The flow boiling heat transfer in small diameter passages is being applied in ... expected to be phase change cooling, utilizing flow boiling of a refrigerant in ...
Flow Boiling Heat Transfer Coefficient In Minichannels – Correlation and Trends Satish G. Kandlikar Mark E. Steinke Mechanical Engineering Department, Rochester Institute of Technology, Rochester, New York 14623, USA
The flow boiling heat transfer in small diameter passages is being applied in many advanced designs, including electronics cooling, fuel cell heat exchangers, and other high heat flux dissipation applications. A number of studies are available in literature comparing flow patterns in minichannels to those observed in conventional channels. The present study is focused on comparing the flow boiling heat transfer coefficient with the correlations developed for conventional channels. It is found that the Kandlikar (1990) correlation developed for conventional diameter tubes is applicable for minichannels as well. The trends in the heat transfer coefficient with quality are also found to be similar to the conventional diameter tubes. One notable difference being the use of laminar flow equation for single phase liquid only heat transfer coefficient at Re below 1500-2300 for small diameter tubes.
1. Introduction The need to dissipate heat fluxes higher than those customarily handled by air cooling (10-20 W/cm2) is forcing the thermal designer to consider single-phase liquid cooling as an option. The next step in this direction is expected to be phase change cooling, utilizing flow boiling of a refrigerant in small diameter passages. Heat pipes, fuel cells, advanced compact evaporators, all utilize channel dimensions that are on the order of 1 mm hydraulic diameter. The classification of channels based on the hydraulic diameter poses considerable challenges as these channels are used in all three modes of heat transfer: single-phase, evaporation and condensation. The criteria for such classification are quite different for each of the processes. In the single-phase application, comparison with the intermolecular distances makes perfect sense. In flow boiling and condensation application, the bubble diameter and droplet diameters respectively have a physical significance. However, for the sake of uniformity, it is desirable to have a classification scheme that is independent of the heat transfer process occurring inside the channels. With this in mind, the following classification based upon hydraulic diameter, Dh, as proposed by Kandlikar (2001) is recommended: Conventional channels – Dh ≥ 3 mm; Minichannels – 3 mm > Dh ≥ 200 µm; Microchannels – 200 µm > Dh ≥ 1 µm. We will use the above classification for microchannels, minichannels and conventional channels in the present work. The available experimental data on flow boiling heat transfer for channels with hydraulic diameters falling within the range of 100 µm - 3 mm for microchannels will be analyzed in the present work.
2. Literature Review There are a number of correlations available in the literature for predicting flow boiling heat transfer coefficient inside a flow channel. The correlations by Chen (1966), Shah (1976), Gungor and Winterton (1987) and Kandlikar (1990, 1991) are among the widely used correlations. An important feature that is often overlooked in comparing the correlations is the trends predicted by these correlations for heat transfer coefficient variation with quality. The heat transfer coefficient can either increase with quality, remain constant, or decrease with quality, depending on two parameters – Boiling number, Bo=q/(GiLG), and liquid to vapor density ratio (ρL/ρG), where G is mass flux, q is heat flux, and iLG is latent heat of vaporization. It was seen that for water at low pressure, the heat transfer coefficient increases with quality, while at higher pressures, corresponding to a low value of density ratio, the heat transfer coefficient decreases with quality, especially at higher heat fluxes. Among the correlations, analyzed, the Kandlikar (1990) correlation was able to predict this trend accurately. The other correlations predict a consistently increasing trend in heat transfer coefficient with quality, although for refrigerants such as R113, R114, R11 (with a low value of liquid to vapor density at operating conditions), a decreasing trend is observed. Kandlikar (1991) developed a flow boiling map to depict the variation of heat transfer coefficient, h, with quality, x. The liquid to vapor density ratio, and the boiling number are used as parameters. For a high density
ratio (ρL/ρG), the convective effects dominate as quality increases. This leads to an increasing trend in h with increasing x. On the other hand, a high boiling number results in a higher nucleate boiling contribution, which tends to decrease as the vapor fraction increases. This leads to a decreasing trend in h with increasing x. The heat transfer coefficient thus exhibits all three trends depending on the values of density ratio and boiling number. This map is based on the trends seen in conventional channels. In the present work, these trends are verified for minichannels. The experimental data available in the literature is used in this comparison. Table 1 shows a list of some of the flow boiling heat transfer studies on minichannels available in the literature. Although there are a number of recent studies reported especially within the last year, the purpose of this study is to provide a representative comparison with the correlation and to verify the data trends for minichannels. A more detailed list of flow boiling studies in minichannels is reported by Kandlikar (2001).
3. Details of the Experimental Data Analyzed The refrigerants used in these studies include R11, R12, R113, R123, R124, R134a, R141b and FC-84. The mass flux range is between 50-1600 kg/m2s, and the heat flux range is between 5-600 kW/m2. Only those channel hydraulic diameters falling within the minichannel diameter range were investigated; the actual range of hydraulic diameters considered is from 400µm – 2.97 mm. The experimental data covers a wide range of parameters. In the present work, only those sets, which reported complete data for analysis, are included.
4. Correlation Details The flow boiling correlation by Kandlikar (1990, 1991) as reported in Kandlikar et al. (1999) is as follows:
hTP , NBD
hTP = larger of
(1)
hTP ,CBD
where hTP,NBD and hTP,CBD are two-phase heat transfer coefficients in the nucleate boiling dominant and convective boiling dominant regions, as given by the following equations.
hTP , NBD = 0.6683Co −0.2 (1 − x ) f (FrLO )hLO + 1058.0 Bo0.7 (1 − x ) FFl hLO 0.8
0.8
hTP ,CBD = 1.136Co − 0.9 (1 − x ) f (Frlo )hLO + 667.2 Bo0.7 (1 − x ) FFl hLO 0.8
0.8
(2,3)
where Co = (ρL/ρG)0.5[(1-x)/x]0.8 and Bo = q/(GiLG) are the convection and boiling numbers respectively, x is the quality. FFl is the fluid-surface parameter, as given in Table 2, that incorporates the effect of surface and fluid properties, and is believed to account for differences in nucleating characteristics. hLO is the single-phase heat transfer coefficient with all flow as liquid. The function f(FrLO) is a Froude number with all flow as liquid. This parameter addresses the stratified flow region. For microchannels, since there is no sustained stratified flow, this parameter is always set at 1.0. The single phase heat transfer coefficient is given by the Gnielinski correlation. h LO =
h LO =
Re LO Pr L ( f / 2 )(λ L / d )
for 104 ≤ReLO ≤ 5×106, and
(4)
(Re LO − 1000 ) PrL ( f / 2 )(λ L / d ) for 2300 ≤ReLO ≤ 104 0.5 2/3 1 + 12.7(Pr L − 1)( f / 2 )
(5)
1 + 12.7
(
)( f / 2)
Pr L2 / 3 − 1
0.5
where f = [1.58ln(ReLO)-3.28]-2, is the friction factor. For ease of use, with a slightly reduced accuracy, DittusBoelter correlation may be used for the single-phase correlation. For cases where the flow is laminar, Re
