**3. Data Reduction and Uncertainty Analysis**

## *3.1. Data Reduction*

Experimental data were analyzed to determine the vapor quality, heat flux, and heat transfer coefficient. The overall heat transfer rate of the test section was reduced using the conservation of heat for both the water side and refrigerant side.

$$Q\_{\mathbf{w}} = c\_{p,ts} m\_{\mathbf{w},ts} (T\_{\mathbf{w},ts,out} - T\_{\mathbf{w},ts,in}) \text{ a } = 1,\tag{1}$$

where *cp,ts* refers to the specific heat of water taken at the average bulk temperature of the test section, *mw,ts* is the mass flow rate of tube-side water acquired by the magnetic flow meter, and *Tw,ts,in* is the water temperature at the inlet and *Tw,ts,out* is the water temperature at the outlet of the test section. Any heat loss in the test section was minimal because of the insulation (verified by the heat loss study). Heat flux, *q*, was based on the inner surface area *Ai* deduced from the internal diameter of the equivalent smooth tube, calculated using the following equation:

$$q = Q\_w / A\_o. \tag{2}$$

Inlet vapor quality (*xin*) was determined using the energy balance of the electric preheater. Total heat measured (*Qph*) by the wattmeter was regarded as the heat imposed in the preheater, and it consisted of two components, sensible heat (*Qsens*) and latent heat (*Qlat*).

$$Q\_{\rm plr} = \lambda\_{\rm plr} \cdot VI = Q\_{\rm lat} + Q\_{\rm scus\_{\prime}} \tag{3}$$

$$Q\_{\rm sens} = c\_{p,l,ref} m\_{ref} (T\_{\rm sat} - T\_{ref,ph,in}) \,\,,\tag{4}$$

$$Q\_{\rm lat} = m\_{ref} h\_{\rm lv} \chi\_{\rm inv} \tag{5}$$

$$\text{Lx}\_{\text{in}} = \frac{\lambda \cdot VI}{m\_{\text{ref}} h\_{\text{lv}}} - \frac{\text{c}\_{p, l, ref}}{h\_{\text{lv}}} (T\_{\text{sat}} - T\_{\text{ref}, ph, in}) \, , \tag{6}$$

where λ*ph*, *V*, *I*, *cp*,*l*,*ref* , *mref*, *Tref*,*ph,in*, and *hlv* refer to the heat conservation factor to account for heat loss of the preheater, electric voltage and current, specific heat of refrigerant obtained at the mean temperature of the preheater, mass flow rate, inlet temperature, and latent heat of the refrigerant, respectively. Accordingly, the vapor quality at the exit of the test section, *xout*, was calculated as

$$\mathbf{x}\_{\rm out} = \mathbf{x}\_{\rm in} - Q\_{\rm w} / \left( m\_{ref} h\_{lv} \right). \tag{7}$$

Average vapor quality of the test section could be determined as

$$\mathbf{x}\_{\text{ave}} = \frac{\mathbf{x}\_{\text{in}} + \mathbf{x}\_{\text{out}}}{2}. \tag{8}$$

The logarithmic mean temperature difference between the tube side and annulus was determined from the inlet and exit temperatures of refrigerant and water.

$$\text{LMTD} = \frac{(T\_{ref,ts,out} - T\_{w,ts,in}) - \left(T\_{ref,ts,in} - T\_{w,ts,out}\right)}{\ln\left[\left(T\_{ref,ts,out} - T\_{w,ts,in}\right) / \left(T\_{ref,ts,in} - T\_{w,ts,out}\right)\right]} \tag{9}$$

where *Tref,ts,in* and *Tref,ts,out* refer to the inlet and outlet temperature of the refrigerant in the annulus, while *Tw,ts,in* and *Tw,ts,out* refer to the inlet and exit temperatures in the water. Assuming that there was no fouling resistance for the internal surface of the tube, the heat transfer coefficient (*href*) for condensation and evaporation was deduced from the following equation:

$$h\_{ref,o} = \frac{1}{A\_o \left[\frac{\text{LMTD}}{Q\_w} - \frac{1}{h\_{wj}A\_i} - \frac{\ln(d\_o/d\_i)}{2\pi Lk}\right]} \tag{10}$$

where *Ai* and *Ao* refer to the tube-side and shell-side heat transfer areas, respectively, *di* and *do* are the internal and external diameters of the tested tubes, and *k* is the thermal conductivity of the tube wall. It is worth noting that *Ai* and *Ao* for the enhanced tubes were determined using the nominal inner and outer diameter of test tubes.

Extensive experimental investigations showed that the Gnielinski [22] correlation can accurately predict the convective heat transfer coefficients in a plain tube or annulus, and the correlation is valid in the range 3000 <sup>&</sup>lt; *Rew* <sup>&</sup>lt; <sup>5</sup> <sup>×</sup> <sup>10</sup><sup>6</sup> and 0.5 <sup>&</sup>lt; *Prw* <sup>&</sup>lt; 2000; this covers the present test conditions. Therefore, the Gnielinski [22] correlation was utilized to predict the in-tube heat transfer coefficients, *hw*, for the smooth tube.

$$h\_{\rm av} = \frac{(f/2)(Re\_{\rm av} - 1000)Pr\_{\rm av}}{1 + 12.7(f/2)^{0.5}(Pr\_{\rm av}^{2/3} - 1)} \Big(\frac{\mu\_{\rm bulk}}{\mu\_{\rm wall}}\Big)^{0.14} \frac{k\_{\rm av}}{d\_{\rm av}}.\tag{11}$$

The ratio, (μ*bulk*/μ*wall*) 0.14 accounts for the influence of viscosity at the water bulk and the internal wall temperature; thermal conductivity (*kw*) values were determined at the mean temperature of the water. Fanning friction factor, *f*, was predicted by the Petukhov correlation [23] for plain tubes, which is applicable for 3000 <sup>&</sup>lt; *Rew* <sup>&</sup>lt; <sup>5</sup> <sup>×</sup> <sup>10</sup>6, and is given by

$$f = \left(1.58 \ln Re\_{\text{w}} - 3.28\right)^{-2}.\tag{12}$$

However, the above predictive procedures were inappropriate to use with the 1EHT tube since the inner surface of 1EHT tube was modified with enhancement patterns. Therefore, Wilson plot tests were used to calculate the water-side heat transfer coefficients *hw*. The overall thermal resistance of the test section for the 1EHT tube was calculated as follows:

$$\frac{1}{h\_{\rm ts}} = \frac{d\_o}{a h\_w d\_i} + \frac{1}{h\_{ref}} + \frac{d\_o \ln(d\_o/d\_i)}{2k},\tag{13}$$

where *hts* refers to the total heat transfer coefficient of the test section, and *a* represents the in-tube heat transfer enhancement ratio (EHT tube compared to an equivalent plain tube). During the Wilson plot tests, the refrigerant mass flow rate was fixed at a relatively large value in order to minimize the experimental error; mass flow rate and the temperature of water were adjusted to obtain a linear relationship between the water-side thermal resistance and the overall resistance. The Wilson plot results for the 1EHT tube are given in Table 1.

All the thermal and transport properties of the refrigerant in the analysis were acquired from REFPROP 9.0, which was developed and released by NIST (National Institute of Standards and Technology). [24]; all the instruments including pressure transducers, Platinum 100 RTDs, and mass flow meters in the test apparatus were calibrated according to an NIST traceable standard.
