Conventional Sized Channels

The concepts of boiling in micro-channels and comparison to conventional size channels are considered in Chap. 6. The mechanism of the onset of nucleate boiling is treated. Specific problems such as explosive boiling in parallel micro-channels, drag reduction and heat transfer in surfactant solutions are also considered. 

In general, the axial heat conduction in the channel wall, for conventional size channels, can be neglected because the wall is usually very thin compared to the diameter. Shah and London (1978) found that the Nusselt number for developed laminar flow in a circular tube fell between 4.36 and 3.66, corresponding to values for constant heat flux and constant temperature boundary conditions, respectively. 

Because most applications for micro-channel heat sinks deal with liquids, most of the former studies were focused on micro-channel laminar flows. Several investigators obtained friction factors that were greater than those predicted by the standard theory for conventional size channels, and, as the diameter of the channels decreased, the deviation of the friction factor measurements from theory increased. The early transition to turbulence was also reported. These observations may have been due to the fact that the entrance effects were not appropriately accounted for. Losses from change in tube diameter, bends and tees must be determined and must be considered for any piping between the channel plenums and the pressure transducers. It is necessary to account for the loss coefficients associated with singlephase flow in micro-channels, which are comparable to those for large channels with the same area ratio. 

Understanding the differences in two-phase flow characteristics between conventional size channels and micro-channels is also important for designing mini- or micro-heat exchangers, since the flow characteristics will affect the phase change heat transfer. 

Flow Patterns in a Single Conventional Size Channel... 

How patterns in conventional size channels deviate significantly from those in micro-channels. Slug and annular flow constitute dominant flow patterns in con-... 

On the other hand, in the study by Serizawa et al. (2002) the cross-sectional averaged void fraction was correlated with the Armand (1946) correlation as shown in Fig. 5.26. This trend does not contradict the data reported for conventional size channels, but it is different from results obtained by Kawahara et al. (2002). Disagreement between results of void fraction in micro-channels obtained by different investigators was shown by Ide et al. (2006) and will be discussed in the next section. 

Zhao and Bi (2001b) measured pressure drop in triangular conventional size channels d = 0.866—2.866 mm). The variations of the measured two-phase frictional multiplier with the Martinelli parameter X for the three miniature triangular channels used in experiments are displayed, respectively, in Fig. 5.29a-c. In Fig. 5.29 also shown are the curves predicted by Eq. (5.25) for C = 5 and C = 20. It is evident from Fig. 5.29 that the experimental data are reasonably predicted by the Lockhart-Martinelli correlation, reflected by the fact that all the data largely fall between the curves for C = 5 and C = 20, except for the case at very low superficial liquid velocities. 

Comparison of Gas-Liquid Two-Phase Flow Characteristics Between Conventional Size Channels and Micro-Channels... 

Me et al. (2006) addressed the differences in gas-liquid two-phase flow characteristics that occur in conventional size channels and micro-channels by examining the two-phase flow pattern, interfacial wave, void fraction and friction pressure drop data obtained in circular and rectangular channels with a hydraulic diameter ranging from 50 pm to 6.0 mm. 

The experimental data obtained in conventional size channels and micro-channels with diameters between 100 pm and 6.0 mm are examined to further elucidate and understand the differences in two-phase flow characteristics between the microchannels and conventional size channels. Since two separate sets of experiments have been conducted using air and water in acrylic channels with diameters between 500 pm and 6.0 mm, and nitrogen gas-water in fused silica channels with diameters between 50 and 500 pm, the authors refer to the former channels as conventional size channels, and the latter channels as micro-channels for convenience. Two different inlet sections were covered in micro-channel experiments, a gradually reducing section and a T-junction. 

The void fraction data obtained in micro-channels and conventional size channels showed significant differences depending on the channel cross-section and inlet geometry. For the micro-channel with a diameter of 100 pm, the effects of the inlet geometry and gas-liquid mixing method on the void fraction were seen to be quite strong, while the conventional size channels have shown a much smaller effect of inlet geometry on the void fraction. 

In eontrast, the conventional size channel void fraction data conform to the Ar-mand correlation (1946). To our knowledge, no unusually low void fraction data have been reported for conventional size channels, so the two-phase flow in conven-... 

Thus, similar void fraction data can be obtained in micro-channels and conventional size channels, but the micro-channel void fraction can be sensitive to the inlet geometry and deviate significantly from the Armand correlation. 

For a micro-channel connected to a 100 pm T-junction the Lockhart-Martinelli model correlated well with the data, however, different C-values were needed to correlate well with all the data for the conventional size channels. In contrast, when the 100 pm micro-channel was connected to a reducing inlet section, the data could be fit by a single value of C = 0.24, and no mass velocity effect could be observed. When the T-junction diameter was increased to 500 pm, the best-fit C-value for the 100 pm micro-channel again dropped to a value of 0.24. Thus, as in the void fraction data, the friction pressure drop data in micro-channels and conventional size channels are similar, but for micro-channels, significantly different data can be obtained depending on the inlet geometry. 

In contrast to conventional size channels, the flow regimes and heat transfer coefficients in micro-channels are not sensitive to the channels inclination. In the range of Rcls = 4-56 and Rcqs = 4.7-270 an increase in Rees leads to a decrease in the heat transfer coefficient (Hetsroni et al.) as opposed to results reported for minichannels. 

Only a few experimental investigations deal with heat transfer of gas-liquid flow in the conventional size channels. There is a significant discrepancy between experimental results on heat transfer presented for channels of dh = 1-100 mm. No data is available in the literature on gas-liquid heat transfer in miero-channels, except for the results on the study of heat transfer in the test section that contains 21 parallel triangular micro-channel of r/h = 130 pm reported in the present chapter. In the range of superficial velocities Uls = 0.015-0.244 m/s, Ugs = 0.50—28.6 m/s the heat transfer coefficient increases with increasing liquid velocity and decreases with increasing air velocity. 

The subject of Chap. 6 is boiling in micro-channels. Several aspects of boiling are also considered for conventional size channels and comparison with micro-channels was carried out. Significant differences of ONB in micro-channels have been discussed compared to conventional channels. Effect of dissolved gases on boiling in water and surfactant solution was revealed. Attention was paid on pressure drop and heat transfer, critical heat flux and instabilities during flow boiling in microchannels. 

Onset of Nucleate Boiling in Conventional Size Channels... 

The first approach developed by Hsu (1962) is widely used to determine ONE in conventional size channels and in micro-channels (Sato and Matsumura 1964 Davis and Anderson 1966 Celata et al. 1997 Qu and Mudawar 2002 Ghiaasiaan and Chedester 2002 Li and Cheng 2004 Liu et al. 2005). These models consider the behavior of a single bubble by solving the one-dimensional heat conduction equation with constant wall temperature as a boundary condition. The temperature distribution inside the surrounding liquid is the same as in the undisturbed near-wall flow, and the temperature of the embryo tip corresponds to the saturation temperature in the bubble 7s,b- The vapor temperature in the bubble can be determined from the Young-Laplace equation and the Clausius-Clapeyron equation (assuming a spherical bubble) ... 

To estimate the value of the bulk liquid temperature at ONB in conventional size channels, as well as in micro-channels the energy and continuity equations should be considered. 

Onset of Nucleate Boiling in Conventional Size Channels where / = 2Tw/(pt/ ), tw is the wall shear stress. 

The pressure spike introduces a disruption in the flow. Depending on the local conditions, the excess pressure inside the bubble may overcome the inertia of the incoming liquid and the pressure in the inlet manifold, and cause a reverse flow of varying intensity depending on the local conditions. There are two ways to reduce the flow instabilities reduce the local liquid superheat at the ONB and introduce a pressure drop element at the entrance of each channel, Kandlikar (2006). Kakac and Bon (2008) reported that density-wave oscillations were observed also in conventional size channels. Introduction of additional pressure drop at the inlet (small diameter orifices were employed for this purpose) stabilized the system. 

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