# Robust and General Model to Forecast the Heat Transfer Coefficient for Flow Condensation in Multi Port Mini/Micro-Channels

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## Abstract

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## 1. Introduction

#### 1.1. Previous Works

#### 1.1.1. Channels’ Classifications

#### 1.1.2. Experimental Research

#### 1.1.3. Previous Models for Condensation HTC

#### 1.1.4. Contributions of the Present Study

## 2. Materials and Methods

#### 2.1. Genetic Programming

#### 2.2. Experimental Data Samples

_{tp}numbers for refrigerants condensation in multi-port mini/micro-channels. Most of these data are available as figures from the database sources listed in Table 1, which have been extracted using the GetData Graph Digitizer.

#### 2.3. Error Analysis

## 3. Results and Discussion

## 4. Conclusions

- The effects of all affecting parameters $\left(R{e}_{l},P{r}_{l},{X}_{tt},Bo,x\right)$ on the HTC were considered in the GP correlation. Using these parameters led to a correlation that estimates the condensation HTC with reasonable accuracy. The new correlation estimated the HTC with a total AARD of 16.87% for a broad range of data samples. In addition, the percentages of all data with error lower than 20% and 30% for the new model were 70.04% and 84.43%, respectively.
- The previous models’ predictions of the HTC were also compared to the measured data. The previous correlations showed significantly higher deviations from the experimental data compared to the new correlation. The total AARD values for the correlations of Kim and Mudawar [52], Dorao and Fernandino [49], Shah (2016) [90], Shah (2019) [57], Crosser [92], Hosseini et al. [56], Bohdal et al. [93], and Akers et al. [91] were, respectively, 36.94%, 41.54%, 43.39%, 43.45%, 44.07%, 44.68%, 164.97%, 191.19%. It was found that the previous models can not be considered as general correlations for estimating the condensation HTC in multi-port channels. However, the new GP correlation provides much-improved estimates for the HTCs.
- The new model and previous correlations were used for estimating the HTC in channels with different sizes. It was shown that the new correlation estimated the data for micro and mini-channels with the AARD of 16.60% and 16.91%, respectively, and was the most accurate for all cases among all correlations. In addition, the new GP correlation estimated more than 80% of all data for both micro and mini-channels with an error of lower than 30%. This is because using the Bond number in the new model explicitly includes the effects of surface tension in different channel sizes. The previous correlations, however, showed relatively large deviations for all cases. Furthermore, their deviations become larger when the channel’s diameter decreases, and all correlations had AARD values of more than 50% for micro-channels.
- The new model developed by GP was shown to be suitable for estimating the condensation HTC in multi-port channels over a broad range of vapor qualities, mass velocities, saturation temperatures, channel diameters, and working fluids.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

h | Coefficient of heat transfer, ${\mathrm{W}\mathrm{m}}^{-2}{\mathrm{K}}^{-1}$ |

Bo | Bond Number $=g\left({\rho}_{l}-{\rho}_{v}\right){D}^{2}{\sigma}^{-1}$, (-) |

$F{r}_{l}$ | Froude number $={G}^{2}{\rho}_{L}^{-2}{\mathrm{g}}^{-1}{D}^{-1}$, (-) |

G | Total flux, k$\mathrm{g}{\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$ |

${J}_{g}$ | Dimensionless velocity of vapor |

${H}_{lv}$ | Latent heat, ${\mathrm{J}\mathrm{Kg}}^{-1}$ |

$Pr$ | Prandtl number, (-) |

k | Thermal conductivity, ${\mathrm{W}\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ |

$N{u}_{tp}$ | Nusselt number = $hD{k}_{l}^{-1}$, (-) |

${P}_{c}$ | Critical pressure, Pa |

${P}_{red}$ | Reduced pressure = ${P}_{s}{P}_{c}{}^{-1}$, (-) |

${P}_{s}$ | Saturation pressure, Pa |

$R{e}_{v}$ | $\mathrm{Vapor}\mathrm{Reynolds}\mathrm{number}=GxD{\mu}_{v}{}^{-1}$, (-) |

$P{r}_{tp}$ | Prandtl number = $P{r}_{l}\left(1-x\right)+xP{r}_{v}$, (-) |

$R{e}_{l}$ | Superficial liquid Reynolds number = $G\left(1-x\right)D{\mu}_{l}{}^{-1}$, (-) |

$R{e}_{lo}$ | Liquid Reynolds number = $GD{\mu}_{l}{}^{-1}$, (-) |

$R{e}_{tp}$ | Flow Reynolds number = $R{e}_{l}$ + $R{e}_{v}$, (-) |

$Su$ | Suratman Number, (-) |

${T}_{s}$ | Saturation temperature, $\mathbb{C}$ |

$W{e}_{vo}$ | Vapor only Weber number = ${G}^{2}D{\rho}_{v}{}^{-1}{\sigma}^{-1}$, (-) |

x | Vapor quality, (-) |

${X}_{tt}$ | $\mathrm{Martinelli}\mathrm{parameter}={\left({\mu}_{l}/{\mu}_{v}\right)}^{0.1}{\left({\rho}_{v}/{\rho}_{l}\right)}^{0.5}{\left(\left[1-x\right]/x\right)}^{0.9}$, (-) |

x | Vapor quality, (-) |

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**Figure 2.**Comparison between the Nusselt number estimated by Equation (13) and the measured data. The solid points represent the outcomes of Equation (13). The solid line represents the best fitting between experimental and estimated data, and the dash lines represent the $\pm 30\%$ error bounds.

**Figure 3.**Comparison of predictions of the previous condensation HTC models with all 3503 experimental data points: (

**a**) Kim and Mudawar [52], (

**b**) Dorao and Fernandino [49], (

**c**) Shah (2016) [90], (

**d**) Shah (2019) [57], (

**e**) Crosser [92] and (

**f**) Hosseini et al. [56]. The solid points represent the outcomes of different models. The solid line represents the best fitting between experimental and estimated data, and the dash lines represent the $\pm 30\%$ error bounds.

**Figure 4.**Comparison of the predictions of the GP correlation (Equation (13)) and the model of Kim and Mudawar [52] with the experimental data [37] for R744 condensing at the saturation temperature of 15 $\mathbb{C}$ inside a 0.13 mm channel under different vapor qualities and mass fluxes. Blue and red points represent the G = 600 $\mathrm{kg}.{\mathrm{m}}^{-2}\xb7{\mathrm{s}}^{-1}$ and G = 800 $\mathrm{kg}\xb7{\mathrm{m}}^{-2}.{\mathrm{s}}^{-1}$, respectively. The solid points, solid lines, and dash lines represent the experimental values, GP outcomes, and Kim and Mudawar [52] outcomes.

**Figure 5.**Comparison of the predictions of the GP correlation (Equation (13)) and the model of Kim and Mudawar [52] with the experimental data [72] for R134a condensing at the mass flux of 800$\mathrm{kg}.{\mathrm{m}}^{-2}.{\mathrm{s}}^{-1}$ inside a 0.33 mm channel under different saturation temperatures. Blue and red points represent the ${\mathrm{T}}_{\mathrm{s}}=50\xb0\mathrm{C}$ and ${\mathrm{T}}_{\mathrm{s}}=60\xb0\mathrm{C}$, respectively. The solid points, solid lines, and dash lines represent the experimental values, GP outcomes and Kim and Mudawar [52] outcomes.

**Figure 6.**Comparisons of the predictions of the GP correlation (Equation (13)) and the model of Kim and Mudawar [52] with the experimental data [82] for R744 condensing at the mass flux of 800$\mathrm{kg}\xb7{\mathrm{m}}^{-2}\xb7{\mathrm{s}}^{-1}$ and saturation temperature of 0 °C inside different channel diameters. Blue and red points represent the D = 68 mm and D = 78 mm, respectively. The solid points, solid lines, and dash lines represent the experimental values, GP outcomes and Kim and Mudawar [52] outcomes.

**Figure 7.**Comparison of the predictions of the GP correlation (Equation (13)) and the model of Kim and Mudawar [52] with the experimental data [73,76] for R290 and R32 condensing at the mass flux of 350$\mathrm{kg}\xb7{\mathrm{m}}^{-2}\xb7{\mathrm{s}}^{-1}$ and saturation temperature of 40 $\mathbb{C}$ inside a 1.16 mm channel. Blue and red points represent the R290 and R32, respectively. The solid points, solid lines, and dash lines represent the experimental values, GP outcomes, and Kim and Mudawar [52] outcomes, respectively.

References | Fluid | Channel Geometry | Hydraulic Diameter (mm) | Mass Flux $(\mathbf{k}\mathbf{g}{\mathbf{m}}^{-2}{\mathbf{s}}^{-1})$ | Reduced Pressure (-) | Number of Points |
---|---|---|---|---|---|---|

Agarwal [72] | R134a | Rectangular, Square | 0.1 to 0.16 | 300 to 800 | 0.19 to 0.42 | 291 |

Belchi et al. [73] | R290 | Square | 1.16 | 175 to 350 | 0.25 to 0.40 | 100 |

Belchi et al. [74] | R32, R410A | Square | 1.16 | 470 to 710 | 0.33 to 0.63 | 163 |

Agarwal et al. [75] | R134a | Barrel, N-shape, Rectangular, Square, Triangular | 0.424 to 0.839 | 150 to 750 | 0.37 | 152 |

Belchi et al. [76] | R32, R410A | Square | 1.16 | 350 to 800 | 0.33 to 0.63 | 515 |

Fronk and Garimella [37] | R744 | Rectangular | 0.1 to 0.16 | 400 to 800 | 0.69 to 0.87 | 189 |

Bandhauer et al. [77] | R134a | Circular | 0.506 to 1.524 | 150 to 750 | 0.41 | 128 |

Cavallini et al. [78] | R134a, R410A | Circular | 1.4 | 200 to 1400 | 0.25 to 0.5 | 61 |

Belchi [79] | R1234yf, R134a | Square | 1.16 | 470 to 710 | 0.25 to 0.49 | 81 |

Belchi et al. [80] | R32, R410A | Square | 1.16 | 475 | 0.38 to 0.49 | 88 |

Derby et al. [54] | R134a | Square | 1 | 75 to 450 | 0.22 | 80 |

Andresen [81] | R410A | Circular | 0.76 to 1.52 | 200 to 800 | 0.80 to 0.90 | 198 |

Heo and Yun [82] | R744 | Rectangular | 0.68 to 1.5 | 400 to 800 | 0.41 to 0.54 | 203 |

Gomez et al. [83] | R1234yf | Square | 1.16 | 350 to 945 | 0.23 to 0.43 | 162 |

Jige et al. [38] | R1234ze(E), R134a, R32 | Rectangular | 0.76 to 1.06 | 100 to 400 | 0.21 to 0.43 | 323 |

Park et al. [84] | R1234ze(E), R134a, R236fa | Rectangular | 1.45 | 100 to 260 | 0.13 to 0.44 | 97 |

Pham et al. [85] | R22, R290, R32, R410A | Rectangular | 0.83 | 50 to 500 | 0.37 to 0.60 | 79 |

Park and Hrnjak [86] | R744 | Rectangular | 0.89 | 200 to 800 | 0.23 to 0.40 | 112 |

Li et al. [87] | R1234ze(E), R134a, R32, R32/R134a (24.5/75/5%), R32/R134a (51/49%) | Circular | 0.86 | 100 to 300 | 0.18 to 0.42 | 151 |

Wang et al. [55] | R134a | Circular | 1.46 | 150 to 750 | 0.45 | 279 |

Rahman et al. [88] | R134a | Rectangular | 0.81 | 50 to 200 | 0.19 to 0.22 | 51 |

Total | 3503 |

**Table 2.**Operating conditions, geometric dimensions, and the range of dimensionless factors used in the present study.

Parameter | Type of Refrigerant/Operating Conditions/Channel Geometry/Dimensionless Factors |
---|---|

Fluids | R744, R1234yf, R1234ze(E), R134a, R22, R236fa, R290, R32, R32/R134a (24.5/75.5%), R32/R134a (51/49%) and R410A |

$G,(\mathrm{k}\mathrm{g}{\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$) | 50–1400 |

$D,\left(mm\right)$ | 0.1–1.524 |

Channel geometry | Rectangular, circular, square, barrel, N-shaped and Triangular mini/micro channels |

Reduced pressure, (-) | 0.13–0.90 |

Vapor quality, x, (-) | 0.002–0.978 |

$R{e}_{l}$, (-) | 11–16886 |

$P{r}_{l}$, (-) | 1.75–4.69 |

${X}_{tt}$, (-) | 0.0088–105.26 |

$Bo$, (-) | 0.015–31.36 |

Reference(s) | Correlation | Remarks |
---|---|---|

Kim and Mudawar [52] | $forannularflow\left(W{e}^{*}7{X}_{tt}\right):$ $N{u}_{tp}=0.048{\left(R{e}_{l}\right)}^{0.69}{\left(P{r}_{l}\right)}^{0.34}\frac{{\varphi}_{v}}{{X}_{tt}}$ $forslugandbubblyflow\left(W{e}^{*}7{X}_{tt}\right):$ $N{u}_{tp}={\left[{\left(0.048{\left(R{e}_{l}\right)}^{0.69}{\left(P{r}_{l}\right)}^{0.34}\frac{{\varphi}_{v}}{{X}_{tt}}\right)}^{2}+{\left(3.2\times {10}^{-7}{\left(R{e}_{l}\right)}^{-0.38}{\left(S{u}_{vo}\right)}^{1.39}\right)}^{2}\right]}^{0.5}$ $W{e}^{*}=2.45\frac{R{e}_{v}^{0.64}}{S{u}_{vo}^{0.3}{\left(1+1.09{X}_{tt}^{0.039}\right)}^{0.4}}forR{e}_{l}\le 1250$ $W{e}^{*}=0.85\frac{R{e}_{v}^{0.79}{X}_{tt}^{0.157}}{S{u}_{vo}^{0.3}{\left(1+1.09{X}_{tt}^{0.039}\right)}^{0.4}}{\left[\left(\frac{{\rho}_{l}}{{\rho}_{v}}\right){\left(\frac{{\mu}_{v}}{{\mu}_{l}}\right)}^{2}\right]}^{0.084}forR{e}_{l}1250$ ${\varphi}_{v}=1+CX+{X}^{2}S{u}_{vo}=\frac{{\rho}_{v}\sigma D}{{\mu}_{v}^{2}}$ C and X are calculated by Kim and Mudawar [89] method. | General correlations for condensation in mini/micro-channels. |

Dorao and Fernandino [49] | $N{u}_{tp}={\left(N{u}_{I}^{9}+N{u}_{II}^{9}\right)}^{\frac{1}{9}}$ $N{u}_{I}=0.023R{e}_{tp}^{0.8}P{r}_{tp}^{0.3}$ $N{u}_{II}=41.5{D}^{0.6}R{e}_{tp}^{0.4}P{r}_{tp}^{0.3}$ | General correlations for condensation in horizontal tubes. |

Shah (2016) [90] | ${h}_{tp}={h}_{I}For{J}_{g}\ge 0.98{\left({\left(\frac{1}{x}-1\right)}^{0.8}{P}_{red}^{0.4}+0.263\right)}^{-0.62}andW{e}_{vo}\ge 100$ ${h}_{tp}={h}_{Nu}For{J}_{g}\le 0.95{\left(2.27{\left({\left(\frac{1}{x}-1\right)}^{0.8}{P}_{res}^{0.4}\right)}^{1.249}+1.254\right)}^{-1}$ ${h}_{tp}={h}_{Nu}+{h}_{I}Forotherregimes$ ${h}_{I}=0.023R{e}_{lo}{}^{0.8}P{r}_{l}{}^{0.4}\left[1+1.128{x}^{0.8170}{\left(\frac{{\rho}_{l}}{{\rho}_{g}}\right)}^{0.3685}{\left(\frac{{\mu}_{l}}{{\mu}_{g}}\right)}^{0.2363}\times {\left(1-\frac{{\mu}_{g}}{{\mu}_{l}}\right)}^{2.144}P{r}_{l}{}^{-0.100}\right]\left(\frac{{k}_{l}}{D}\right)$ ${h}_{Nu}=1.32R{e}_{l}{}^{\frac{-1}{3}}{\left[\frac{{\rho}_{l}\left({\rho}_{l}-{\rho}_{v}\right)g{k}_{l}^{3}}{{\mu}_{l}^{2}}\right]}^{\frac{1}{3}}$ ${J}_{g}=\frac{xG}{{\left(gD{\rho}_{v}\left({\rho}_{l}-{\rho}_{v}\right)\right)}^{0.5}}W{e}_{vo}=\frac{{G}^{2}D}{{\rho}_{v}\sigma}$ | General correlations for condensation in horizontal mini/micro-tubes. |

Shah (2019) [57] | $For{J}_{g}\ge 0.98{\left({\left(\frac{1}{x}-1\right)}^{0.8}{P}_{red}^{0.4}+0.263\right)}^{-0.62},F{r}_{l}0.012andW{e}_{vo}\ge 100:$ ${h}_{tp}={h}_{I}$ $For{J}_{g}\le 0.95{\left(2.27{\left({\left(\frac{1}{x}-1\right)}^{0.8}{P}_{res}^{0.4}\right)}^{1.249}+1.254\right)}^{-1}andF{r}_{l}0.012$ ${h}_{tp}={h}_{Nu}$ $Forotherregimes:$ ${h}_{tp}={h}_{Nu}+{h}_{I}$ $F{r}_{L}=\frac{{G}^{2}}{{\rho}_{l}^{2}gD}$ ${h}_{I}$$,{h}_{Nu}$$,{J}_{g}$$\mathrm{and}W{e}_{vo}$ are calculated by Shah (2016) method. | |

Akers et al. [91] | $N{u}_{tp}={\mathit{CPr}}_{\mathrm{l}}^{\frac{1}{3}}{\left\{G\left[\left(1-x\right)+x{\left(\frac{{\rho}_{\mathrm{l}}}{{\rho}_{V}}\right)}^{0.5}\right]\frac{D}{{\mu}_{\mathrm{l}}}\right\}}^{n}$ $C=0.026,n=0.8{\mathit{for}\mathit{Re}}_{\mathit{eq}}50000$ $C=5.3,n=\frac{1}{3}{\mathit{for}\mathit{Re}}_{\mathit{eq}}50000$ $R{e}_{eq}=G\left[\left(1-x\right)+x{\left(\frac{{\rho}_{l}}{{\rho}_{v}}\right)}^{0.5}\right]\left(\frac{D}{{\mu}_{l}}\right)$ | Condensations for horizontal plain tubes |

Crosser [92] | $N{u}_{tp}=0.0265P{r}_{l}{}^{\frac{1}{3}}{\left(G\left(x{\left(\frac{{\rho}_{l}}{{\rho}_{v}}\right)}^{0.5}\right)\frac{D}{{\mu}_{l}}\right)}^{n}$ $n=0.8for\frac{Gx}{{\mu}_{l}}60000$ $n=0.2for\frac{Gx}{{\mu}_{l}}60000$ | |

Bohdal et al. [93] | $N{u}_{tp}=25.084R{e}_{l}{}^{0.258}P{r}_{l}{}^{-0.495}{P}_{res}{}^{-0.288}{\left(\frac{x}{1-x}\right)}^{0.266}$ | R134a and R410A condensation in mini-channels |

Hosseini et al. [56] | $\mathit{For}G\le 200\mathrm{k}\mathrm{g}{\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$: $N{u}_{tp}=0.0022\times R{e}_{tp}\times \left(\frac{\rho l-\rho v}{\rho l}\right)+0.0342\times W{e}_{vo}\times {\left(\frac{\rho l-\rho v}{\rho l}\right)}^{2}+\frac{Sin\left(39.8963\times {P}_{red}\right)-Ln\left(W{e}_{vo}\right)}{-0.0298-0.2203\times F{r}_{l}}-P{r}_{tp}$ $\mathit{For}G200\mathrm{k}\mathrm{g}{\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$: $N{u}_{tp}=ABS\left(0.0169\ast R{e}_{tp}^{0.8620}-0.00146\ast \frac{R{e}_{tp}}{P{r}_{tp}\ast \left(\frac{\rho l-\rho v}{\rho l}\right)}+\phantom{\rule{0ex}{0ex}}\frac{0.0036+0.0171\ast W{e}_{vo}}{F{r}_{l}}+17.9480\ast \mathrm{sin}\left(\frac{0.0036+0.0171\ast W{e}_{vo}}{F{r}_{l}}\right)+\phantom{\rule{0ex}{0ex}}\mathrm{tan}\left(27.6370106546243\ast \left(\frac{\rho l-\rho v}{\rho l}\right)\right)-\mathrm{tan}\left(369.8572+\phantom{\rule{0ex}{0ex}}\mathrm{sin}\left(\frac{0.0036+0.01712\ast W{e}_{vo}}{F{r}_{l}}\right)\right)\right)$ | General correlations for condensation in single-port horizontal plain tubes |

Model $\mathit{A}\mathit{A}\mathit{R}\mathit{D}\mathit{\%}$ $\mathit{A}\mathit{A}\mathit{D}\mathit{\%}$ | |||||||||
---|---|---|---|---|---|---|---|---|---|

References | Akers et al. [91] | Crosser [92] | Bohdal et al. [93] | Shah (2016) [90] | Shah (2019) [57] | Dorao and Fernandino [49] | Hosseini et al. [56] | Kim and Mudawar [52] | GP correlation |

Agarwal [72] | 44.06 41.63 | 83.56 −83.56 | 40.09 36.40 | 68.35 −68.35 | 68.35 −68.35 | 70.93 −70.93 | 76.33 −76.33 | 72.94 −72.94 | 17.91 −4.55 |

Belchi et al. [73] | 144.97 144.97 | 30.61 −30.48 | 128.72 128.72 | 21.23 18.65 | 21.23 18.65 | 15.00 10.95 | 24.72 1.19 | 16.38 11.37 | 17.54 −7.91 |

Belchi et al. [74] | 184.29 184.29 | 20.74 −5.72 | 190.63 190.63 | 60.45 60.45 | 60.45 60.45 | 59.83 59.83 | 63.26 63.26 | 41.05 41.05 | 16.41 14.16 |

Agarwal et al. [75] | 143.40 143.25 | 47.80 −47.80 | 100.93 100.27 | 22.77 −1.92 | 22.77 −1.92 | 23.80 −4.88 | 24.78 −5.76 | 23.85 −14.58 | 22.59 −4.98 |

Belchi et al. [76] | 153.28 153.28 | 26.62 −20.03 | 170.31 170.31 | 35.13 34.54 | 35.13 34.54 | 34.78 34.16 | 39.60 39.50 | 23.50 21.82 | 9.96 −2.49 |

Fronk and Garimella [37] | 273.45 273.45 | 57.49 −57.49 | 170.52 170.52 | 31.09 −30.41 | 31.09 −30.41 | 30.72 −30.44 | 34.61 −34.27 | 37.78 −37.78 | 14.59 2.43 |

Bandhauer et al. [77] | 129.60 129.60 | 40.92 −40.92 | 87.58 86.65 | 12.08 5.42 | 12.08 5.42 | 11.94 3.60 | 15.61 4.01 | 12.66 −8.10 | 17.72 −4.01 |

Cavallini et al. [78] | 63.59 57.97 | 43.90 −43.90 | 53.81 44.01 | 8.91 −4.03 | 8.91 −4.03 | 9.82 −5.27 | 12.25 1.68 | 19.04 −17.93 | 25.98 −25.98 |

Belchi [79] | 315.23 315.23 | 34.81 21.10 | 224.80 224.80 | 117.50 117.50 | 117.50 117.50 | 105.43 105.43 | 122.73 122.73 | 92.85 92.85 | 52.30 51.82 |

Belchi et al. [80] | 177.70 177.70 | 26.17 −25.28 | 200.52 200.52 | 32.07 32.07 | 32.07 32.07 | 31.03 31.03 | 38.50 38.50 | 22.41 21.95 | 8.00 −4.25 |

Derby et al. [54] | 182.16 182.16 | 55.93 −55.93 | 149.56 149.56 | 11.79 9.57 | 11.79 9.57 | 14.55 −11.18 | 35.33 1.75 | 13.38 −11.13 | 17.07 16.75 |

Andresen [81] | 201.77 201.77 | 17.66 −11.44 | 91.15 90.09 | 39.38 39.28 | 39.38 39.28 | 40.96 40.96 | 17.46 0.43 | 22.03 19.10 | 21.31 11.21 |

Heo and Yun [82] | 384.25 384.25 | 55.87 42.53 | 382.29 382.29 | 132.05 132.05 | 132.05 132.05 | 134.14 134.13 | 123.45 123.38 | 116.22 116.22 | 21.74 10.60 |

Gomez et al. [83] | 84.08 84.08 | 44.40 −44.33 | 43.28 43.28 | 7.65 −1.02 | 7.65 −1.02 | 10.42 −8.00 | 6.52 −0.57 | 15.81 13.42 | 13.46 −12.03 |

Jige et al. [38] | 147.22 147.22 | 57.47 −57.47 | 123.73 123.73 | 17.26 −7.32 | 17.26 −7.32 | 30.92 −23.76 | 30.87 −18.22 | 26.94 −21.78 | 14.50 0.25 |

Park et al. [84] | 244.99 244.99 | 42.44 −42.44 | 173.49 173.49 | 27.50 20.80 | 27.72 23.84 | 22.14 20.59 | 34.50 23.67 | 21.13 18.64 | 14.06 −0.97 |

Pham et al. [85] | 652.27 652.27 | 46.23 1.14 | 680.51 680.51 | 179.40 179.40 | 179.40 179.40 | 103.09 102.63 | 116.14 102.92 | 111.40 111.22 | 42.09 28.05 |

Park and Hrnjak [86] | 232.11 232.11 | 33.01 −33.01 | 251.06 251.06 | 38.77 38.77 | 38.77 38.77 | 27.22 23.67 | 34.06 33.46 | 24.47 24.04 | 13.07 −11.26 |

Li et al. [87] | 338.36 338.36 | 31.81 −29.64 | 353..18 353.18 | 57.92 57.03 | 57.92 57.03 | 30.78 25.07 | 37.10 27.87 | 40.40 37.87 | 15.73 6.26 |

Wang et al. [55] | 167.58 167.58 | 49.10 −49.10 | 89.72 89.72 | 17.11 11.22 | 17.67 12.87 | 15.43 12.93 | 28.34 19.57 | 9.90 −5.32 | 10.36 8.29 |

Rahman et al. [88] | 108.70 107.50 | 72.09 −72.09 | 99.34 98.03 | 24.01 −21.90 | 24.01 −21.90 | 47.80 −47.80 | 49.91 −49.56 | 38.66 −38.42 | 20.98 −2.42 |

Total | 191.19 190.87 | 44.07 −33.87 | 164.97 164.35 | 43.39 22.94 | 43.45 23.15 | 41.54 15.95 | 44.68 15.92 | 36.94 8.17 | 16.87 2.33 |

**Table 5.**Comparison of the accuracy of the available models for estimating the HTC in multi-port micro and mini-channels.

Channel Diameter | Micro-Channels $\left(\mathit{D}\le 0.2\mathit{m}\mathit{m}\right),$ 480 Data Points | Mini-Channels $\left(0.2<\mathit{D}<3\mathit{m}\mathit{m}\right),$ 3023 Data Points | All Data, 3503 Data Points | ||||||
---|---|---|---|---|---|---|---|---|---|

Models | Percentage of Data within the AARD of 20% | Percentage of Data within the AARD of 30% | AARD (%) | Percentage of Data within the AARD of 20% | Percentage of Data within the AARD of 30% | AARD (%) | Percentage of Data within the AARD of 20% | Percentage of Data within the AARD of 30% | AARD (%) |

Akers et al. [91] | 14.36 | 20.83 | 134.39 | 1.36 | 1.72 | 200.21 | 3.14 | 4.34 | 191.19 |

Crosser [92] | 0.00 | 0.00 | 73.31 | 22.23 | 36.09 | 39.43 | 19.18 | 31.14 | 44.07 |

Bohdal et al. [93] | 16.86 | 25.83 | 91.45 | 4.30 | 6.55 | 176.64 | 5.99 | 9.19 | 164.97 |

Shah (2016) [90] | 10.21 | 16.67 | 53.68 | 40.13 | 55.94 | 41.76 | 36.03 | 50.56 | 43.39 |

Shah (2019) [57] | 10.21 | 16.67 | 53.68 | 39.93 | 55.71 | 41.82 | 35.86 | 50.36 | 43.45 |

Dorao and Fernandino [49] | 10.00 | 16.25 | 55.09 | 40.46 | 56.17 | 39.39 | 36.28 | 50.70 | 41.54 |

Hosseini et al. [56] | 9.38 | 13.96 | 59.91 | 32.09 | 49.49 | 42.27 | 28.98 | 44.62 | 44.68 |

Kim and Mudawar [52] | 4.17 | 7.29 | 59.10 | 49.19 | 63.44 | 33.42 | 43.05 | 55.75 | 36.94 |

New Correlation | 68.75 | 84.58 | 16.60 | 70.66 | 84.75 | 16.91 | 70.37 | 84.73 | 16.87 |

${\mathit{T}}_{\mathit{s}}(\mathbb{C})$ | ${\mathit{\rho}}_{\mathit{l}}\left(\mathbf{k}\mathbf{g}{\mathbf{m}}^{-3}\right)$ | ${\mathit{\rho}}_{\mathit{v}}\left(\mathbf{k}\mathbf{g}{\mathbf{m}}^{-3}\right)$ | ${\mathit{k}}_{\mathit{l}}\left(\mathbf{w}{\mathbf{m}}^{-1}{\mathbf{K}}^{-1}\right)$ |
---|---|---|---|

50 | 1102.3 | 66.27 | 0.070427 |

60 | 1052.9 | 87.38 | 0.066091 |

Fluids | ${\mathit{T}}_{\mathit{s}}(\mathbb{C})$ | ${\mathit{\rho}}_{\mathit{l}}\left(\mathbf{k}\mathbf{g}{\mathbf{m}}^{-3}\right)$ | ${\mathit{\rho}}_{\mathit{v}}\left(\mathbf{k}\mathbf{g}{\mathbf{m}}^{-3}\right)$ | ${\mathit{H}}_{\mathit{l}\mathit{v}}\left(\mathbf{k}\mathbf{J}\mathbf{K}{\mathbf{g}}^{-1}\right)$ |
---|---|---|---|---|

R290 | 40 | 467.46 | 30.165 | 307.06 |

R32 | 40 | 893.04 | 73.268 | 237.10 |

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## Share and Cite

**MDPI and ACS Style**

Hosseini, S.H.; Ayari, M.A.; Khandakar, A.; Moradkhani, M.A.; Jowkar, M.; Panahi, M.; Ahmadi, G.; Tavoosi, J.
Robust and General Model to Forecast the Heat Transfer Coefficient for Flow Condensation in Multi Port Mini/Micro-Channels. *Processes* **2022**, *10*, 243.
https://doi.org/10.3390/pr10020243

**AMA Style**

Hosseini SH, Ayari MA, Khandakar A, Moradkhani MA, Jowkar M, Panahi M, Ahmadi G, Tavoosi J.
Robust and General Model to Forecast the Heat Transfer Coefficient for Flow Condensation in Multi Port Mini/Micro-Channels. *Processes*. 2022; 10(2):243.
https://doi.org/10.3390/pr10020243

**Chicago/Turabian Style**

Hosseini, Seyyed Hossein, Mohamed Arselene Ayari, Amith Khandakar, Mohammad Amin Moradkhani, Mehdi Jowkar, Mohammad Panahi, Goodarz Ahmadi, and Jafar Tavoosi.
2022. "Robust and General Model to Forecast the Heat Transfer Coefficient for Flow Condensation in Multi Port Mini/Micro-Channels" *Processes* 10, no. 2: 243.
https://doi.org/10.3390/pr10020243