Literature Review

In sizing the small channels, Kandlikar and Grande [1] proposed that Dh >3mm for the conventional channels, 200μm< Dh <3mm for the mini-channels, 10μm < Dh <200μm for the micro-channels, 0.1μm < Dh <10μm for the transitional channels, 1μm < Dh <10μm for the transitional micro-channels, 0.1μm < Dh <1μm for the transitional nano-channels, and Dh

≤

introduced a dimensionless group named as the Confinement number,

0.5

which represents the importance of the restriction of the flow by the small size of the channel. They showed that when Nconf

1.2.1 Stable Flow Boiling Heat Transfer

>0.5, the effects of the channel size become very important.

The literature on stable flow boiling heat transfer is reviewed at first. Here the stable

well known that boiling heat transfer for flow inside channels can be regarded as a combination of convective heat transfer from the wall to the liquid and nucleate boiling at the wall. In convection-dominated flow boiling, the heat transfer coefficient is independent of the wall heat flux but increases with increasing mass flux and vapor quality. On the contrary, in nucleation-dominated flow boiling the boiling heat transfer coefficient is independent of the mass flux and vapor quality. However, it increases with the heat flux and is sensitive to the refrigerant saturation pressure level.

Hsieh et al. [3] examined the stable flow boiling heat transfer and associated bubble characteristics of R-410A in a horizontal annular duct. They showed that raising the imposed heat flux can increase the boiling heat transfer coefficient. Wang et al. [4]

compared the two-phase heat transfer characteristics of refrigerants R-22 and R-410A.

Their results indicate that the evaporative heat transfer coefficients for R-410A are about 10-20% higher than that for R-22. Ebisu and Torikoshi [5] examined the evaporative heat transfer for R-410A, R-407C and R-22. They showed that evaporative heat transfer coefficient of R-410A was about 20% higher than that of R-22 up to the vapor quality of 0.4, while the heat transfer coefficients of R-410A and R-22 became almost the same at the quality of 0.6.

Fujita et al. [6] studied flow boiling heat transfer and pressure drop for refrigerant R-123 in a horizontal small-diameter tube (D_h=1.12 mm). They showed that the flow boiling was dominated by bubble nucleation in the small tube rather than the forced convective evaporation because of very weak influences of the mass velocity and vapor quality. Hsieh et al. [7] investigate the effect of the channel size on R-407C saturated flow boiling heat transfer in a narrow annular duct. The gap of the duct is fixed at 1.0 mm and 2.0 mm. They reported that the saturated flow boiling heat transfer coefficient increased with a decrease in the duct gap. Besides, Lie & Lin [8,9] examined the flow boiling heat transfer and associated bubble characteristics of R-134a in the same duct (Dh = 2&4 mm).

The effects of the refrigerant mass flux and saturated temperature on the boiling heat transfer coefficient were found to be small.

Flow boiling of refrigerants R-11 and R-123 in a small horizontal copper tube (Dh=1.95 mm) investigated by Bao et al. [10] showed that the heat transfer coefficients were independent of the refrigerant mass flux and vapor quality, but were a strong function of the heat flux. Nucleate boiling was noted to be the dominant mechanism over a wide

range of flow conditions. A similar study from Tran et al. [11] examined flow boiling of refrigerant R-12 in small circular and rectangular channels (D_h=2.46, 2.4 mm). Two distinct two-phase flow regions were noted, convective boiling dominant region at lower wall superheat (< 2.75K) and nucleate boiling dominant region at higher wall superheat (>

2.75K). Kandlikar and Steinke [12] noted that for a high liquid-vapor density ratio (ρl/ρg), the convective effects dominated as the vapor quality increased. This led to an increasing trend in the boiling heat transfer coefficient at increasing vapor quality. A high Boiling number results in a higher nucleate boiling contribution, which tends to decrease as the vapor quality increases. This leads to a decreasing trend in heat transfer coefficient with increasing vapor quality. Oh et al. [13] examined flow boiling heat transfer characteristics of R-134a in a capillary tube heat exchanger (Dh=2, 1, 0.75 mm). Their data showed that the heat transfer in the forced convection dominated region was more influenced by the mass flux than by the Boiling number and the heat transfer coefficient was controlled by the Reynolds number.

Yin et al. [14] investigated the subcooled flow boiling heat transfer for refrigerant R-134a flowing in a horizontal annular duct. The gap of duct is 5.16 mm. They found that boiling heat transfer is insignificantly affected by the mass flux, imposed heat flux and refrigerant saturation temperature. But a decrease in the inlet subcooling results in much better heat transfer. Chen et al. [15] investigate how the channel size affects the subcooled flow boiling heat transfer of refrigerant R-407C in a horizontal narrow annular duct(D_h = 1.0 and 2.0 mm). They indicated that the temperature overshoot at ONB is relatively significant. Besides, the subcooled flow boiling heat transfer coefficient increases with a reduction in the duct gap, but decreases with an increase in the inlet liquid subcooling.

1.2.2 Time Dependent Flow Boiling Heat Transfer

In examining two-phase flow instabilities in a circular channel (D_h=9.525mm), Comakli et al [16] found that the periods and amplitudes of the pressure drop and density wave type oscillations decreased with decreasing mass flow rate and increased with decreasing inlet temperature. Recently, some detailed characteristics associated with these intrinsic instabilities were investigated through experimental measurement and theoretical modeling. An experimental investigation of thermal instabilities in forced convection boiling of R-11 in a vertical annular channel (Dh =17 mm) was conducted by Kakac et al.

assumption were used to predict the condition leading to the thermal oscillation. And their predicted periods and amplitudes of the oscillations were in a good agreement with their measured data. In a continuing study for R-11 in a horizontal tube of 106 cm long, Ding et al. [18] examined the dependence of the oscillation amplitude and period on the system parameters and located the boundaries of various types of oscillations on the steady-state pressure-drop versus mass flux characteristic curves.

Wang et al. [19] noted that the boiling onset in a upward flow of subcooled water in a vertical tube of 7.8-m long connected with a liquid surge tank could cause substantial flow pressure and density-wave oscillations. These boiling onset oscillations were attributed to a sudden increase of pressure-drop across the channel and a large fluctuation in the water flow rate at the onset of nucleate boiling. This in turn results from the feedback of the pressure-drop and flow rate by the system, causing the location of the boiling onset to move in and out of the channel. Experimental investigation on the critical heat flux was conducted under the forced flow oscillation condition by Ozawa et al. [20]. They found that the reduction of the CHF from the steady state value was larger for increases in the amplitude and period of the flow oscillation.

Kotaoka et al. [21] investigated transient flow boiling of water over a platinum wire subject to an exponentially increasing heat input. The wire diameter and length respectively vary from 0.8 to 1.5 mm and from 3.93 to 10.4 cm. Two types of transient boiling were observed. In A-type (heating period is 20 ms, 50 ms or 10 s) boiling, the transient maximum critical heat flux increases with decreasing heating period at constant flow velocity. Whereas in the B-type (heating period is 5ms, 10ms, or 14ms) boiling, the transient maximum critical heat flux decreases first with the period and then increases.

Two-phase flow and heat transfer in a small tube of 1 mm in the internal diameter using R-141b as the working fluid were studied by Lin et al. [22]. At a low heat flux input, a relatively constant wall temperature was obtained. Besides, forced convection evaporation occurs towards the outlet end of the tube and the fluctuations in the wall temperature are small. With a high heat flux input, however, significant fluctuation in the wall temperature can appear. This is caused by a combination of time varying heat transfer coefficient and time varying local pressure and fluid saturation temperature.

The dynamic behavior for a horizontal boiling channel connected with a surge tank for liquid supply has also received some attention. Mawasha and Gross [23] used a

constitutive model containing a cubic nonlinearity combined with a homogeneous two-phase flow model to simulate the pressure-drop oscillation. Their prediction is matched with the measured data. Later, the channel wall heat capacity effects were included [24] to allow the wall temperature and heat transfer coefficient to vary with time.

1.2.3 Flow Patterns and Bubble Characteristics

To elucidate the flow boiling heat transfer mechanisms in small channels, we require to delineate the prevailing flow regimes. Cornwell and Kew [25] examined various flow regimes for boiling of refrigerant R-113 in a vertical rectangular multi-channel with D_h

However, bubble characteristics such as bubble departure frequency, growth, sliding and departure size are known to play an important role in flow boiling heat transfer.

Visualization of subcooled flow boiling of upward water flow in a vertical annular channel (D

= 1.03 and 1.64 mm. Based on visualization of the flow and measurement of the heat transfer, three flow regimes have been suggested, namely, the isolated bubble, confined bubble and annular-slug bubble flows. In the isolated bubble regime, heat transfer coefficient depends on the heat flux and hydraulic diameter. In the confined bubble regime, heat transfer coefficient depends on the heat flux, mass flux, vapor quality and hydraulic diameter.

While in the annular-slug bubble regime, heat transfer coefficient depends on the mass flux, vapor quality and hydraulic diameter.

h=19 mm) by Situ et al. [26] suggested that generally the bubble departure frequency increased as the heat flux increased. The averaged bubble growth rate drops sharply after lift-off. An experimental analysis was carried out by Thorncroft et al. [27] to investigate the vapor bubble growth and departure in vertical upflow and downflow boiling of FC-87.

They found that the bubble growth rate and bubble departure diameter increased with the Jacob number(increasing △Tsat

Kandlikar [28] examined the subcooled flow boiling of water in a rectangular horizontal channel. They noted that the bubble growth was slow at high subcooling and the departure diameter decreased as the flow rate increased. The influence of the heat flux on ) and decreased at increasing mass flux in both the upflow and downflow. Hsieh et al. [3] examined saturated flow boiling heat transfer and associated bubble characteristics of R-410A in a horizontal annular duct. They concluded that a higher refrigerant mass flux results in a smaller bubble departing size and a higher bubble departure frequency.

the waiting time between two cycles is much weaker. Chang et al. [29] studied the near-wall bubble behavior for water in a vertical rectangular channel with one-side heated (Dh=4.44 mm). They showed that the size of coalesced bubbles decreased for an increase in the mass flux and the mass flux only exhibited a strong effect on the bubble size. Del Balle and Kenning [30] examined the subcooled flow boiling for water in a rectangular vertical channel and found that the maximum bubble diameter was independent of the heat flux. Yin et al. [14] examined the bubble characteristics associated with subcooled flow boiling of refrigerant R-134a in a horizontal annular duct (Dh=10.31 mm). They noted that the bubble departure frequency was suppressed by raising the mass flux and subcooling of R-134a, and only the subcooling showed a strong effect on the bubble size. The study of water boiling in a horizontal rectangular channel with one side heated (Dh=40 mm) conducted by Maurus et al. [31] found that the waiting time between two bubble cycles decreased significantly at increasing mass flux. An experimental study on bubble rise path after the departure from a nucleation site for water in a vertical upward tube (Dh

1.2.4 Correlation Equations for Flow Boiling Heat Transfer

=20 mm) by Okawa et al. [32] suggested that the inertia force significantly influenced the onset of bubble detachment and the shear force induced a lift force to detach the bubble from the wall.

An early general correlation model for the flow boiling in channels was proposed by Chen [33]. He divided the boiling heat transfer coefficient into two parts: a microconvective (nucleate boiling) contribution estimated by the pool boiling correlations and a macroconvective (non-boiling forced convection) contribution estimated by the single-phase correlation such as the Dittus-Boelter equation [34]. In order to account for the diminished contribution of nucleate boiling, as the convective boiling effects increased at a higher vapor quality he introduced the enhanced factor E and suppression factor S to respectively accommodate the forced convective and nucleate boiling contributions.

Gungor and Winterton [35] modified the Chen’s correlation and proposed the correlations for the enhanced and suppression factors. A new correlation from Liu and Winterton [36]

introduced an asymptotic function to predict the heat transfer coefficient for vertical and horizontal flows in tubes and annuli. Zhang et al. [37] modified the Chen’s correlation to predict the heat transfer in mini channels. Besides, Tran et al. [11] modified the heat transfer correlation of Lazarek and Black [38] with the Reynolds number of the flow

replaced by the Weber number to eliminate viscous effects in favor of the surface tension.

Similar correlations were proposed by Fujita et al. [6].

Kandlikar [39] proposed a general correlation for saturated flow boiling heat transfer inside horizontal and vertical tubes. The correlation was based on a model utilizing the contributions due to nucleate boiling and convective mechanisms. In a following study [40,41], he developed correlations to predict transition, laminar and deep laminar flows in minichannels and microchannels. A new correlation for boiling heat transfer in small diameter channels was proposed by Kew and Cornwell [2]. The correlation was divided by three flow regimes based on the values of the Confinement number. Some empirical correlation equations proposed in the literature for flow boiling heat transfer coefficients in the small channels were summarized in Table 1.2.