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Two effects have been introduced as responsible factors in enhancement of heat transfer rate in non-boiling two-phase flows: 1) internal circulations in the slugs, leading to a

Solid - Liquid Flow Solid - Liquid Flow

L L/d = 1 L/d = 4 L/d = 6 L/d = 10 L/d = 1 L/d = 4 L/d = 6 L/d = 10 L

Gas - Liquid Flow Gas - Liquid Flow

Gas

Liquid

Liquid

Fig. 1 - Gas-Liquid plug flow for different liquid slug lengths. Rather, Prothero and Burton [3] only considered the

effect of void fraction in a limited sense. Their data will be presented in this study in a general plot in a later sec- tion, but cannot be re-reduced according to the approach suggested in this paper due to the lack of information on liquid plug lengths.

Oliver and Wright [5] conducted a series of measure- ments to investigate the effect of plug flow on heat trans- fer and friction in laminar flow. They surmised that the internal circulation would increase the heat transfer coef- ficient significantly, and therefore one would not be able to use Graetz -Leveque theory. They attributed the increase in heat transfer coefficient to both the effects of internal circulation and increased liquid velocity that results at constant mass flow rates due to the void fraction. They concluded that the effect due to void fraction is indepen- dent of plug length but that circulation effects would be strongest for shorter plugs. They reserved the assessment of plug length for a later study since the present apparatus used to collect data could not control liquid plug lengths very well. As part of a their study, Oliver and Wright [5] did develop simple correlations based upon their ex- perimental data and modification of the Graetz-Leveque model.

Hughmark [9] proposed a simple correlation using a modified Graetz-Leveque theory. However, his modifi- cations were based on the experimental observations of Oliver and Wright [5] and contained no new insights. Fur- ther, no rational basis was given for the proposed modi- fication. The proposed model was reported as:

hT PD√αL k = 1.75  ˙ mCp αLkL 1/3 µ µw 0.14 (1) Oliver and Young-Hoon [6,7] developed an experi- mental facility to produce liquid plugs of constant length using gas as a segmenting medium. This study was moti- vated by the earlier study of Oliver and Wright [5] which

observed increased enhancement for Newtonian and non- Newtonian flows. Oliver and Young-Hoon [6,7] conducted similar experiments as Oliver and Wright [5], except that plug length and liquid fraction were carefully controlled. They obtained data for a segmented fluid stream of con- stant liquid mass flow rate which contained liquid plugs of uniform length and distribution. They reported data for different two liquid flow rates and for plugs varying in length from 1 to 20 inches in a 1/4 inch diameter tube. They could also control the rate of gas flow while main- taining the plug size to study the effect of gas stream velocity and hence plug velocity. Heat transfer data were reported as a Nusselt number for the liquid phase versus a combined or two phase flow Graetz number. This was the first reported study to assess the affect of liquid plug length and liquid fraction on heat transfer.

Horvath et al. [3] obtained mass transfer data for liquid plugs of varying length for four Reynolds num- bers, using gas as a segmenting medium. They reported their data as a Nusselt number for the liquid plug phase only versus plug length at various Reynolds numbers for a stream having a constant liquid fraction of 0.5. The effect of plug velocity was studied by varying the two phase flow Reynolds number. Horvath et al. [5] also examined the effect of dimensionless tube length for very short plugs, but these data cannot be used since the liquid fraction varies from point to point and is not reported. However, they did show that dimensionless tube length (L/D), has a small effect on the overall heat transfer rate. We will delve into this issue in a later section.

Vrentas et al. [8] used solid steel spheres as a seg- menting medium in a stream of silicone oil. They re- ported liquid phase Nusselt data as a function of the stream Peclet number for three plug lengths. They also considered two different Prandtl numbers. The primary distinguishing feature of this work is that the liquid plug ends cannot be assumed to be approximately adiabatic as in a gas-liquid flow, as the authors report that the steel

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Figure 1.8: Gas-liquid slug flows for different slug lengths.

greater radial heat transfer rate, and 2) increased slug velocity when compared with the same single phase mass flow rate, which is a consequence of reduced phase fraction. Muzychka et al. [30] recently showed that only the first one is valid. As they argued, increasing the convective heat transfer coefficient, h, does not necessarily lead to a greater heat transfer since a segmented flow has smaller contact area compared with a single phase flow. Figure 1.9 shows the internal circulations caused by shear forces in the moving plugs.

Figure 1.9: Internal liquid plug circulation a) hydrophobic surface b) hydrophilic surface.

The internal circulations inside liquid slugs bring fresh liquid from center of the slug to the wall, where heat transfer process occurs. This provides a renewal mechanism to the thermal boundary layer and increases heat transfer. However, diffusion is important in this process as well, so the boundary layer grows until the circulation center (circulation eye) receives the heat. Figure 1.10 shows effects of the internal circulations on heat removal process for a constant wall temperature.