The thermal-hydraulic performance of plain tubes with and without wire coils in turbulent regimes is investigated experimentally and numerically. The effects of wire coil distribution (circular cross section) within the tube were explored experimentally, and water was employed as the working fluid. The numerical simulation was carried out using software programmer ANSYS Fluent 2019 R3 using the finite-volume approach. In the turbulent regime, six cross-sectioned wire coils were analyzed, including: circular, rectangular, hexagonal, square, star shape, and triangle. The utilization of a tube with a wire coil has been shown to increase heat transfer rate and pump consumption. The results indicate a high level of concurrence, as the deviations are all below 8%. Compared with plain tube, the wire coils, according to the arrangement (TWD), gave the best PEC. The heat transfer enhancement ability of different cross sections follows the following order: StCS > RCS > HCS > SqCS > CCS > TCS. Also, the sequence of pump consumption for each cross section is as follows: RCS > StCS > SqCS > HCS > CCS > TCS.

Heat transfer mechanisms are regarded as fundamental components of all systems in the industrial sector. Energy conservation and heat exchanger size reduction are two methods that can be employed to enhance the thermal efficacy of such systems. Given that the heat transfer in a single conduit (channel) serves as a proxy for the performance of the entire device, it is frequently possible to assess the effectiveness of a heat exchanger by looking at that channel. Many experimental and numerical studies were reviewed, the most important of which are: Kongkaitpaiboon et al. [_{2}O_{3}+MWCNT hybrid Nano fluid. The results showed that the inserting of type D wire coils gave the best heat transfer performance compared to other types. Also, the heat transfer coefficient and pressure losses increase as the twisted tape width and twisting ratio decrease. Twisted tapes with a V-cut shape also show a higher performance index than wire coils. Xiong et al. [

In the above-mentioned literature, extensive studies have been carried out on the topics of improving the thermal and hydraulic performance of heat exchangers. Complex mechanisms related to heat transfer phenomena were used while inserting turbulence into the flow path, such as twisted taps, extended surfaces, fluid additives, etc., wire coils, one of the most promising heat enhancement elements. There is a need for more in-depth analysis of the techniques of using wire coils as turbulent bodies for flow inside tubes. However, the influence of the wire coil cross section shape has yet to be documented. The current effort focuses on three important challenges with wire coil performance: (1) Three various wire coil distributions (circular cross section) within the tube are experimentally studied to determine the optimal distribution to improve heat transfer performance. (2) The influence of cross-section shape is investigated numerically for six distinct wire coils. (3) Discuss the mechanisms of fluid flow and heat transfer characteristics to describe the heat transfer processes of tube and wire coils.

The present part describes the experimental test rig and provides a simple description of the devices used.

The test section is a copper tube with an inner diameter of 22 mm and a length of 1 m. The outer surface of the tube is electrically heated by a tungsten coil of 3 m length and diameter of 1.5 mm with a heating power of 3000 W, which is wound over an electrical insulator distributed along the length of the tube to generate a uniform heat flow as shown in

The main goal of the present experimental study is to conduct an experimental analysis to compare the distributed of the wire coils that circular cross section within the flow path to achieve the best performance evaluation criterion (PEC).

By experimentally simulating a circular horizontal tube with a constant heat flow on its outer surface, it was able to analyses the efficiency of the present heat exchanger.

Using the following formula [

Calculating how much heat is delivered from the heating wire to the distilled water is done using the following formula:

Before doing any calculations, it is essential to understand the water’s heat transfer coefficient. Calculating the local heat transfer coefficient is as follows:

The following equation has been used to compute the local Nusselt Number:

Kármán-Prandtl’s resistance equation for turbulent flow in smooth tubes provides a definition of the friction factor and may be used to simulate the change of the friction factor with Re when the tube surface is smooth [

The criterion of the performance evaluation criterion (PEC) is the basis of comparison for each addition to improve heat transfer in heat exchangers. The increase in the amount of heat transferred through the pipes is not considered an improvement unless it is compared with the friction factor that causes a decrease in pressure due to the addition of any specific object intended to improve heat transfer [

The first experiment tested a tube without inserting wire coils. After making sure that there is no water leakage, the pump is started and the water flow rate is determined by the valves. All tests are performed under fully developed turbulent flow with a Reynolds number range (3000–5000). After that, the amount of voltage entering the heater is determined by variac transformer and according to the heat flux required to be applied to the surface of the tube (1000–2500) W/m^{2}. The thermocouple readings are observed at the inlet and outlet of the test section and along the tube until a steady state is reached. After completing the experiments for the plain tube, one of the wire coil arrangement is inserted into the tube and the mentioned test steps are repeated.

The material of the tube is copper. The smooth circular tube has the following dimensions: length 1 m, wall thickness 1.5 mm, and inner diameter 22 mm. In this paper, the geometric values of the tube are presumed to be constant. ^{3}, λ = 0.6 W/(m.K), Cp = 4182 (J/Kg.K) and μ = 0.001003 (Pa.s).

Design Considerations: Selection of the cross-section shape of a threaded wire coil depends on various factors, including specific heat transfer requirements, fluid properties, pressure drop constraints, and manufacturing considerations. Computational fluid dynamics (CFD) simulations or experimental studies can be performed to optimize the shape and dimensions of a threaded wire coil for a specific application. It is important to note that the effect of cross shape on heat transfer is only one aspect of the overall heat transfer performance of threaded wire coil heat exchangers. Other factors such as wire coil diameter, pitch, and tube material properties play important roles in determining the overall heat transfer properties. The numerical study focuses on the performance of a tube in which wire coils of different cross-section are inserted and compares the characteristics of the flow structure, heat transfer and friction factor. The distribution of wire coils inside the tube depends on the results of the experimental side of the current study. Five different shapes for the cross-section of the coil wire were proposed in addition to the circular cross-section of the conventional coil wire that was used in the practical aspect because it is available locally. The proposed cross section shapes included: Hexagonal cross section (HCS), Star cross section (StCS), Rectangle cross section (RCS), Square cross section (SqCS), and Triangle cross section (TCS). The cross-sectional area of all proposed shapes is 3.14 mm^{2}. The sketch of different cross section of wire coil is shown in

The following are the stable mathematic equations for continuity, momentum, and energy:

The conventional k−ω turbulence model is used in the numerical simulation. The two equations in question are the turbulent kinetic energy (k) and dissipation rate (ω) equations.

The variables ρ, t,

Fluent 2019 R3, a commercial 3D double-precision CFD program, solves the whole simulation task. As shown in ^{−}^{6}, the convergence criterion stipulates that the normalized residuals for mathematical equations must be less than 1 × 10^{−}^{4}.

^{2} in order to validate the numerical procedure described above. It is evident that the CFD results are in excellent accord, as the Nusselt number deviate by less than 8% and 7%.

The results of the current study will provide useful information’s that helps in thermal designing, selecting the best cross section shape for wire coil and the wire coil distribution mechanism within the flow path. ^{2} and a Reynolds numbers range of (3000–5000), it can be observed that the value of the Nusselt number when compared with a plain tube increases by 67% when inserting the FWD and the percentage reaches to 73% and 82% when inserting (SWD and TWD), respectively.

From the experimental results, it can be concluded that distributing the wire coils according to the arrangement (TWD) gave the best PEC. Therefore, the arrangement (TWD) was adopted to start the numerical study.

Distributed wire coils within tubes serve to increase turbulence and improve hydrothermal performance in many applications. I will provide a scientific explanation of the effect of wire coil cross-sectional shapes (circular, rectangular, hexagonal, square, star shape, and triangle) on hydrothermal performance. In general, the cross-sectional shape of the coiled wire can be designed to direct and distribute fluid flow in specific ways within the pipe. This can result in better channeling of thermal currents and better distribution of heat through the tube. Therefore, the heat transfer efficiency can be improved and distributed more effectively. The Nu, Nu/Nup, f, f/fp and PEC of seven different cases are shown in ^{2}, shown the contours of temperature, turbulence kinetic energy, flow velocity, and velocity vector.

For every wire coil suggested in this research,

From

It can be seen from

From the figures, it can be seen that the wire coil with circular cross-section causes uniform distribution of flow velocity, which reduces flow resistance and pressure loss. Thanks to the homogeneous and smooth flow across the surfaces of the wire coil, the heat exchange efficiency increases. A wire coil with a rectangular cross-section can affect how heat is distributed, causing heat to concentrate in certain places and disperse in others. On the other hand, this cross-section shape enhances heat transfer by increasing the surface area of the wire.

Due to the multifacetedness of the wire coil with a hexagonal cross-section, the flow resistance increases and the fluid velocity distribution inside the pipe changes. Which causes the thermal and hydraulic performance inside the pipe to be clearly affected. Heat exchange is improved when the wire coil has a square cross-section. The edges and spatial overlaps of the wire coils improve heat exchange due to smooth flow and uniform velocity distribution which reduces pressure loss.

Thermal and hydraulic performance is affected when wire coils with a triangular cross section are inserted into the tube. It can be notice that the heat exchange between the liquid, the wire coil, and the tube walls is affected due to the change in the flow path of the liquid as a result of the sharp angles possessed by the wire coil with a triangular cross section. It is obvious that a clear improvement in heat transfer when using wire coils with a star-shaped cross-section. The star shape increases the active surface area available for heat exchange, allowing for higher heat exchange efficiency. On the other hand, due to the complex geometry of the shape and having multiple surfaces and edges, the flow resistance and interference increase, resulting in increased pressure loss and uneven velocity distribution.

It is important to consider the balance between enhanced heat transfer and associated pressure reduction when designing. The cross-sectional shape of the coiled wire can be designed to direct and distribute the fluid flow in specific ways within the pipe. This can result in better channeling of thermal currents and better distribution of heat through the tube. Therefore, the heat transfer efficiency can be improved and distributed more effectively.

The average PEC enhancement ratio compared with a plain tube without wire coil reached about 9.1% for a TWD, 5.5% for an SWD, and 4.6% for an FWD. The wire coils, according to the arrangement (TWD), gave the best PEC.

The addition of a wire coil enhances the values of Nu and increases f compared to a plain tube. 62%, 72%, 66%, 64%, 79%, and 57%, respectively, is the average increase ratio for Nu in wire coils featuring circular, rectangular, hexa, square, star, and triangle cross sections. The wire coils featuring circular, rectangular, hexa, square, star, and triangle cross sections exhibit average increase ratios for f of 352%, 473%, 372%, 405%, 431%, and 316%, respectively.

The enhancement of heat transfer capability of various cross-sections is as follows: StCS > RCS > HCS > SqCS > CCS > TCS.

The pump consumption of various cross-sections is as follows: RCS > StCS > SqCS > HCS > CCS > TCS.

Reynolds number

Nusselt number

Nusselt number for plain tube

Mass flow rate (kg/s)

Tube diameter (m)

_{i}

Internal tube diameter (m)

Velocity of the fluid (m/s)

Heat transfer coefficient (W/m^{2}.K)

Friction factor

Friction factor for plain tube

Specific heat (kJ/kg.K)

Electric voltage (V)

Electric current (A)

Water inlet temperatures (K)

Water exit temperatures (K)

Inner wall temperature at a distance z (K)

Water temperature at a distance z (K)

Dynamic viscosity (Pa.s)

Thermal conductivity (W/m.K)

First wire coil distribution

Second wire coil distribution

Third wire coil distribution

Polyvinyl chloride

Performance evaluation criterion

Author would like to thank Mustansiriyah University (

The author received no specific funding for this study.

The author A. S. G confirms contribution to the paper as follows: study conception, design, data collection, analysis, interpretation of results and draft manuscript.

The data are available when requested.

The author declares that they have no conflicts of interest to report regarding the present study.