# CFD-Based Approach to Propose a Zigzag-Shaped Tube Heat Exchanger without Fins

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Finless Zigzag-Shaped Tube Heat Exchanger Design

_{o}) of tubes arranged in a zigzag pattern at certain intervals, which acted as a tube bundle. The tubes were set side-by-side at different distances, allowing in-depth research into their performances in different configurations. The scope of this study was limited to two rows (N = 2), with air as a working fluid to evaluate the performances of these new heat exchangers across the air flow. To assess the effectiveness of the zigzag shape, several zigzag angles (30°, 45°, and 60°) were examined, while the increase in the tube zigzag angles also increased the tube total heat transfer area significantly. The study included a comparison of the proposed zigzag tube heat exchanger (ZTHX) and a conventional parallel tube heat exchanger (PTHX). To ensure a fair comparison, the configurations of the ZTHX and PTHX had the same parameters, such as the same number of rows (N = 2), the same diameter of tubes, and the same distance between the tubes and the air flow. The primary objective of this study was to explore the potential advantages and disadvantages of the finless ZTHX design and to identify possible improvements to enhance its performance in various applications.

## 3. CFD Modeling

^{−3}for continuity, speed, kinetic energy (k), and eddy viscosity (ε) and at 10

^{−6}for energy. These strict criteria ensured that the solutions were numerically stable and accurate. The intensity was taken as 10%.

_{k}was as follows.

_{i}and u

_{k}are the fluid velocity vector components, p is the pressure, μ is the dynamic viscosity, T is the temperature, k is the thermal conductivity, and c

_{p}is the specific isobaric heat.

## 4. Boundary Conditions

## 5. Data Reduction

_{Do}

_{, C}is the Reynolds number, D

_{o}is the outer tube diameter, P

_{t}is the transverse pitch (mm), and P

_{l}is the longitudinal tube pitch (mm).

_{w}and the refrigerant side resistance H

_{ref}both are negligible because the tube wall temperature was fixed here. $\dot{m}$

_{air}is the mass flow rate (ks/s), is the heat transfer amount (W), U

_{air}is the heat transfer coefficient (W/m

^{2}.K), A

_{fr}is the flow cross-sectional area, A

_{o}is the total surface area, u

_{max}is the maximum flow velocity, σ is the contraction ratio, ρ

_{in}is the fluid inlet density, ρ

_{out}is the fluid outlet density, LMTD is the logarithmic mean temperature difference (K), and A is the total heat transfer area (m

^{2}). delta P refers to the pressure difference between the inlet and outlet of the domain.

_{p}is the capacity ratio, Nu is the Nusselt number, and K is the thermal conductivity (W/m.K).

## 6. Results and Discussion

#### 6.1. Heat Transfer Area Improvement Percentage

#### 6.2. Flow Characteristics

#### 6.3. Heat Flux Percentage Improvement

#### 6.4. Calculation of Friction Factor

_{o}was used as the characteristic length scale. The friction factor was calculated from the pressure drop equation proposed by Kays and London 1984 [22]. In Figure 10, different colors of dots show other zigzag tubes and bare tubes. Here, we discuss the influences of the Reynolds number, the distance between tubes, and the tube zigzag angles over the air friction factor.

#### 6.5. hA Value Calculation

#### 6.6. Parallel Tube Data Validation

_{Dmax}≥ 500, F = 0.76, C = 1.04, n = 0.4, and m = 0.36.

#### 6.7. Volume Goodness Factor

## 7. Conclusions

**/**s) were observed. Using numerical simulations, the performance of the zigzag tube bundle was evaluated and compared with that of a parallel tube bundle. The results are presented below.

- Heat transfer enhancement was obtained by increasing the total heat transfer area over that of the parallel tube bundle by incorporating different tube zigzag angles. The heat transfer area increased mainly for the tube zigzag angle of 60° by 63.9%.
- Heat flux increased to 37% over the parallel tube bundle for the tube zigzag angle of 60° and at an air velocity of 2 m/s.
- The friction factor of the zigzag tube bundle was minimal compared to that of the parallel tube bundle when the air velocity was 2 m/s and the distance between the tubes was 2.0 mm.
- To achieve a better performance of the zigzag tube bundle compared to the parallel tube bundle, in this study a zigzag angle of the tube of 60°, a distance between the tubes of 2.0 mm, and maximum air velocity were recommended.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

D_{o} | Tube outer diameter | mm |

A, A_{o} | Tube total outer heat transfer area | mm^{2} |

T_{air} | Temperature of air | K |

$\Delta P$ | Pressure difference | Pa |

A_{fr} | Area of frontal air flow | mm^{2} |

j | Colburn j factor | - |

f | Friction factor | - |

K | Thermal conductivity | W/m-K |

LMTD | Log mean temperature difference | K |

$\dot{m}$ | Mass flow rate | kg/s |

h, HTC | Heat transfer coefficient | W/m^{2}k |

N | Number of rows of tube banks | - |

Pr | Prandtl number | - |

$\dot{Q}$ | Heat transfer rate | W |

Re | Reynolds number | - |

u | Velocity | m/s |

U | Overall heat transfer coefficient | W/m^{2}K |

θ | Tube zigzag angle | ° |

ρ | Density | kg/m^{3} |

σ | Contraction ratio | - |

T | Temperature | K |

P | Pressure | Pa |

Nu | Nusselt number | - |

g | Distance between tubes | mm |

V_{max} | Maximum velocity | m/s |

${C}_{\epsilon 1}$${C}_{\epsilon 2}$$,\text{}{C}_{\mu}$ | $\mathrm{Constants}$ equation | - |

${\sigma}_{k}$$,\text{}{\sigma}_{\epsilon}$ | Effective Prandtl | - |

Subscripts | ||

fr | Frontal cross-section | |

I, In | Inlet | |

O, Out | Outlet | |

Max | Maximum | |

Min | Minimum | |

W | Wall |

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**Figure 1.**The design of the new heat exchanger was as follows: (

**a**) zigzag tube heat exchanger (ZTHX); (

**b**) zigzag angles and surfaces of sections; (

**c**) tube diameter and tube distance; (

**d**) parallel tube heat exchanger (PTHX).

**Figure 8.**Side views of the temperature contours of zigzag tube at 30°, 45°, and 60° at different tube distances.

**Figure 9.**Improvement percentages of heat flux relative to PTHX: (

**a**) tube distance of 0.0 mm; (

**b**) tube distance of 0.5 mm; (

**c**) tube distance of 1.0 mm; (

**d**) tube distance of 2.0 mm.

**Figure 10.**Variation in friction factor: (

**a**) tube distance of 0.0 mm; (

**b**) tube distance of 0.5 mm; (

**c**) tube distance of 1.0 mm; (

**d**) tube distance of 2.0 mm.

**Figure 12.**Volume goodness factor: (

**a**) distance between tubes of 0 mm; (

**b**) distance between tubes of 0.5 mm; (

**c**) distance between tubes of 1 mm; (

**d**) distance between tubes of 2 mm.

Mesh | Element Number | HTC (W/m ^{2} K) | Pressure Drop (Pa) | Deviation in HTC | Deviation in Pressure Drop |
---|---|---|---|---|---|

Fine | 1314365 | 335.520 | 0.373645 | - | - |

Medium | 319883 | 338.457 | 0.375305 | 0.87% | 0.4% |

Coarse | 201049 | 339.509 | 0.357134 | 1.17% | 4.6% |

Conditions | Flow | Heat Transfer |
---|---|---|

Inlet | Velocity inlets of 0.5, 1, 1.5, and 2 m/s | Uniform temperature at 298 K |

Outlet | Pressure Outlet | $\frac{\partial T}{\partial x}=0$ |

Wall of the tube | No-slip wall and no penetration | Uniform temperature at 313 K |

Symmetry plane | Symmetry | Symmetry |

Coefficient | Bare Tube | |
---|---|---|

j | f | |

C1 | 0.31692086 | 0.37714526 |

C2 | 0.3472705 | 0.26992253 |

C3 | −0.51134999 | −0.04481229 |

C4 | −0.00401654 | 0.01138922 |

C5 | 0.09334736 | −0.04293416 |

C6 | 0.52999408 | 0.77274225 |

C7 | −0.97703628 | 0.2170995 |

C8 | 3.10160601 | 1.73124835 |

C9 | −0.30758351 | −4.97083301 |

C10 | −0.73451673 | −0.1859046 |

C11 | 0.002349867 | −0.01814594 |

C12 | 1.34217805 | 0.56056314 |

C13 | −0.07168253 | 0.04926124 |

Air Velocity (m/s) | Correlation Data | CFD Data | % of Error | |||
---|---|---|---|---|---|---|

j Factor | f Factor | j Factor | f Factor | j Factor | f Factor | |

2 | 0.1600 | 0.1354 | 0.1426 | 0.1182 | 10.8843 | 12.7593 |

3 | 0.1098 | 0.1165 | 0.1085 | 0.1286 | 1.1389 | 10.3528 |

4 | 0.0847 | 0.1048 | 0.0895 | 0.1355 | 5.5683 | 29.2240 |

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**MDPI and ACS Style**

Rayhan, S.; Kariya, K.; Miyara, A.
CFD-Based Approach to Propose a Zigzag-Shaped Tube Heat Exchanger without Fins. *Thermo* **2023**, *3*, 309-328.
https://doi.org/10.3390/thermo3020019

**AMA Style**

Rayhan S, Kariya K, Miyara A.
CFD-Based Approach to Propose a Zigzag-Shaped Tube Heat Exchanger without Fins. *Thermo*. 2023; 3(2):309-328.
https://doi.org/10.3390/thermo3020019

**Chicago/Turabian Style**

Rayhan, Sabit, Keishi Kariya, and Akio Miyara.
2023. "CFD-Based Approach to Propose a Zigzag-Shaped Tube Heat Exchanger without Fins" *Thermo* 3, no. 2: 309-328.
https://doi.org/10.3390/thermo3020019