat transfer coefficient was observed in the square microchannel as compared to the circular cross sectional microtube because of square corners acting as active nucleation sites. The reader is advised to refer [86–113] for more information.

2.6 Some Effects on CHF

2.6.1 Effect of Mass flux on CHF

The CHF increases with increase in mass flux Fig. 2.4 [38] and exit pressure [40, 63, 65, 114]. CHF also increases with smaller hydraulic diameter and conjugate effects. Slope of CHF vs. mass flux curve also depends on pressure.

Fig. 2.4
figure 4

Effect of mass flux on CHF [38]

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2.6.2 Effect of Inlet Subcooling

At high mass flux, for high inlet subcooling, CHF decreases with decrease in inlet subcooling. But for low subcooling, the CHF increases with decrease in subcooling. The exit quality at CHF is close to zero. Figure 2.5 shows effect of inlet subcooling on CHF [40]. Parallel channel instability occurs [38] with the approach of CHF since then vapor mixes with subcooled inlet fluid in the plenum and the inlet subcooling loses its influence [40].

Fig. 2.5
figure 5

Inlet subcooling effect on CHF [40]

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2.6.3 Effect of Exit Quality on CHF

The CHF increases with quality [115], Fig. 2.6 and CHF is high in the region close to saturation when compared to the high subcooled region due to change in void fraction and the flow velocity. References [115–117] may be read for more information.

Fig. 2.6
figure 6

Variation of CHF with exit quality [40]

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2.6.4 Effect of Tube Diameter on CHF

CHF increases substantially with a reduction in tube diameter, [40, 63, 70, 114], Fig. 2.7 [40].

Fig. 2.7
figure 7

Variation of CHF with heated length [40]

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2.6.5 Effect of Heated Length on CHF

CHF decreases with an increase in heated length [40, 118].

Note: References [119–139] may be read for more information.

2.7 Some Important Results and Observations

As shown in Fig. 2.8, critical site number preventing the liquid supply to the microlayer under the bubble is to be determined before the CHF is evaluated [15]. Figure 2.9 shows effect of surface wettability on CHF [15]. The active nucleation density, the bubble departure diameter and their product are affected by contact angle which in turn affects CHF.

Fig. 2.8
figure 8

Comparison of predictions by assuming critical site number and the experimental data for several contact angles [15]

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Fig. 2.9
figure 9

Effect of surface wettability on CHF [15]

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Figure 2.10 compares the predicted and measured fraction of dry area near CHF [15]. The estimated fraction of dry out area at CHF is not constant. It depends on boiling condition. The fraction of dry area is high for the high wall void fraction at CHF. Figure 2.11 shows comparison between experimental and calculated CHF at inlet conditions with contact angle 50° [16]. The average predicted to measured CHF ratios (CHFR) decrease with the increase in contact angle. In this study [16], a dry spot model of CHF has been developed for both pool boiling and subcooled forced convection boiling. Figure 2.12 shows the CHF behavior with quality based on the flow regime map. There are two transition points and these transitions depend on the condition of operating parameters. The mechanism changes from DNB type behavior in the subcooled region to dryout behavior at high qualities [29]. For critical qualities below point of net vapor generation (PNVG), CHF decreases with quality and for above PNVG, CHF increases with quality as shown in Fig. 2.13 [30].

Fig. 2.10
figure 10

Comparison of predicted and measured fraction of dry area near CHF [15]

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Fig. 2.11
figure 11

Experimental vs. calculated CHF at contact angle 50° [16]

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Fig. 2.12
figure 12

Speculation on the trends of CHF with exit quality [29]

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Fig. 2.13
figure 13

CHF variations with quality in the subcooled region [30]

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It is important to identify CHF conditions based on the criteria for such description and the repeatability of the measurements must be ensured. The slope of the heat flux vs. temperature curve is high at the beginning of two-phase region and the gradient decreases as the boiling crisis approaches. Figure 2.14 [32] shows this and, in such a way, the integrity of the test setup is ensured.

Fig. 2.14
figure 14

Boiling curves [32]

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Figure 2.15 shows the curves for CHFs with mass velocity [33]. While CHF increases with mass velocity, its rate of rise is less at high mass velocities. CHF increases moderately with increasing inlet subcooling.

Fig. 2.15
figure 15

CHF with mass velocity [33]

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CHF virtually does not depend on dissolved gas concentration from near zero to the saturation level as shown in Fig. 2.16, [34]. The CHF correlation for a horizontal channel may be obtained by multiplying a constant as shown in Fig. 2.17 [36].

Fig. 2.16
figure 16

CHF vs. dissolved oxygen concentration [34]

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Fig. 2.17
figure 17

The correction factor [36]

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With heat flux approaching CHF, the intense parallel channel instability causes vapor backflow and mixing of vapor in the incoming subcooled liquid, the slope of the boiling curve increases indicating flow boiling near the outlet. However, when the heat flux approaches CHF, the slope again decreases and the heat transfer becomes less effective, Fig. 2.18 [38].

Fig. 2.18
figure 18

Boiling curves [38]

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Flashing evaporation causes non-linear variation of the mass quality along the microtube as shown in Fig. 2.19 [39]; mass quality increases rapidly near the outlet. The evolution of the heat flux is shown in Fig. 2.20 [40]. Initially, the heat flux increases linearly with a small increase of the wall temperature; reaches the maximum when lot of vapor forms and the liquid becomes unable to wet the surface continuously. Consequently, heat transfer coefficient falls and the temperature rises and further heating must be stopped.

Fig. 2.19
figure 19

Local flow boiling heat transfer characteristics at (a) low, (b) medium and (c) high heat flux [39]

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Fig. 2.20
figure 20

Determination of CHF by experiment [40]

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The variation of boiling number at CHF with different parameters is shown in Fig. 2.21 [41]. This is obtained from the data of different investigators. Figure 2.22 shows that the deviation of the predicted data for CHF from the correlations developed is often +30 to +50 % from the experimental data and the availability of widely applicable correlation remains as a remote possibility [49]. Figures 2.23 and 2.24 [50] show the dependency of various parameters on pressures. Figures 2.25 and 2.26 [93] show confinement effects on CHF in buoyancy driven microchannels.

Fig. 2.21
figure 21

Variation of boiling number at CHF with various parameters as obtained from the experimental data of different investigators [41]. (a) Wojtan et al.’s R134a data [140]. (b) Roday and Jensen’s water data [141]. (c) Park and Thome’s R134a data [109]

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Fig. 2.22
figure 22figure 22figure 22

Comparison of predicted CHF from the correlation with that from the experiment [49]

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Fig. 2.23
figure 23

Parameter dependencies with pressure [50]

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Fig. 2.24
figure 24

Parameter dependencies with pressure [50]

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Fig. 2.25
figure 25

CHF depends on channel aspect ratio for asymmetric heating [93]

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Fig. 2.26
figure 26

CHF depends on channel aspect ratio for symmetric channel [93]

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