# Numerical Analysis on Natural Convection Heat Transfer in a Single Circular Fin-Tube Heat Exchanger (Part 1): Numerical Method

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## Abstract

**:**

## 1. Introduction

_{o}/D) of 1.2 to 2.8, and fin pitch to tube diameter ratios (s/D) of 1.2 to 2.6.

## 2. Numerical Simulation

#### 2.1. Equations Governing the Circular Fin-Tube Heat Exchanger

_{o}: diameter of the circular fin,

#### 2.2. Numerical Simulation Method

^{3}, the constant pressure heat capacity was 1004.4 J/(kg·K), thermal conductivity was 0.025 J/(m·K), and dynamic viscosity was $1.71\times {10}^{-5}$ kg/(m·s). Pr was 0.687.

## 3. Validation of the Computational Fluid Dynamics Method

#### 3.1. Circular Tube

#### 3.2. Comparison with Experimental Data

## 4. Results and Discussion

#### 4.1. Velocity

#### 4.2. Temperature

#### 4.3. Fin Efficiency

## 5. Conclusionsigure

- In a circular fin-tube heat exchanger, the heat transfer of natural convection can be simply expressed via a fin-tube model, and unsteady time marching was proposed to analyze time sweeping for various Ra values. This method is based on practical experiments with lumped temperature.
- Validation of the numerical analysis results via comparisons with empirical correlations such as those of Morgan [2] and Churchill and Chu [3] showed a limited range of errors. The proposed method underpredicted Kang’s experimental values by approximately 16%, but the overall trend coincided with his data. It was considered that the overestimation originated from the additional heat loss, except for the pure natural convection, which served as an artificial cause in the experiment. The accuracy of the natural convection data with the proposed numerical method can be guaranteed when ${\mathrm{Ra}}_{D}>400$, which is thought to be the limitation of numerical errors due to instability. Small differences in the temperature can affect the data severely. However, the proposed numerical simulation is far more stable than experiments where larger oscillations were observed for higher Ra values (${\mathrm{Ra}}_{D}\approx 3000)$
- The effective limit for a circular fin-tube heat exchanger is reached when ${\mathrm{Ra}}_{s}\ge 100$ because at low Ra values, the air gap between the fins is rarely affected by the natural convection from the outer air or stagnates when the fluid provides heat resistance. Therefore, the fin best serves its purpose when ${\mathrm{Ra}}_{s}$ exceeds 100. At low Ra values (${\mathrm{Ra}}_{s}=15$), shorter fins or a higher $s/D$ ratio provide better efficiency.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Numerical domain and grid in the present work: (

**a**) computational domain, (

**b**) grid (

**c**) zoom in near the fin-tube.

**Figure 5.**Comparison of Nu

_{L}with experimental data of circular fin-tubes. (Experimental Data from Kang and Chang [10]).

**Figure 6.**Velocity contours of the airflow in the present numerical experiment: (

**a**) s/D = 0.119, ${\mathrm{Ra}}_{s}$ = 15; (

**b**) s/D = 0.256, ${\mathrm{Ra}}_{s}$ = 150.

**Figure 7.**Isotherm lines for air-sides in the present numerical experiment: (

**a**) s/D = 0.119, ${\mathrm{Ra}}_{s}$ = 15; (

**b**) s/D = 0.256, ${\mathrm{Ra}}_{s}$ = 150.

Case | D | D_{o} | P_{f} | t | D_{o}/D | s/D | |
---|---|---|---|---|---|---|---|

D12 | P12 | 15.88 | 19.1 | 2.89 | 1.0 | 1.20 | 0.119 |

P17 | 3.68 | 0.169 | |||||

P21 | 4.26 | 0.205 | |||||

P26 | 5.06 | 0.256 | |||||

D18 | P12 | 27.8 | 2.89 | 1.75 | 0.119 | ||

P17 | 3.68 | 0.169 | |||||

P21 | 4.26 | 0.205 | |||||

P26 | 5.06 | 0.256 | |||||

D22 | P12 | 15.88 | 34.9 | 2.89 | 1.0 | 2.20 | 0.119 |

P17 | 3.68 | 0.169 | |||||

P21 | 4.26 | 0.205 | |||||

P26 | 5.06 | 0.256 | |||||

D28 | P12 | 44.5 | 2.89 | 2.80 | 0.119 | ||

P17 | 3.68 | 0.169 | |||||

P21 | 4.26 | 0.205 | |||||

P26 | 5.06 | 0.256 |

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**MDPI and ACS Style**

Lee, J.H.; Shin, J.-H.; Chang, S.-M.; Min, T.
Numerical Analysis on Natural Convection Heat Transfer in a Single Circular Fin-Tube Heat Exchanger (Part 1): Numerical Method. *Entropy* **2020**, *22*, 363.
https://doi.org/10.3390/e22030363

**AMA Style**

Lee JH, Shin J-H, Chang S-M, Min T.
Numerical Analysis on Natural Convection Heat Transfer in a Single Circular Fin-Tube Heat Exchanger (Part 1): Numerical Method. *Entropy*. 2020; 22(3):363.
https://doi.org/10.3390/e22030363

**Chicago/Turabian Style**

Lee, Jong Hwi, Jong-Hyeon Shin, Se-Myong Chang, and Taegee Min.
2020. "Numerical Analysis on Natural Convection Heat Transfer in a Single Circular Fin-Tube Heat Exchanger (Part 1): Numerical Method" *Entropy* 22, no. 3: 363.
https://doi.org/10.3390/e22030363