In what follows the literature relevant to the present study is reviewed, especially on the use of boiling of dielectric liquids for cooling of electronic equipments including the single-phase and boiling heat transfer.
1.2.1 Steady single-phase and stable flow boiling heat transfer
Incropera et al. [2] investigated single-phase convective heat transfer of water and FC-77 from single array and four-row arrays of 12 flush-mounted heat sources in a horizontal rectangular channel for the channel Reynolds numbers ranging from 1,000 to 14,000. They developed a model to predict the relation between the Reynolds number and Nusselt number for the turbulent flow regime with 5,000< ReD <14,000. Unfortunately, the measured data were significantly under-predicted in the laminar flow regime. Investigation of single-phase and subcooled flow boiling heat transfer from a small heated patch with R-113 and FC-72 was carried out by Samant and Simon [3]. They combined the experimental data for R-113 and FC-72 to develop an empirical correlation. In addition, they observed large temperature excursions at the onset of nucleate boiling and a boiling hysteresis near the onset of nucleate boiling in the subcooled boiling. Garimella and Eibeck [4] analyzed the heat transfer characteristics of an six-row array of 30 heat sources in single-phase forced convection of water for the channel Reynolds number ranging from 150 to 5,150. They reported that the heat transfer coefficient decreased with decreasing Reynolds number and the Nusselt number decreased with increasing ratio of the channel height to protruding element height. Gersey and Mudawar [5] studied the orientation effect on the single-phase forced convection and subcooled flow boining of FC-72 over a nine in-line microelectronic chips. They proposed an empirically generalized equation based on their experimental data. Heindel et al. [6,7] examined single-phase liquid convection and flow boiling of water and FC-72 over a 1 x 10 array of flush
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mounted discrete heat sources in a horizontal rectangular channel. In investigating the critical heat flux of FC-72 for four in-line simulated electronic chips in vertical channel flow boiling experiments, Tso et al. [8] found that temperature of the chip surface decreased with the increases in the flow velocity and liquid subcooling in the partial boiling region and this result was opposed to that of Willingham and Mudawar [9] . The fluid velocity and subcooling temperature have smaller effect on the surface temperature in the fully-developed boiling region. They observed that increases in the fluid velocity and liquid subcooling resulted in a delay in the incipience of nucleate boiling and in an increase in the critical heat flux.
The single-phase heat transfer correlations proposed in some of the above studies are listed in Table 1.2.
1.2.2 Transient pool boiling heat transfer
Hohl et al. [10] conducted pool boiling of FC-72 subject to an increasing heating rate and found that CHF increased with the heating rate. Besides, the transient CHF is higher than the steady state CHF. Sakurai and Shiotsu [11] investigated transient pool boiling of water over a platinum wire of 1.2 mm in diameter and 97.9 mm in length to simulate a step input of reactivity in a nuclear reactor in which the reactor power rised exponentially with time. The incipient boiling heat flux was found to increase exponentially with time for the exponential period ranging from 5 ms to 10s.
Besides, the wire surface temperature at first increases with the heat input. Moreover, the heat transfer coefficient and heat flux at the incipient boiling point are higher for a shorter heating period.
Okuyama et al. [12] conducted pool boiling of R-113 at large stepwise power generation in a 7-μm thick copper foil focusing on the transient critical heat flux above which the effective heat removal in transient nucleate boiling could not be expected. They noted that the transient critical heat flux was lower than the critical heat flux in the steady state under a low system pressure. In the case of the low system pressure, the bubble near the transient critical heat flux has a peculiar shape like a
“straw hat” which was considered to be due to the consumption of the nucleate boiling liquid layer.
In the case of high system pressure, no more vapor bubble appears in transient nucleate boiling and
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transition occurs due to filling of the fine initial bubbles on the heat transfer surface. Besides, at low heat generation rate the wall superheat drops for a moment after boiling incipience. But at high heat generation rate this becomes hard to see, because the duration of nucleate boiling becomes extremely short. Later Okuyama and Iida [13] moved further to investigate liquid nitrogen pool boiling over a platinum wire with a stepwise heat generation. In the case of a low heat generation rate, boiling transition was observed to occur due to the coalescence of nucleate boiling bubbles.
While in the case of a high heat generation rate, a vapor sheath grows along the test wire since the excess superheat energy is stored in the liquid layer at boiling incipience. Besides, in the case of an extremely high heat generation rate, a lot of fine initial bubbles grow rapidly and simultaneously.
Boiling transition occurs due to the filling of the bubbles on the heater.
Transient nucleate boiling of several highly wetting fluids on a thick flat sample and a wire also with a stepwise heat generation was experimentally studied by Duluc et al. [14]. They observed that for the cases with high thermal inertia, fewer transient pool boiling was developed owing to the large heat capacity of the heater. Besides for the transient experiments subject to very fast heating, the wall superheat at boiling onset may be higher than the steady condition. Auracher and Marquardt et al. [15] investigated transient pool boiling from a thick copper with FC-72. They observed a hysteresis between the heating and cooling transient conditions. Under steady boiling conditions and with a clean heater surface, no hysteresis was observed.
1.2.3 Transient single-phase forced convection heat transfer
Girault and Petit [16] investigated transient single-phase forced convection in a horizontal plane channel with different time varying imposed heat fluxes on the channel walls. On the bottom plate the imposed heat flux varies like a sinusoidal wave. While on the top plate the imposed heat flux is like a rectangular wave. During the power-on period both the top and bottom plate temperatures were found to vary smoothly. There is a small wall temperature oscillation for the power-off situation. This is considered to result from the existence of internal energy in the channel walls even when the power is turned off. Bhowmik and Tou [17, 18] performed an experiment to
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study transient FC-72 forced convection heat transfer from a four-in-line chip module that is flush-mounted onto one wall of a vertical rectangular channel. The Reynolds number based on the heat source length ranges from 800 to 2,625 for the heat flux varying from 1 to 7 W/cm2. Their data suggest that the transient characteristics of the overall heat transfer coefficient are both of importance in the thermal systems during the power-on and power-off periods. Besides, the hear transfer coefficient was noted to be affected strongly by the number of chips. In a similar experiment [19] they investigated the transient heat transfer characteristics from an array of 4 x 1 flush mounted simulated electronic chips using water as the working fluid during the power-off periods. The Reynolds number based on the heat source length ranges from 1,050 to 2,625. The transient heat transfer regime in the period of 75s after the heater power is cut-off is examined.
They observed that the Nusselt numbers of the four chips at the beginning of power-off were close but then they diverged with time. However, the Nusselt number increases with time, due to the chip wall temperature decrease with time. When compared with water, an overall increase of 70% in the Nusselt number is obtained by using FC-72.
1.2.4 Transient flow boiling heat transfer
Kataoka et al. [20] 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 20ms, 50ms, or 10s) boiling, the transient maximum critical heat flux increases with decreasing period at constant flow velocity. Whereas, in the B-type (heating period is 5ms, 10ms, or 14ms) boiling, the transient maximum heat flux decreases first with the period and then increases. Two-phase flow and heat transfer in a small tube of 1 mm internal diameter using R-141b as the working fluid were studied by Lin et al. [21]. 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 be observed. This is caused by a
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combination of time varying heat transfer coefficient and time varying local pressure and fluid saturation temperature.
Two-phase flow instability in the flow boiling of various liquids in a long heated channel has been recognized for several decades [22, 23]. On a certain operating condition significant temporal oscillations in pressure, temperature, mass flux and boiling onset occur. Recently, some detailed characteristics associated with these instabilities were investigated through experimental measurement and theoretical modeling. Specifically in flow boiling of refrigerant R-11 in a vertical channel, the pressure-drop and thermal oscillations were observed by Kakac et al. [24]. Two-phase homogeneous model along with the thermodynamic equilibrium assumption was 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. Kakac and his colleagues [25]
further noted the presence of the density wave oscillation superimposed on the pressure-drop oscillations. Moreover, the dirft flux model was employed in their numerical perdiction. In a continuing study for R-11 in a horizontal tube of 106 cm long, Ding et al. [26] examined the dependence of the oscillation amplitude and period on the system parameters and located the boundary of various types of oscillations on the steady-state pressure-drop versus mass flux characteristic curves. A similar experimental study was carried out by Comakli et al. [27] for a 319.5 cm long tube. They showed that the channel length has an important effect on the two-phase flow dynamic instabilities.
The dynamic behavior for a horizontal boiling channel connected with a surge tank for liquid supply has also received some attention. Mawasha and Gross [28] used a constitutive model containing a cubic nonlinearity combined with a homogeneous two-phase flow model to simulate the pressure-drop oscillstion. Their prediction is matched with the measured data. Later, the channel wall capacity effects was included [29] to allow the wall temperature and heat transfer coefficient to vary with time.
Wang et al. [30] noted that the boiling onset in a upward flow of subcooled water in a vertical
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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.
Brutin et al. [31] reported the pressure-drop oscillations of n-pentane liquid in a vertical small rectangular channel (Dh=0.889mm, L=50mm & 200mm). A non-stationary state of two-phase flow was observed. The effects of the inlet flow condition on the boiling instabilities were found to be relatively significant [32]. A similar study for subcooled flow boiling of deionized water was conducted by Shuai et al. [33] and the pressure-drop oscillations were also noted.
1.2.5 Bubble Characteristics
Literature relevant to the bubble characteristics in boiling flow is briefly reviewed. A recent experiment conducted by Chang et al. [34] focused on the behavior of near-wall bubbles in subcooled flow boiling of water. The population of the near-wall bubbles was found to increase with the increase in the heat flux and in the superheated liquid layer very small bubbles were noted to attach to the heated wall. In addition, the coalesced bubbles are smaller for a higher mass flux of the flow. Cornwell and Kew [35] examined various flow regimes for boiling of refrigerant R-113 in a vertical rectangular multi-channel with Dh = 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. Lie and Lin [36, 37] examined flow boiling heat transfer and associated bubble characteristics of R-134a in a narrow annular duct (Dh=4, 2 mm). They concluded that the bubbles are suppressed to become smaller and less dense by raising the refrigerant mass flux and
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inlet subcooling. The mean bubble departure frequency increases with the increasing refrigerant mass flux and saturated temperature and with the decreasing duct size. Moreover, the active nucleation site density is much higher at a lower refrigerant mass flux particularly at a high imposed heat flux. Bang et al. [38] examined boiling of R-134a in a vertical rectangular channel focusing on the characteristic structures in the near-wall region. They noted the presence of the vapor remnants below the discrete bubbles and coalesced bubbles and the presence of an interleaved liquid layer between the vapor remnants and bubbles. Besides, the bubble layer was divided into two types, a near-wall bubble layer dominated by small bubbles and a following bubble layer prevailed by large coalesced bubbles. Kandlikar [39] examined the subcooled flow boiling of water in a rectangular horizontal channel. They concluded that the bubble growth was slow at high subcooling and the departure diameter decreased as the flow rate increased.
By using optical measurement techniques, Maurus et al. [40,41] examined the bubble size distribution and local void fraction in subcooling flow boiling of water at atmospheric pressure.
They reported that the bubble size increased with an increase in the heat flux but reduced with an increase in the mass flux. The total bubble life time, the remaining lifetime after the detachment process and the waiting time between two bubble cycles decreased significantly as the mass flux increased. In a recent study Maurus and Sattelmayer [42] further defined the bubbly flow region by the ratio of the averaged phase boundary velocity to the averaged fluid velocity. On the other hand, an experimental analysis was carried out by Thorncroft et al. [43] 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) and decreased at increasing mass flux in both upflow and downflow. Bubble rise characteristics after the bubble departure from a nucleation site in vertical upflow tube boiling were investigated by Okawa et al. [44-46]. They noted that the flow inertia had a significant influence on the onset of detachment but the influence was gradually reduced with time. They also observed three different bubble rise paths after the departure from nucleation sites. Specifically, some bubbles slide upward along the vertical wall, some bubbles detach from the wall after sliding, and
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other bubbles remain close to the wall and reattach to the wall. Forced convection boiling experiments conducted by Situ et al. [47,48] for water in a vertical annular channel revealed that the bubble departure frequency increased as the heat flux increased. Moreover, the experimental results indicate that bubble lift-off diameter increases at increasing inlet temperature and heat flux.
In addition, Yin et al. [49] examined the subcooled flow boiling of R-134a in a horizontal annular duct and noted that both the bubble departure size and frequency reduced at increasing liquid subcooling. They found that only the liquid subcooling showed a large effect on the bubble size.