*4.1. Heat Transfer Characteristics of Condensation*

In the condensation study, two test sections with different inner diameters of the outer tube were employed to investigate the influence of the annulus gap. The relationship of the condensation heat transfer and mass velocity is given in Figure 6a; the corresponding heat flux values are also given in Figure 6b for a comparison. These results differ from similar experimental investigations reported by Tang and Li [18] and Chen et al. [26]; the results of the present study show that the heat transfer coefficient increased with increasing mass flux, implying that the convective condensation component occupied an important role in the overall heat transfer for the present test conditions. Additionally, increased mass fluxes could also improve the interfacial shear stress and move the accumulated condensate at the bottom of the annulus to the upper part, improving the overall performance.

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**Figure 6.** Variation of (**a**) heat transfer coefficient and (**b**) heat flux as a function of mass flux during condensation for a smooth tube with a different annulus spacing.

The heat transfer coefficient for the wide annulus case showed heat transfer that was approximately 33% to 50% larger than the narrow annulus case; this can be attributed to the improvement of the convective heat transfer. According to Cavallini et al. [27], the in-tube condensation flow patterns can be divided into two types: ΔT-dependent flow and ΔT-independent flow; in a horizontal tube, ΔT-dependent flow occurs when gravity is the dominant force. A similar classification can be applied to the annulus condensation cases; they all fall into the ΔT-dependent flow case due to the relatively low mass fluxes and large channel gap dimensions. For the ΔT-dependent flow case, the film condensation heat transfer component and the convective heat transfer component should be included in order to achieve an accurate prediction. Chen [28] solved the boundary layer equation for laminar film condensation of quiescent vapor on a single horizontal smooth tube; the theoretical equation for the heat transfer coefficient was given as

$$h\_o = 0.728 \left( \frac{\rho\_l (\rho\_l - \rho\_{\mathcal{S}}) g h\_{lv} k\_l^3}{\mu\_l d\_o (T\_{\rm sat} - T\_{\rm null})} \right)^{1/4},\tag{15}$$

where the physical properties are acquired at the mean temperature between the wall and the saturation temperature of the refrigerant. Tang and Li [18] introduced a modified heat transfer equation that could be used to predict the present data; this model added a retention angle, α, into the Chen [28] equation in order to account for the effect of vapor quality.

It should be noted that the average vapor quality along the test section was employed for the prediction of heat transfer coefficients for simplification. In addition, little difference was found between the predicted values calculated from average vapor quality and the average value in the vapor quality range. The comparison between the experimental and predicted values of Chen [28] and Tang and Li [18] correlation is illustrated in Figure 7. There was an obvious deviation between hexp and hpre for the Chen correlation; all these data points were overpredicted with a mean absolute deviation (MAD) of 42.5%. When using the Tang and Li [18] correlation, an acceptable prediction was given with a MAD of 7.9%; 84.6% of the data points could be predicted in an error band of ±30%. However, neither of the above correlations could accurately predict the variation of the heat transfer coefficient versus mass flux, which would be an important contribution to the thermal performance during condensation in the annulus. Additional investigations and experimental data are demanded to explore the heat transfer mechanisms during this phenomenon.

**Figure 7.** Prediction of Chen, and Tang and Li [18] correlation against the present data for condensation on the smooth tube.

Values of the MAD were determined as follows:

$$\text{MAD} = \frac{1}{N} \sum\_{1}^{N} \frac{|h\_{\text{exp}} - h\_{\text{pre}}|}{h\_{\text{exp}}} \times 100\%. \tag{16}$$

Figure 8a shows the variation of the heat transfer coefficient with mass flux during condensation on the outside of the 1EHT tube in the annulus; results were compared to the smooth tube. Figure 8b provides the heat flux variation for all of the test conditions. As can be seen, there was little variation between the 1EHT tube and the smooth tube; therefore, it is reasonable to compare their thermal performance under the same mass flux. It should be noted that all the results in Figure 8 were acquired for condensation in an annulus with an outer diameter Di = 25 mm, with the heat flux ranging from 8–18 kW/m2. The results demonstrate that the 1EHT tube provided an enhancement to the annulus condensation heat transfer performance (when compared to a smooth tube) in the range of 98–178%. According to Chen et al. [28], the superior performance of the 1EHT tube for condensation in an annulus was explained by the turbulence and flow pattern change caused by the enhanced surface structure. Additionally, surface tension might be a dominant contributor to the condensation heat transfer for Gref < 50 kg/(m2·s). Tang and Li [18] concluded that increasing the mass flux in the annulus may change the flow pattern; two possible flow patterns are given in Figure 9. Generally, the cross-sectional liquid distribution depends on the joint actions of three forces, including gravity, surface tension, and

shear stress. At low mass fluxes, the condensate would accumulate at the bottom due to gravity being dominant; as the mass flux increases, shear stress begins to have a greater influence. In addition, the specific structures of the external tube surface can augment the convective heat transfer and begin to produce more turbulence, fluid mixing enhancement, boundary layer disruption, and creation of secondary flows.

**Figure 8.** Variation of (**a**) heat transfer coefficient and (**b**) heat flux as a function of mass flux during condensation on the 1EHT tube in the annulus with *Dh* = 5.95 mm compared to a smooth tube.

The effect of vapor quality on the condensation characteristics in the annulus was also investigated at fixed mass velocities *Gref* <sup>=</sup> 80 kg/(m2·s) and *Gref* <sup>=</sup> 100 kg/(m2·s); results are given in Figure 10a. The results indicate that the heat transfer coefficient increased rapidly with increasing vapor quality, especially for the vapor quality *xave* < 0.6, and the thermal performance of the 1EHT tube at *Gref* <sup>=</sup> 80 kg/(m2·s) was slightly worse than that at *Gref* = 100 kg/(m2·s). The steep slope for the heat transfer coefficient versus vapor quality resulted from the increasing cross-sectional void fraction; the condensate redistributed circumferentially and produced a decrease in the average film thickness on the tube. Figure 10b shows that the heat flux was fixed in a narrow range of 3–5 kW/m2. Heat transfer coefficients at *xave* = 0.5 were nearly two times higher than those data points in Figure 8a at the same mass flux. This could have been caused by the increased film thermal resistance on the external surface of 1EHT tube with the increased heat flux. The negative relationship between heat transfer coefficient and heat flux seems to have a steeper slope than predicted in the Chen et al. [28] and Tang and Li [18] correlation. The steeper slope may be attributed to the increasing condensate on the tube, and the severely flooded dimples on the surface with increasing heat flux. Generally, gravity causes the condensate on the surface to flow down the tube and accumulate at the bottom of the annulus; however, increased heat flux and dimples may increase the film thickness and degrade the thermal performance.
