# Heat Transfer Enhancement by Perforated and Louvred Fin Heat Exchangers

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## Abstract

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^{3}/h corresponding to Reynolds numbers between 6000 and 30,000. It was found that the louvred fins produced the highest heat transfer rate due to the availability of higher surface area, but it also produced the highest pressure drops. Conversely, while the new perforated design produced a slightly higher pressure drop than the plain fin design, it gave a higher value of heat transfer rate than the plain fin especially at the lower liquid flow rates. Specifically, the louvred fin gave consistently high pressure drops, up to 3 to 4 times more than the plain and perforated models at 4 m/s air flow, however, the heat transfer enhancement was only about 11% and 13% over the perforated and plain fin models, respectively. The mean heat transfer rate and pressure drops were used to calculate the Colburn and Fanning friction factors. Two novel semiempirical relationships were derived for the heat exchanger’s Fanning and Colburn factors as functions of the non-dimensional fin surface area and the Reynolds number. It was demonstrated that the Colburn and Fanning factors were predicted by the new correlations to within ±15% of the experiments.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Rig

^{3}/h), the heat exchanger testing unit, pressure transducers (IMP, with 0–10 V analogue output signal and range 0–4 bars), T-type thermocouples (with accuracy of ±0.15 °C), thermocouples data logger, RTD sensors (PT100, with range of −75–250 °C) and data acquisition system. Figure 1a–f includes various details including a schematic representation of the experimental setup and photos of the various test rig components. These have been use d for numerous previous experimental campaigns [20,21,22,23] with a high degree of consistency and reliability.

#### 2.1.1. Heat Exchanger Testing Unit

^{3}/h airflow rate. The speed of the fan’s electric motor was controlled using a potentiometer.

#### 2.1.2. Fin Geometries

- Plain fin
- Perforated plain fin
- Louvred fin

#### 2.1.3. Experimental Procedure

^{3}/h) were varied. The above indicates that the flow within the tubes is fully turbulent. The test matrix for the experiments carried out in this study are presented in Table 1. It shows that a total of 25 tests were carried out for up to 0.36 m

^{3}/h water flow rate with 0.7–4 m/s air velocities for each water flow rate.

#### 2.2. Data Analysis

_{o}is the total surface area of the air side; the variables ${K}_{c}$ and ${K}_{e}$ are the entrance and exit pressure loss coefficients. Equation (6) was developed by Kays and London [21] using the data from Figures 14–26 in McQuiston et al. [2]. Additionally, the Stanton and the Prandtl numbers used to define the Colburn j-factor in Equation (5) are, respectively, given as:

## 3. Results

#### 3.1. Performance Comparison of Fin Geometry

^{3}/h. The error bars represent the combined uncertainty of the thermocouples and deviation between repeated measurements. The uncertainties were determined to be ±5%.

^{3}/h for different heat exchanger geometries. It can be seen from the figure that the louvred fins heat exchanger exhibited a higher mean heat transfer rate when compared with the perforated plain, and plain fin heat exchangers. For all cases, the average heat transfer rate increases as the water flow rate increases, first at a faster rate at lower air velocities and the rate of increase starts to decrease, more noticeably beyond 3 m/s. Figure 5b shows a similar trend but the rate of heat transfer increase beyond 3 m/s is now higher than the previous case and this is maintained for water flow rates of 0.24, 0.3 and 0.36 m

^{3}/h as shown in Figure 5c–e, respectively. The louvred fin geometry produced correspondingly higher increase in the average heat transfer rates especially at 0.3 and 0.36 m

^{3}/h water flow rates than at the lower water flow rates.

^{3}/h, an increase in heat transfer rate was noticed for the louvred fins as compared to plain fins (about 13% lower) and plain perforated fins (2.7% lower). These values change to about 15% for plan fins and 6% for the perforated plain fin model at a water flow rate of 0.18 m

^{3}/h. At flow rate of 0.24 m

^{3}/h again the corresponding values were 13% and 11%. However, such significant increase of the heat transfer was made at the expense of a significant air pressure drop (Figure 6). It is assumed that the perforated fins increased the flow vorticity. At 0.3 m

^{3}/h almost similar levels of change in heat transfer rate was noticed. In general, there is an increasing trend in heat transfer as the water flow rate increases for all types of heat exchangers. This is evidenced by an increase in the rate of heat transfer from about 500 to 600 W for louvered fins heat exchanger, 400 W to 523 W for plain fin heat exchanger, and 488 to 528 W for perforated plain fin heat exchanger at ${V}_{a}$ = 4 m/s. Nevertheless, the perforated plain fin model appears to be least affected by an increase in water flow rate. Its heat transfer rate has only marginally increased at higher water flow rates. This may be because the perforations have reduced the heat transfer area below a certain threshold where the fluid flow rates can have a significant effect. As a result, in certain situations this aspect should be kept in view whilst designing a perforated plain heat exchanger.

#### 3.2. Development of New Empirical Relations for Fanning f and Colburn j-Factor

^{®}which are based on the least squares’ method. The dimensionless parameters used to develop the predictive correlation are, as mentioned earlier, the Reynolds number, $R{e}_{D}$ and the ratio between total fin surface area to the total heat transfer surface area $\left({A}_{f}/{A}_{t}\right)$ of the heat exchanger which is a design parameter used by Palmer et al. [26] that can be used for estimating heat transfer areas needed for a given amount of heat to be transmitted. Other authors have used similar dimensionless groupings to correlate the heat transfer properties of fin and tube heat exchangers [13,17,18]. The newly derived equations are as follows:

_{c}is the outside diameter of the fin’s collar (m): ${A}_{f}$ is the total surface area of the fins (m

^{2}); ${A}_{t}$ is the heat exchanger’s overall heat transfer surface area (m

^{2}). The Equations (9) and (10) show that the Colburn and Fanning factors are inversely proportional to the Reynolds numbers which are consistent with experimental observations (in Figure 7a,b). Additionally, the relatively large indices (29.218 and 12.811) for the $\left({A}_{f}/{A}_{t}\right)$ parameter reflects the small magnitude of the $\left({A}_{f}/{A}_{t}\right)$ ratio. It is advised that the equations are valid within the Reynolds number range: $6\times {10}^{3}\le R{e}_{D}\le 30\times {10}^{3}$ and for the heating cycle in forced convection heat transfer.

^{2}values of 0.931 and 0.979 for the j and f factors, respectively, and the predictions of the new correlations are well within ±15% of the underlying CFD and experimental data. The two new correlations are given below as follows:

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Schematic of the experimental setup: (

**a**) overall schematic of a heater flow loop, (

**b**) insulated 5 litre water tank, (

**c**) water heater, (

**d**) heater controller unit, (

**e**) water pump, (

**f**) water flow meter.

**Figure 2.**(

**a**) Schematic representation of the heat exchanger testing unit (

**b**) dimensions of the plain fin heat exchanger (

**c**) Arrangement of thermocouples at the specific measurement location.

**Figure 3.**(

**a**) Picture of perforated plain fin type heat exchanger, (

**b**) perforated holes’ arrangement, (

**c**) louvred fins heat exchanger, (

**d**) louvred fin shape.

**Figure 4.**Starting up test showing experimental and transient CFD temperatures for air and water outlets.

**Figure 5.**Variation of $({\dot{Q}}_{avg}\text{}\left[\mathrm{W}\right])$ against V

_{a}for various heat exchangers; (

**a**) for water flow rate 0.12 m

^{3}/h, (

**b**) for water flow rate 0.18 m

^{3}/h, (

**c**) for water flow rate 0.24 m

^{3}/h, (

**d**) for water flow rate 0.3 m

^{3}/h and (

**e**) for water flow rate 0.36 m

^{3}/h.

**Figure 6.**Variation of $\left(\Delta P/L\left[\mathrm{Pa}/\mathrm{m}\right]\right)$ against ${V}_{a}$ for various heat exchanger; (

**a**) at water flow rate of 0.12 m

^{3}/h, (

**b**) at water flow rate of 0.18 m

^{3}/h, (

**c**) at water flow rate of 0.24 m

^{3}/h, (

**d**) at water flow rate of 0.3 m

^{3}/h and (

**e**) at water flow rate of 0.36 m

^{3}/h.

**Figure 7.**Variations of (

**a**) friction f-factor (

**b**) Colburn j-factor and (

**c**) efficiency index j/f for different fin arrangements as a function of Reynolds number.

**Figure 8.**Comparisons of predicted (by Equations (9) and (10)) and experimental values of (

**a**) Colburn j-factor and (

**b**) Fanning f-factor (

**c**) plain fin Colburn factor (

**d**) plain fin Fanning factor.

Test ID | Water Side | Air Side | ||
---|---|---|---|---|

Water Flow Rate (m^{3}/h) | Water Inlet Temperature (°C) | Air Velocity (m/s) | Air Inlet Temperature (°C) | |

Test case 1.1 | 0.12 ± 0.0018 | 60 ± 1 | 0.705 | 24 ± 1 |

Test case 1.2 | 1.546 | |||

Test case 1.3 | 2.183 | |||

Test case 1.4 | 3.177 | |||

Test case 1.5 | 3.991 | |||

Test case 2.1 | 0.18 ± 0.0018 | 60 ± 1 | 0.705 | 24 ± 1 |

Test case 2.2 | 1.546 | |||

Test case 2.3 | 2.183 | |||

Test case 2.4 | 3.177 | |||

Test case 2.5 | 3.991 | |||

Test case 3.1 | 0.24 ± 0.0018 | 60 ± 1 | 0.705 | 24 ± 1 |

Test case 3.2 | 1.546 | |||

Test case 3.3 | 2.183 | |||

Test case 3.4 | 3.177 | |||

Test case 3.5 | 3.991 | |||

Test case 4.1 | 0.3 ± 0.0018 | 60 ± 1 | 0.705 | 24 ± 1 |

Test case 4.2 | 1.546 | |||

Test case 4.3 | 2.183 | |||

Test case 4.4 | 3.177 | |||

Test case 4.5 | 3.991 | |||

Test case 5.1 | 0.36 ± 0.0018 | 60 ± 1 | 0.705 | 24 ± 1 |

Test case 5.2 | 1.546 | |||

Test case 5.3 | 2.183 | |||

Test case 5.4 | 3.177 | |||

Test case 5.5 | 3.991 |

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**MDPI and ACS Style**

Altwieb, M.; Mishra, R.; Aliyu, A.M.; Kubiak, K.J.
Heat Transfer Enhancement by Perforated and Louvred Fin Heat Exchangers. *Energies* **2022**, *15*, 400.
https://doi.org/10.3390/en15020400

**AMA Style**

Altwieb M, Mishra R, Aliyu AM, Kubiak KJ.
Heat Transfer Enhancement by Perforated and Louvred Fin Heat Exchangers. *Energies*. 2022; 15(2):400.
https://doi.org/10.3390/en15020400

**Chicago/Turabian Style**

Altwieb, Miftah, Rakesh Mishra, Aliyu M. Aliyu, and Krzysztof J. Kubiak.
2022. "Heat Transfer Enhancement by Perforated and Louvred Fin Heat Exchangers" *Energies* 15, no. 2: 400.
https://doi.org/10.3390/en15020400