Review Reports - Intensification of Thermal Performance of a Heat Exchanger Tube with Knitted Wire Coil Turbulators Installed

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript focuses on the way of Intensification of Thermal Performance of a Heat Exchanger Tube with Knitted Wire Coil Turbulators Installed.

The introduction to the paper contains an interesting literature review on the influence of turbulators on heat exchange parameters.

Have you really achieved such precision for these values on lines 26, 30, 396 and 397?

In the experimental section, please mention the cross-sectional shape of all the wires used.

Please explain the nature of the flex point in Fig. 13.

I suggest shortening the manuscript by placing general formulas and detailed information in the supplementary information, along with the experimental setup images, as well as figures 13a and 14a.

Formulas (19), (20) and (21) contain N to the power of x < 1, meaning that Nu, f and TPI have no upper limit with respect to the N parameter. Is this correct? Please add a discussion about this and/or specify N range in this section.

Author Response

The authors would like to thank the editors and reviewers for their thorough review and constructive comments. The specific changes and clarifications requested are outlined below.

Manuscript Number: eng-3900134

Intensification of thermal performance of a heat exchanger tube with knitted wire coil turbulators installed

Comments and Suggestions for Authors

Reviewer #1:

This manuscript focuses on the way of Intensification of Thermal Performance of a Heat Exchanger Tube with Knitted Wire Coil Turbulators Installed. The introduction to the paper contains an interesting literature review on the influence of turbulators on heat exchange parameters.

Have you really achieved such precision for these values on lines 26, 30, 396 and 397?

Response: In the current study, all of the results were verified with uncertainty.

Uncertainty analysis was performed using the McClintock method [32]. The uncertainties for the dimensionless Nusselt number (Nu) and the friction factor (f) were estimated at ±4.1 and ±3.4%, respectively. Table 4 presents all measured parameters along with the uncertainty analysis results.

Nusselt number (Nu):

(14)

where

(15)

where

Friction factor (f):

(16)

where and

Table 4. Experimental uncertainties.

Variable Uncertainties (%)

Air flow velocity, U ±2.98

Air viscosity, µ ±0.07

Pressure, P ±4.1

Ammeter, I ±2.2

Air temperature, T ±0.14

Thermal conductivity, k ±0.37

Voltmeter, V ±0.97

In the experimental section, please mention the cross-sectional shape of all the wires used.

Response: Detail has been added in section 2.1.

The knitted wire coil turbulators were made of 0.7 mm diameter copper wires wound around 1.0 mm diameter flexible core rods, as depicted in Figs. 2–3. Fabrication began by forming the copper wire into helical turns and inserting it into the gap be-tween two twisted central core rods, shaping it into the desired looped or petal-like pattern. Prior to assembly, the wire positions were pre-marked using a circular tem-plate based on CAD design to guarantee uniform spacing and alignment. The wire loop density (N) was varied at 6, 8, 10, and 12 loops per pitch (1.0 pitch = 6.8 mm). For ex-perimental analysis, the knitted wire coil turbulators were inserted into a 19 mm inner diameter heat exchanger tube, maintaining a constant 600 W/m² wall heat flux.

Please explain the nature of the flex point in Fig. 13.

Response: The TPI trend (Fig. 13) decreases as the Reynolds number increases; however, this trend is calculated from the ratio of the Nusselt number to the friction factor under constant pumping power. Therefore, the trend may vary at certain Reynolds numbers due to fluctuations in the Nusselt number ratio.

I suggest shortening the manuscript by placing general formulas and detailed information in the supplementary information, along with the experimental setup images, as well as figures 13a and 14a.

Response: Equation (1-16) provides the specifics of data reduction, which are required for the current undertaking. Section 2.3 of the experiment has been updated to include additional information.

Response: The Nu, f, and TPI have a limit with wire loop densities (N = 6, 8, 10, and 12 loops per pitch), and it has been mentioned in the above equations (19-21).

Least squares regression analysis was employed to establish experimental correlations for the Nusselt number (Nu), friction factors (f), and thermal performance index (TPI) using a tube mounted with knitted wire coil turbulators. This methodology employed water as the test fluid under turbulent conditions with Reynolds numbers ranging from 5,000 to 15,000, heat flux at 600 W/m², and wire loop number densities (N = 6, 8, 10, and 12 loops per pitch) as the independent variable.

(19)

(20)

(21)

We sincerely appreciate the reviewer’s comments and suggestions, which contributed significantly to strengthening the manuscript.

…………………………………….

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Intensification of Thermal Performance of a Heat Exchanger Tube with Knitted Wire Coil Turbulators Installed

The biggest problem I find when reading this paper is the way the authors present each of its sections. From the way they present the images to the way they analyse them, they cause the reader to lose interest in the paper, despite the fact that it contains valuable results. Given my previous comments, I believe that this paper is not a candidate for publication in the Journal Eng.

Additionally, I would like to point out some other issues that the authors should address.

The Introduction section is very long. I would recommend merging Figure 1 into Table 1. To do this, include two columns in the table summarizing the most important points about what was done and what was found in each cited work. This will help reduce the amount of text in this section.
Figures 5 and 6: the numbers are not displayed correctly.
Line 197: Tests were conducted at three different Reynolds numbers, 1000, 2500, and 5000, but in lines 221-222, it was adjusted to achieve the desired Reynolds number (5000 ≤ Re ≤ 15,000).... What are the correct conditions?
Line 227-228: All experimental measurements were conducted under steady- state conditions…. How did you determine that the system met this condition?
Figures 11 and 12 may be one figure.
Line: 434: Figures 15(a–b) illustrate the thermal performance index (TPI) results…. There is no Figure 15b.
Line 448: The experimental data were used to develop empirical correlations for the Nusselt number (Nu), friction factor (f), and thermal performance index (TPI)… Did you use any parameterization or dimensional analysis methods to arrive at these equations?
Why is there no quantitative comparison of your results with those already published in the same field?
The bibliography is not in the style requested by the journal.

Among others...

Best regards.

Author Response

The authors would like to thank the editors and reviewers for their thorough review and constructive comments. The specific changes and clarifications requested are outlined below.

Manuscript Number: eng-3900134

Intensification of thermal performance of a heat exchanger tube with knitted wire coil turbulators installed

Comments and Suggestions for Authors

Reviewer #2:

The Introduction section is very long. I would recommend merging Figure 1 into Table 1. To do this, include two columns in the table summarizing the most important points about what was done and what was found in each cited work. This will help reduce the amount of text in this section.

Response: Thank you for the comments, we modified the more summarized previous works and have incorporated Figure 1 into Table 1.

Table 1. Summary of previous work.

Authors	Summary of Experimental Circular Tube Thermal performance index (TPI)
Fan et al. [1]	Numerical study of a circular tube with conical strip inserts for turbulent flow (Re = 12,000–42,000). Larger slant angles and smaller pitches improved heat transfer but increased resistance, with slant angle having a stronger influence.
Gunes et al. [3]	Coiled wire inserts (Re = 4,105–26,400). Results showed Nu/Nu_p = 2.38–3.03, f/f_p = 7.13–8.22, and TPI ≈ 1.51. Optimal performance occurred at P/D = 1.0, s = 1.0 mm, Re ≈ 4,220, giving ~50% higher efficiency than the smooth tube. Decreasing the pitch ratio and wall gap enhanced both Nusselt number and friction factor
Karakaya and Durmus [4]	Conical spring turbulators (CST) at angles of 30°, 45°, and 60° (Re = 10,000–34,000). The inserts enhanced heat transfer and increased pressure drop compared to a smooth tube. Optimal conditions were found at moderate spring angles, where Thermal performance index and exergy efficiency were improved. Conical-shaped springs with a 30° cone angle exhibited the highest heat transfer enhancement.
Keklikcioglu and Ozceyhan [6]	Triangular coiled-wire inserts placed 1 mm from the wall (Re = 2,851–27,732). The best configuration (e/D = 0.0892, P/D = 1.0) achieved Nu/Nu_p = 2.12–3.41, f/f_p = 4.2–8.8, and TPI ≈ 1.68, showing ~18% higher enhancement than earlier wire designs. The optimal configuration (e/D = 0.089, P/D = 1.0) achieved up to 1.68 times higher thermal performance than a smooth tube.
Nanan et al. [7]	Helically twisted tape inserts inducing co- and counter-swirl flows (Re = 6,000–20,000). Results showed Nu/Nu_p = 2.82–3.29, f/f_p = 33.2–36.7, and TPI ≈ 1.29. Counter-swirl tapes gave higher heat transfer but lower overall efficiency, while co-swirl tapes provided better thermal performance index at larger pitch ratios. Helically twisted tapes inducing co-swirl flows achieved higher thermal performance factors than counter-swirl tapes, while reducing pitch ratios increased Nusselt number and friction factor but lowered thermal performance.
Akhavan-Behabadi et al. [8]	Double-pipe heat exchanger with coiled wire inserts during oil heating (Re based on oil flow). Wire diameters of 2.0 and 3.5 mm with pitches of 12–69 mm were tested. The inserts significantly increased the heat transfer coefficient and friction factor compared to a smooth tube. Empirical correlations for Nu/Nu_p and f/f_p were developed, predicting results within ±20%, with optimal performance at smaller pitch and larger wire diameter. Wire coil inserts with smaller wire diameters demonstrated superior thermal performance, particularly at low Reynolds numbers, while variations in coil pitch had only a minor influence on heat transfer enhancement.
Gunes et al. [10]	Triangular coiled-wire inserts placed 1 mm from the wall (Re = 3,500–27,000). Results showed Nu/Nu_p = 2.12–3.41 and f/f_p = 4.2–8.8. The best performance occurred at a/D = 0.0892, P/D = 1, Re ≈ 3,858, with ~36.5% overall enhancement, especially effective at low Reynolds numbers for compact heat exchanger design. Increasing wire thickness and decreasing pitch ratio improved heat transfer, with the highest overall enhancement efficiency of 36.5% achieved at a/D = 0.0892 and P/D = 1.0 for a Reynolds number of 3,858
Hong et al. [11]	Wire coil (WC) inserts of uniform, varying pitch, and gradually varying width (Re = 6,000–20,000). Heat transfer was enhanced with Nu/Nup = 1.46–2.49 and friction factor increased to f/fp = 8.36–18.62. The highest TPI ≈ 1.14 was achieved for uniform pitch WCs at p/d = 1.034, while varying pitch and width provided no further efficiency improvement despite higher Nu.
Nanan et al. [21]	Wire-rod bundle turbulators (Re = 6,000–20,000). Results showed Nu/Nu_p = 1.04–1.69 and f/f_p = 2.56–4.53, depending on rod number and pitch ratio. The TPI ≈ 1.02 was achieved at high rod numbers with low pitch ratios, indicating minor efficiency gains but consistent enhancement trends. Increasing the number of wires and reducing the pitch ratio improved the Nusselt number and thermal performance.
Naphon and Suchana [22]	Concentric tube heat exchanger with twisted wire brush inserts (Re = 6,000–20,000). Increasing brush density (100–300 wires/cm) enhanced heat transfer but also caused significant pressure loss. Compared to the plain tube, heat transfer rose markedly (Nu/Nu_p> 1) while friction increased substantially, with no optimal TPI beyond unity due to high flow resistance. Increasing the density of full-length twisted wires enhanced heat transfer and Nusselt number, with the 300-wire insert giving the best results.
Bhuiya et al. [23]	Twisted wire brush inserts (Re = 7,200–50,200). Heat transfer and friction were significantly enhanced, with Nu/Nu_p ≈ 2.15 and f/f_p ≈ 2.0 over the plain tube. The TPI ≈ 1.85 was obtained at higher wire densities, confirming strong thermo-hydraulic improvement under constant blower power.
Chompookham et al. [27]	Serrated wire coil (SWC) inserts combining coiled wire and V-shaped ribs (Re = 5,114–14,752). Heat transfer increased with decreasing pitch and larger coil diameter, giving Nu/Nu_p = 1.75–2.46 and f/f_p = 3.31–8.16. The maximum TPI ≈ 1.41 was achieved at DC = 47.9 mm, PC = 10 mm, Re = 5,114, confirming SWC as a more effective turbulator than conventional coils. Smaller pitch lengths and larger coil diameters improved heat transfer enhancement.
Hashemian et al. [29]	Helically coiled tubes with helical wire inserts under single-phase (water) and two-phase (air–water) flow. Water flow rates of 2–8 L/min and air flow rates of 1.0–5.0 L/min were tested (VF = 0.11–0.714). Results showed enhanced heat transfer but increased pressure drop, with exergy efficiency reduced by up to 87% when inserts were used in single-phase flow. Optimal use was suggested for two-phase flow with turbulator where heat transfer improvement outweighs friction losses. For single-phase flow, exergy efficiency is higher without a turbulator.
Hong et al. [30]	Traverse corrugated tubes (TCTs) with twin and triple wire coil (WC) inserts (Re = 6,000–18,000). Heat transfer rose with coil number and reduced spacing, giving Nu/Nu_p = 1.74–2.61 and f/f_p = 4.57–21.34. The maximum TPI ≈ 1.09 was found for twin WCs at S/D = 18.1, while the TCT alone reached TPI ≈ 1.26. Entropy analysis showed reduced Bejan number, with the lowest augmented entropy generation at triple WCs, S/D = 0.0, Re ≈ 6,428. Heat transfer improved with more coils and smaller spacing, though the best overall performance occurred with twin WCs at the largest spacing

Figures 5 and 6: the numbers are not displayed correctly.

Response: It has been corrected.

Line 197: Tests were conducted at three different Reynolds numbers, 1000, 2500, and 5000, but in lines 221-222, it was adjusted to achieve the desired Reynolds number (5000 ≤ Re ≤ 15,000).... What are the correct conditions?

Response: In the current experimental study, two methods of experimental setups were employed. Initially, the flow visualization in the laminar flow region of Reynolds number 1,000, transition flow of Reynolds number 2,500, and turbulent flow of Reynolds number 5,000 are investigated using the dye visu-alization setup (Figures 4-6). Secondly, the heat transfer test apparatus (Figure 7) is employed to investigate the heat transfer, friction factor and thermal performance index characteristics in the turbulent flow region with a Reynolds number between 5,000 and 15,000.

Line 227-228: All experimental measurements were conducted under steady- state conditions…. How did you determine that the system met this condition?

Response: All experimental measurements were conducted under steady-state conditions. Steady-state conditions were assumed when all temperature readings at the inlet, out-let, and wall positions varied by less than ±0.2 °C over a 10-minute period, and the electrical power input and mass flow rate remained constant.

Figures 11 and 12 may be one figure.

Response: It has been merged into one figure.

Line: 434: Figures 15(a–b) illustrate the thermal performance index (TPI) results…. There is no Figure 15b.

Response: Thank you very much for the comment. The sentence has been revised.

Line 448: The experimental data were used to develop empirical correlations for the Nusselt number (Nu), friction factor (f), and thermal performance index (TPI)… Did you use any parameterization or dimensional analysis methods to arrive at these equations?

Response: Least squares regression analysis was employed to establish experimental correlations for the Nusselt number (Nu), friction factors (f), and thermal performance index (TPI) using a tube mounted with knitted wire coil turbulators. This methodology employed water as the test fluid under turbulent conditions with Reynolds numbers ranging from 5,000 to 15,000, heat flux at 600 W/m2, and wire loop number densities (N = 6, 8, 10, and 12 loops per pitch) as the independent variable.

Why is there no quantitative comparison of your results with those already published in the same field?

Response: Thank you very much. It has been added in section 4.6.

The thermal performance index of the knitted wire coil turbulators at wire loop number densities (N = 12 loops) is compared to that of previous modified turbulators, including the coiled-wire [6], conical ring turbulator [34], and conical braided wire turbulator [35]. Figure 16 illustrates this comparison. A comparison was conducted between all of the turbulators that have been identified at a comparable Reynolds number (Re). The thermal performance index of the present work is higher than that of other turbulators at low Reynolds numbers, as evidenced by the figure. Conversely, in the turbulent flow region, the present work has the lowest thermal performance index, which is lower than that of the conical ring turbulator [34]. It is intriguing to observe that the thermal performance index of knitted wire coil turbulators is greater than unity for all Reynolds numbers investigated. This suggests that they can be utilized effectively for energy conservation and compactness objectives in comparison to other modified turbulators. It is evident that the thermal performance index of the present knitted wire coil turbulators is significantly constrained by the presence of high flow obstruction or friction.

Figure 16. Comparison work with coiled-wire [6], conical ring turbulator [34], and conical braided wire turbulator [35].

It is crucial to note that the knitted wire coil turbulator shape exhibits not only exceptional thermal performance but also practical advantages in terms of fabrication. The design necessitates only a meshing wire. This simplicity results in increased feasibility for commercial-scale heat exchanger applications, where effectiveness and manufacturing simplicity are critical factors. In light of this, the knitted wire coil design for a turbulator is a greatly prospective approach for the development of potential thermal technology.

The bibliography is not in the style requested by the journal.

Among others...

Response: The references have been carefully revised to ensure complete uniformity and full compliance with the journal’s formatting guidelines.

We sincerely appreciate the reviewer’s comments and suggestions, which contributed significantly to strengthening the manuscript.

…………………………………….

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript investigates the thermal-hydraulic performance of a heat exchanger tube fitted with knitted wire coil turbulators. The topic is relevant to the field of heat transfer enhancement and compact heat exchangers, and the experimental approach provides valuable insights. However, the manuscript would benefit from clarifications and additional details regarding the experimental setup, data interpretation, and comparison with existing literature.

Some comments on the manuscript:

It would be very helpful to include a real photograph of the complete heat exchanger system in addition to the schematic diagrams.
Please explain how the symmetric arrangement of the internal wires was ensured during fabrication and installation.
Tables 5–6: The numbering is not clearly visible. Please revise the formatting.
Figure 4: It is recommended to name all components and number the measurement points. Please indicate the location of the sensors (temperature, pressure, flow) used to collect the data.
Figure 7: Provide a more detailed description, including the location of measuring devices and the names of the main components.
Figure 10: The figure is difficult to follow in its current form. Please improve its clarity.
The description of the test bench is currently insufficient. Please provide a clearer explanation of how the experimental rig operates, including the interaction between the components, to allow reproducibility.
Two different figures (Figures 4 and 7) are used to describe the test bench, which is confusing. Please clarify the function of each bench and harmonise the presentation.
Please specify the conditions assumed to estimate the Reynolds number inside the test bench.
Discuss how the presence of the knitted wires influences velocity distribution and flow regime (laminar, transitional, or turbulent).
The uncertainty of the calculated parameters Nu and f should be explicitly reported in the results section. Providing error bars in the figures would also strengthen the analysis.
Please indicate the operational ranges (Re, heat flux, geometry) for which the proposed correlations are valid. This is important for practical application by future researchers.
A detailed comparison with results from existing literature would help highlight the novelty and advantages of the proposed solution.
Please discuss whether the knitted wire coil approach outperforms or complements existing turbulators reported in previous studies.
Please provide a discussion on the limitations or restrictions of the proposed solution (e.g., pressure drop penalties, manufacturing complexity, scalability), as well as the potential applications.

Comments on the Quality of English Language

The writing is generally clear, but minor grammatical corrections are needed throughout the text.

Author Response

The authors would like to thank the editors and reviewers for their thorough review and constructive comments. The specific changes and clarifications requested are outlined below.

Manuscript Number: eng-3900134

Intensification of thermal performance of a heat exchanger tube with knitted wire coil turbulators installed

Comments and Suggestions for Authors

Reviewer #3:

It would be very helpful to include a real photograph of the complete heat exchanger system in addition to the schematic diagrams.

Response: It has been added in Fig. 7(b).

(b) Photograph of experimental setup

Please explain how the symmetric arrangement of the internal wires was ensured during fabrication and installation.

Response: In the experiments, the heater wire was coiled around the test tube with a consistent pitch length of 70 mm throughout the test section, where thermocouples were positioned along the test tube between the heater wire coils. It has been added in Fig. 7(c).

Figure 7. Details of the heat transfer apparatus: uniform heat flux tube, cooling tank, water pump, rotameter, T-type thermocouples, RTDs, data logger, controller box, Variac transformer, Watt meter, U-tube manometer and digital pressure manometer, and computer.

Tables 5–6: The numbering is not clearly visible. Please revise the formatting.

Response: Figures 5-6 have been revised.


Isometric view	Side view

Front view	Side view

Figure 5. Details of the flow visualization apparatus: (1) inlet pipe, (2) over head pipe, (3) acrylic pipe, (4) outlet pipe, (5) bellmouth entry, (6) glass ball, (7) over flow pipe, (8) dye system, and (9) flow meter.


Rear view

Figure 6. Details of the dye injection system: (1) dye reservoir, (2) dye flow control valve, and (3) dye injection needle.

Figure 4: It is recommended to name all components and number the measurement points. Please indicate the location of the sensors (temperature, pressure, flow) used to collect the data.

Response: It has been added in Fig. 7(c).

Figure 7: Provide a more detailed description, including the location of measuring devices and the names of the main components.

Response: It has been added in Fig. 7(b-c).

Figure 10: The figure is difficult to follow in its current form. Please improve its clarity.

Response: Figure 10 have been revised.

Figure 10. Flow pattern in a plain tube with a knitted wire coil turbulator at different dye injection locations.

The description of the test bench is currently insufficient. Please provide a clearer explanation of how the experimental rig operates, including the interaction between the components, to allow reproducibility.

Response: More details has been added in section 2.3.

All experimental measurements were conducted under steady-state conditions. Steady-state conditions were assumed when all temperature readings at the inlet, outlet, and wall positions varied by less than ±0.2 °C over a 10-minute period, and the electrical power input and mass flow rate remained constant. Furthermore, tables 2 and 3 have comprehensive information relating knitted wire coils and the test conditions. The module for temperature and pressure measurement is divided into two subsystems. Utilizing a constant-temperature plenum, the inlet water temperature was maintained at 25°C. Water/Fluid temperatures were measured at both the inlet and exhaust using Pt100 RTDs (accuracy ±0.12°C). The inlet RTD was installed at the centerline of the plenum outlet (r/D = 0.0), and three outlet RTDs were installed radially along the tube (r/D = 0, 0.3, and 0.45). In order to reduce the impact of radial temperature gradients, the arithmetic mean of the measurements at both the inlet and the outlet was implemented. Ten T-type thermocouples were distributed equally along the axial orientation of the test section, from 700 mm (40D) downstream of the inlet to 350 mm (20D) upstream of the outlet. To improve thermal contact, every thermocouple was placed into a blind hole with a diameter of 1.0 mm that was drilled to a depth of 0.33 mm, which was two-thirds of the wall thickness. The hole was then filled with thermal conductivity (k ≥ 1.2 W/m·K). Three auxiliary thermocouples were positioned at 120° intervals around the midsection of the tube to confirm circumferential temperature uniformity. A dual-gauge parallel monitoring strategy was utilized by the pressure measurement system. The overall pressure drop was measured using a pressure differential gauge (±1.0 Pa accuracy), while static pressures at both the inlet and the outlet were monitored using a digital pressure gauge (±0.1% accuracy). The total uncertainty in the pressure drop measurement was assured by comparison of the two readings, which was less than ±0.5%. Signals from the thermocouples, RTDs, power meter, and pressure gauges were simultaneously recorded by a multi-channel data recorder at a sampling interval of 1 s. Steady-state conditions were considered to have been achieved when the water temperature fluctuation remained within ±1.0°C/min and the wall temperature difference within ±0.5°C/min for a minimum of 30 seconds. In order to eliminate transient effects, data were collected continuously for 10 minutes after steady-state was attained, with the exception of the initial 2 minutes. The representative data point for each operating condition was the arithmetic mean of the remaining 8 minutes.

Two different figures (Figures 4 and 7) are used to describe the test bench, which is confusing. Please clarify the function of each bench and harmonise the presentation.

Please specify the conditions assumed to estimate the Reynolds number inside the test bench.

Response: This study examines the turbulent zone characterized by an initial Reynolds number of 5,000 to 20,000 which it is the range for many engineering applications such as heat exchanger tube and solar water/air heater.

Discuss how the presence of the knitted wires influences velocity distribution and flow regime (laminar, transitional, or turbulent).

Response: It has been added in section 4.1.1

The flow behaviors in a tube with no turbulator assessed using a dye injection technique at Reynolds numbers (Re) of 1,000, 2,500, and 5,000 are shown in Fig. 8(a). At Re = 1000, the flow is smooth and stable, with well-defined, parallel dye streaks indicating laminar behavior. At Re = 2,500, small disturbances and waviness appear, marking the onset of transition. Finally, at Re = 5,000, the flow becomes fully turbulent, with chaotic mixing, vortices, and irregular patterns.

The uncertainty of the calculated parameters Nu and f should be explicitly reported in the results section. Response: In the current study, all of the results were verified with uncertainty and it hass been added in section 3.3.

Nusselt number (Nu):

(14)

where

(15)

where

Friction factor (f):

(16)

where and

Table 4. Experimental uncertainties.

Variable Uncertainties (%)

Air flow velocity, U ±2.98

Air viscosity, µ ±0.07

Pressure, P ±4.1

Ammeter, I ±2.2

Air temperature, T ±0.14

Thermal conductivity, k ±0.37

Voltmeter, V ±0.97

Providing error bars in the figures would also strengthen the analysis.

Response: The addition of error bars will make the interpretation of the graph more difficult due to the fact that the data for each parameter does not appear to be significantly different from one another.

Please indicate the operational ranges (Re, heat flux, geometry) for which the proposed correlations are valid. This is important for practical application by future researchers.

Response: Thank you very much, it has been added in section 4.5.

A detailed comparison with results from existing literature would help highlight the novelty and advantages of the proposed solution.

Response: It has been added in section 4.2.

The experimentally obtained Nusselt number and friction factor data for the tube with no turbulators were validated using standard correlations to assess the reliability of the setup. The Nusselt number results were compared with the standard empirical correlation by Dittus-Boelter [33].

(17)

The friction factor (f) results were compared with the Blasius correlation [33] under similar conditions:

(18)

Figures 11(a-b) demonstrate good agreement between the experimental results of the present data and standard correlations, with deviations not exceeding 3.9% for the Nusselt number (Nu) and 5.2% for the friction factor (f). This finding confirms the reliability of the experimental data and setup. Consequently, the experimental results of the plain tube serve as a valid reference for assessing the performance of tubes with knitted wire coil turbulators.

Please discuss whether the knitted wire coil approach outperforms or complements existing turbulators reported in previous studies.

Response: Thank you very much. It has been added in section 4.6.

The thermal performance index of the knitted wire coil turbulators at wire loop number densities (N = 12 loops) is compared to that of previous modified turbulators, including the coiled-wire [6], conical ring turbulator [34], and conical braided wire turbulator [35]. Figure 16 illustrates this comparison. A comparison was conducted between all of the turbulators that have been identified at a comparable Reynolds number (Re). The thermal performance index of the present work is higher than that of other turbulators at low Reynolds numbers, as evidenced by the figure. Con-versely, in the turbulent flow region, the present work has the lowest thermal performance index, which is lower than that of the conical ring turbulator [34]. It is intriguing to observe that the thermal performance index of knitted wire coil turbulators is greater than unity for all Reynolds numbers investigated. This suggests that they can be utilized effectively for energy conservation and compactness objectives in comparison to other modified turbulators. It is evident that the thermal performance index of the present knitted wire coil turbulators is significantly constrained by the presence of high flow obstruction or friction.

Figure 16. Comparison work with coiled-wire [6], conical ring turbulator [34], and conical braided wire turbulator [35].

Please provide a discussion on the limitations or restrictions of the proposed solution (e.g., pressure drop penalties, manufacturing complexity, scalability), as well as the potential applications.

Response: It is crucial to note that the knitted wire coil turbulator shape exhibits not only exceptional thermal performance but also practical advantages in terms of fabrication. The design necessitates only a meshing wire. This simplicity results in increased feasibility for commercial-scale heat exchanger applications, where effectiveness and manufacturing simplicity are critical factors. In light of this, the knitted wire coil design for a turbulator is a greatly prospective approach for the development of potential thermal technology.

We sincerely appreciate the reviewer’s comments and suggestions, which contributed significantly to strengthening the manuscript.

…………………………………….

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have adequately justified the comments made, so I have no further observations to make on the work.

Reviewer 3 Report

Comments and Suggestions for Authors

The reviewer is satisfied with the new version of the manuscript