In this study, the primary objective was to enhance the hydrothermal performance of a dimpled tube by addressing areas with low heat transfer compared to other regions. To accomplish this, a comprehensive numerical investigation was conducted using ANSYS Fluent 2022 R1 software, focusing on different diameters of dimples along the pipe’s length and the distribution of dimples in both in-line and staggered arrangements. The simulations utilized the finite element method to address turbulent flow within the tube by solving partial differential equations, encompassing Re numbers spanning from 3000 to 8000. The study specifically examined single-phase flow conditions, with water utilized as the cooling fluid. The results of the investigation indicated that increasing the Reynolds number resulted in higher average Nusselt numbers, pressure drops, the overall performance criterion, and a reduction in average thermal resistance across all models analyzed. Notably, both proposed models demonstrated improved heat transfer when compared to the conventional model. Out of all the models evaluated, the tube featuring staggered dimples (Model B) demonstrated the most notable improvement in the Nu number. It exhibited an enhancement of approximately twice the value compared to the conventional model. The mean thermal resistance for the tube with dimples in the staggered arrangement (Model B) is 0.0057 k/W, compared to 0.0118 k/W for the traditional model. The maximum overall performance criterion for Model -A- and Model -B- is 1.22 and 1.33, respectively.

Heat exchangers are devices widely used in many industrial and engineering applications around the world. So, it has become necessary to improve the hydrothermal performance and efficiency of such devices to reduce their size, reduce their cost, and make them more suitable for many different applications. Generally, there are two main techniques to improve heat transfer: passive and active techniques. The current study will focus on the passive technique because it does not require external devices and is thus less costly as compared to the active technique. Increasing the surface roughness of pipe is one of the better passive techniques that can be achieved by using different configurations like ribs, dimples, and corrugation. All these configurations are meant to increase flow mixing, enhance turbulent flow, and redevelop the boundary layer, thus improving the rate of heat transfer [

Despite the huge number of research studies that tried to enhance the thermal response of dimpled tubes, most of these studies did not take into account the regions where the heat transfer is less than in other areas. So, the objective of the current study is to address the issue of low heat transfer in these areas of dimpled tubes by focusing on those areas and implementing certain modifications. The researchers aimed to increase the surface area for heat transfer and enhance the randomness of the working fluid. This was achieved by increasing the diameter of dimples present on the surface of the dimpled tube. The dimpled tube consists of three primary regions, each with a distinct dimple diameter. The dimple diameters in the first, second, and third regions were 1, 2, and 3 mm, respectively. There were differences in the spacing between the dimple centers for each region; the first, second, and third regions used 3, 5, and 7 mm, respectively. Furthermore, for all three regions, a 90-degree angle was maintained between the dimples surrounding the pipe. Additionally, the study looked into two dimple arrangements: staggered and in-line. These configurations describe how the dimples are positioned in relation to one another. The dimples are offset from one another in a staggered arrangement, whereas they are aligned in a straight line in an in-line arrangement. The current study intends to improve the thermal performance of dimpled tubes by enhancing heat transfer in areas that previously exhibited low performance by examining these various dimple configurations and arrangements. This current study focused on double pipe heat exchanger type. The water is used inside the tube while outside the tube (annular tube), instead of the working fluid (water), the constant heat flux is used in order to simplify the case study.

The present study is focused on carrying out a numerical analysis of hydrothermal improvement in a 3-D circular tube with different sizes and arrangements of dimples. The main objective of this study is to investigate the flow behavior within the dimpled tube and improve its hydrothermal performance.

In the current work, the grid employed for the numerical calculations consists of tetrahedral elements in both the wall and flow domains. This grid is generated with an increased density near the wall to effectively capture the abrupt temperature and velocity gradients, as shown in

Model | Mesh element number (million) | Temperature difference (°C) | Difference error (%) |
---|---|---|---|

Traditional model | 2.12 | 21.953 | 3.929 |

3.01 | 22.851 | 0.798 | |

4.13 | 23.035 | – | |

Model -A- | 2.11 | 25.051 | 3.098 |

3.25 | 25.852 | 0.796 | |

4.27 | 26.058 | – | |

Model -B- | 2.21 | 27.106 | 2.682 |

3.33 | 27.853 | 0.776 | |

4.36 | 28.071 | – |

In the current analysis, turbulent flow within a pipe of a heat exchanger was investigated. The Reynolds number (Re) range under study was 3000–8000, indicating a flow regime characterized by turbulence. Water was chosen as the working fluid for the simulations. To simplify the analysis, the physical properties of water are assumed to remain constant throughout the study. This assumption was reasonable because the operational temperature range within the heat exchanger was small, specifically at a temperature of 300 K. The water temperature at the inlet is 300 K, and the water flow rate is uniform, with the flow rates corresponding to Reynolds numbers of (3000, 4000, 5000, 6000, 7000, and 8000). The zero-pressure outlet boundary condition was employed in the simulations. This condition implies that the pressure at the outlet of the pipe was assumed to be atmospheric pressure. Additionally, a constant heat flux of 10,000 W/m² was applied to the outer surface of the dimpled tube, as depicted in

The working fluid employed was water, which possessed the following properties: an initial density of 998.2 kg/m³, a specific heat of 4.182 kJ/kg·°C, a dynamic viscosity of 1.003 × 10^{−}³ kg/m·s, a thermal conductivity of 0.6 W/m·°C, and a thermal expansion rate of 0.000149 K^{−}¹ [

The equations of continuity, momentum, and heat transport were solved using steady Reynolds Averaged Navier-Stokes (RANS) [

1. The flow is assumed to be steady, turbulent, and incompressible.

2. The properties of the water and the pipe material are considered to be independent of temperature and are assumed to remain constant.

3. The contribution of radiation heat transfer is believed to be negligible and can be disregarded.

4. The effect of gravity is considered to be negligible and is not taken into account.

5. The surface of the pipe wall is assumed to be smooth, and a constant heat flux is applied to it.

6. The effects of vibration are not considered in this analysis.

Based on the preceding assumptions, we can express the governing equations for fluid flow and thermal convection through the following partial differential equations:

Continuity equation:

Momentum equation:

Energy equation:

The Realizable k-turbulence model with improved wall treatment was employed in this study to simulate the turbulence. Based on the current model, the equations of the modelled transport for both K and ε are given below [

where

The default values of the model constant were defined (

The amount of heat transferred to water from the wall of the tube can be calculated as follows:

where

To estimate the average heat transfer coefficient, Newton’s law of cooling can be used [

where

The mean bulk temperature of water is calculated as follows [

To calculate the average Nu number,

where D represents the inner diameter of the tube, while

One of the most significant parameters that is used to estimate the hydraulic performance of the dimpled tube is the friction factor, which can be calculated from

where ΔP, ρw, Vm, and L represent the pressure drop across the tube, water density, the mean velocity of water, and tube length, respectively.

Usually, the overall performance criteria are used to assess the overall hydro-thermal response of the new proposal models according to the Nu number and friction factor as follows [

where

Overall Performance Criteria (OPC) is a metric used to measure hydrothermal performance improvements compared to the conventional model. It represents the correlation between heat transfer and pressure drop, with a value greater than one indicating a positive change in the heat transfer process as compared to pressure drop.

To demonstrate the validity of the numerical results, this section compares the present results of the (CFD) with the experimental findings from earlier investigations. Both the geometry and the boundary conditions are used exactly in line with the experimental investigation conducted in Reference [

^{2}. The main aim of this figure is to clarify the effect of dimples on fluid flow and demonstrate the consistent turbulent flow around the dimple. In a smooth tube, the inner surface is considered to be completely smooth and free of any irregularities or roughness, and hence the flow is relatively simple, consisting of regular and well-defined layers or streamlines, as shown in

The effect of the dimple arrangement under study on the average Nusselt number (Nu) for different Reynolds numbers under a constant heat flux of 10,000 W/m^{2} and an inlet temperature of 293 K is demonstrated in

The effect of different configurations of the tubes under study (traditional tube and dimpled tube for both arrangements) on average thermal resistance for various Reynolds numbers under a constant heat flux of 10,000 W/m^{2} and an inlet temperature of 293 K is exhibited in

^{2} and the inlet temperature of water of 293 K. This figure reveals that the increase in pressure drop is associated with an increase in flow rate. The suggested tube configurations exhibited higher pressure drops compared to the traditional model. This phenomenon can be attributed to the interaction between the fluid and the dimples present along the tube. Moreover, the two proposed models demonstrated similar pressure drops due to an equal number of dimples. Furthermore, it was observed that Models -A- and -B- showed significant increases in pressure drop, with increments of 69.28% and 67.95%, respectively, compared to the traditional model.

The impact of different tube configurations under study on the friction factor at various Reynolds numbers under a constant heat flux of 10 KW/m^{2} and an inlet water temperature of 293 K is depicted in

^{2}, and an inlet temperature of 300 K. The arrangement of the dimples had a significant influence on the hydraulic and thermal performance of the tubes. Therefore, a thorough examination of the performance index was undertaken to determine the optimal choice among the innovative dimpled tubes. The performance index of the novel models showed an increasing trend. This observation can be attributed to the disturbance of the boundary layer by the dimples, which promotes turbulence near the pipe’s surface. Consequently, these configurations result in a substantial improvement in heat transfer but also lead to higher pressure drops compared to conventional tubes [

The present study investigates the impact of dimple arrangements on the fluid flow, heat transfer, thermal resistance, pressure drop, and overall performance characteristics of tubes. The numerical simulation model was validated by comparing it with previously published experimental results as well as the outcomes from some correlation equations. The comparison revealed a strong agreement, with a maximum deviation of 10%. This study yields numerous noteworthy conclusions.

1. The staggered arrangement of dimples (Model -B-) outperforms the in-line arrangement (Model -A-), transferring more heat from the pipe surface to the fluid. The average Nu number for Model -A- and Model -B- is 46% and 38.7% higher, respectively, compared to the traditional model. The reason behind that is the staggered arrangement of dimples that makes the flow more turbulent, hence increasing the heat transfer.

2. Model -B- demonstrates a superior average thermal resistance reduction of 51% compared to the traditional model, while Model -A- achieves a reduction of 43%. That is due to increased turbulent fluid flow as a result of the staggered arrangement of dimples and increased surface area.

3. Both Model -A- and Model -B- demonstrate significant increases in pressure drop compared to the traditional model, with increments of 69.28% and 67.95%, respectively.

4. The overall performance criterion values for both Model -A- and Model -B- exceed the threshold of (1), indicating the feasibility of all proposed models. Model -B- exhibits a higher overall performance criterion of 1.33 compared to Model -A-’s 1.22 at higher Reynolds numbers. That means that the improvement in heat transfer outweighs the downside of the increased pressure drop in the proposed models under the current study compared to smooth tubes.

In conclusion, the results of the current study provide valuable insights for the design and optimization of tube configurations for various applications that require efficient heat transfer and performance.

Definition Unit

The tube surface area
mm^{2}

Specific heat at constant pressure KJ/Kg.K

Diameter of tube mm

Average heat transfer coefficient of water W/m^{2}.k

Thermal conductivity of water W/m.K

Mass flow rate Kg/s

Nusselt number

The average Nu number of the traditional smooth tube

The tube length m

Fraction factor

Friction factor of the traditional smooth tube

The overall performance criterion

Pressure Pa

The heat flux W/m^{2}

Rate of Heat flow W

The inlet temperature of water K

The outlet temperature of water K

The mean temperature of the tube wall K

The mean bulk temperature of water K

The mean velocity of water m/s

Density of water kg/m^{3}

Pressure drop N/m^{2}

The authors would like to thank Mustansiriyah University in Baghdad, Iraq (

The authors received no specific funding for this study.

The authors confirm their contribution to the paper as follows: study conception and design: A.H.; data collection: B.S.; analysis and interpretation of results: A.H., B.F.; draft manuscript preparation: B.S. All authors reviewed the results and approved the final version of the manuscript.

The data are available when requested.

The authors declare that they have no conflicts of interest to report regarding the present study.

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_{4}-water nanofluids in a corrugated tube