Analyzing The Influence of Diameter and Winding on Heat Transfer Efficiency in Spiral Tube Heat Exchangers: A CAD-Integrated CFD Study Using Solidworks Flow Simulation

Spiral tube heat exchangers (STHE) are coiled metal devices with two fluid channels around a central core, enabling counterflow or parallel flow of gases, liquids, or both. Compared to traditional straight-tube heat exchangers, STHEs offer a larger heat transfer surface area. This study used Computational Fluid Dynamics (CFD) simulation integrated with Computer Aided Design (CAD) to investigate STHE’s heat transfer performance. The STHE dimensions, a 12-mm copper tube, and a 10-inch PVC shell were adopted from a previous study. Cold and hot water at 20°C and 70°C flowed in parallel at specific flow rates. The objective was to explore the impact of STHE dimensions on heat transfer efficiency and performance. The parameters varied were the internal diameter of the copper tube and the number of spiral coil windings. Results revealed that changing the spiral heat exchanger’s diameter affected the heat transfer rate and coefficient. Larger diameters reduced efficiency due to lower flow velocities and convective heat transfer coefficients. The number of windings significantly affected heat transfer performance, with winding 5 demonstrating the highest rate and winding 7 showing the highest coefficient. CFD analysis reliability was validated by convergence with analytical solutions for heat transfer simulations with varying diameters and windings.


Introduction
A heat exchanger is a device designed to facilitate the efficient transfer of thermal energy between two or more fluids that are at different temperatures, ensuring they do not come into direct contact with each other.These devices are essential in various industrial processes and everyday applications like air conditioning, refrigeration, power generation, and chemical processing, where heat exchange is critical.The efficiency and performance of heat exchangers depend on various factors, including their design parameters and operating conditions.A significant body of research has been conducted to investigate the design and performance of different types of heat exchangers.The STHE is a specialized type of heat exchanger, known for its unique coiled design, where two long metal strips or plates are tightly wound in a concentric pattern, creating multiple channels for the flow of the two fluids.It typically employs a counterflow arrangement, allowing the fluids to move in opposite directions within the spiral channels, maximizing the temperature difference and thus enhancing heat transfer efficiency along the flow path.Due to its coiled configuration, the spiral heat exchanger has a significantly smaller footprint compared to traditional shell-and-tube heat exchangers with similar heat transfer capabilities, making it particularly suitable for applications with limited space constraints.Moreover, the turbulent flow pattern generated by the coiled channels increases the heat transfer coefficient, further improving its thermal performance.One of the notable advantages of the spiral heat exchanger is its reduced fouling tendency.The continuous flow path and absence of stagnant areas minimize the accumulation of unwanted deposits on the heat exchanger surfaces, which can reduce efficiency over time.This feature makes the spiral heat exchanger ideal for applications involving viscous fluids, sludges, or fluids prone to fouling.In the context of STHE, several studies have focused on understanding their thermal and hydraulic characteristics.Vivekanandan et al. analyzed the performance of a spiral coil heat exchanger by concentrically positioning a 12mm copper coil inside a 10-inch PVC shell, using hot and cold water as the fluid medium [1].Anish et al. studied a compact spiral coil thermal storage unit to analyze the heat transfer process during the phase change of xylitol, considering factors such as inlet temperature and flow rate of the heat transfer fluid [2].Abdelmagiad compared the thermal and hydrodynamic characteristics of a triple spirally coiled tube heat exchanger (TSCTHE) with a double spirally coiled tube heat exchanger (DSCTHE) [3].Other studies have explored the impact of various parameters on heat transfer performance.Ravikumar et al. investigated the use of fin and tube heat exchangers made of copper and aluminum, aiming to enhance heat transfer rates through modifications in tube and fin designs [4].Lu et al. studied the effects of changes in geometrical elements, such as tube pitch, space bar thickness, and tube diameter [5][6][7][8][9], on flow and heat transfer performance in multi-stream spiralwound heat exchangers [5].Additionally, CFD simulations have been employed [10][11][12] to analyze the heat transfer characteristics of helical coils and investigate the relationship between coil parameters and Nusselt number [6].While these studies have contributed valuable insights into the design and performance of STHEs, there are still research gaps that need to be addressed.There is a need for a comprehensive understanding of the optimal configuration and operating conditions to maximize heat transfer efficiency.Furthermore, the application of computational fluid dynamics (CFD) analysis in studying STHE remains limited.The efficiency and performance of heat exchangers are critical factors in various industrial processes and applications.Among heat exchangers, the STHE stands out for its unique coiled design, offering advantages such as high heat transfer efficiency, compact size, and reduced fouling tendency.However, there is a need for a comprehensive understanding of the influence of varying the diameter and winding of the STHE on heat transfer efficiency.The objective of this study is to address this research gap and analyze the performance of STHE by conducting thermal simulations using SolidWorks Flow Simulation.The CFD results will be compared with analytical solutions for heat transfer rate and overall heat transfer coefficient.Additionally, convergence validation between the CFD analysis and the analytical approach will be performed to assess the accuracy and reliability of the CFD simulations.Furthermore, the study aims to investigate the influence of varying the diameter and winding of the STHE on heat transfer efficiency.By analyzing different configurations, the research aims to identify the best options for diameter and winding that maximize heat transfer efficiency.Through validation, convergence validation, and parameter analysis, this research aims to provide valuable insights into the accuracy and validity of CFD simulations for heat transfer in STHE.

Aided Design Computational Fluid Dynamics Simulation
Computer Aided Design (CAD) Computational Fluid Dynamics (CFD) simulation is a powerful tool that combines CAD software with CFD analysis capabilities.It allows engineers and designers to virtually model and analyse fluid flow and heat transfer phenomena in complex geometries without the need for physical prototypes or experiments.In this paper, involves utilizing SolidWorks Flow Simulation, a CAD-based Computational Fluid Dynamics (CFD) software, to perform simulations on a STHE.The dimensions of the STHE used in the study are adopted from M. Vivekanandan et al. [1], wherein a 12-mm copper tube is employed for hot fluid flow, and a 10-inch PVC shell is used for the cold fluid.The STHE operates in a parallel flow system with cold and hot water entering and exiting at 20°C and 70°C, respectively, with flowrates of 0.12 kg/s and 0.03 kg/s.The primary objective of this study is to investigate the influence of variations in STHE dimensions on heat transfer efficiency and overall performance.Specifically, the internal diameter of the copper tube is adjusted among 12mm, 12.5mm, and 13mm to determine the surface area that facilitates the most effective heat transfer.Additionally, the number of spiral coil windings inside the STHE is varied to 3, 5, and 7 as an additional parameter during the analysis.In Figure 1, the STHE configuration exhibits a concentric pattern of spiral windings within the shell, enabling efficient heat exchange between the hot and cold fluids.

Governing Equation in Spiral Tube Heat Exchanger
The heat exchange rate (Q) and heat transfer coefficient (UA) of the STHE were determined based on the collected data.The optimal variations in each specification of the STHE will be justified through a combination of mathematical modeling and numerical investigation.Notably, N. Ghorbani et al.'s methods for solving numerical heat transfer problems using simple formulas have demonstrated excellent performance in achieving experimental data [13][14][15].The heat exchange performance of the STHE can be evaluated using the heat exchange rate (Q), as depicted in Eq. ( 1): As defined, Q represents the heat exchange rate of the STHE, where cp denotes the specific heat of water flowing within both the PVC and copper tubes of the STHE, with a constant value of 4182 J/kg℃.The variable m signifies the mass flow rate of water, while ΔT represents the temperature difference between the hot and cold fluid sections of the STHE, as defined in Eq. ( 2) and Eq. ( 3): or It is crucial to thoroughly consider the uncertainties associated with the experimental calculations of the results, as is customary in any report of experimental research [15].On the other hand, the equation for the heat transfer coefficient (UA) can be written as shown in Eq. ( 4): Where, ̇ is the mass flowrate of fluid, cp is the specific heat capacity of the fluid, ΔT is the temperature difference between the two fluids and LMTD is the logarithmic mean temperature difference.

Computer Aided Design Computational Fluid Dynamics Simulation Convergence Validation with Analytical Solution
The convergence validation between CAD CFD simulation and the mathematical approach aims to ensure consistent and accurate solutions.The process involves formulating governing equations and obtaining analytical solutions, which are then used as validation data.Percentage differences are defined to quantify the agreement between CFD results and analytical solutions.Lower values of these metrics indicate a stronger agreement between the two sets of data, signifying higher accuracy and reliability of the simulation approach.The percentage difference is given by:

Effect of diameter on STHE
Surface area of a heat exchanger has a direct impact on the overall heat transfer rate [16], with a larger surface area allowing for more efficient heat exchange between hot and cold fluids via increased contact area and convective heat transfer opportunities, resulting in increased overall heat transfer efficiency.In this experiment, the mass flow rate was deliberately set to a constant value of 0.03 kg/s to study the impact of changing the diameter of the spiral heat exchanger on the overall heat transfer performance.Three primary geometric parameters of internal tube diameters were modeled.The aim was to identify the optimal technical variables.Internal tube diameters of 12mm, 12.5mm, and 13mm were selected to explore the options that offer the highest heat transfer rate and heat transfer performance while keeping the external domain parameters constant for each unit.The experimental data presented in this study, including three data points at diameters of 12 mm, 12.5 mm, and 13 mm, reveals a potential inverse relationship between diameter and heat transfer rate, with a decrease of approximately 4.1% in heat transfer rate from 2072.91 W at 12 mm to 1986.86 W at 13 mm.Additionally, the heat transfer coefficient exhibits a slight reduction of approximately 4.4% from 56.81 W/m²°C at 12 mm to 54.33 W/m²°C at 13 mm, suggesting that larger diameters may lead to a slight reduction in heat transfer efficiency [17], potentially attributed to changes in surface area and fluid flow characteristics.With the increase in diameter and the subsequent expansion of the flow path, the fluid flow experienced a decrease in flow velocity.The decrease in flow velocity was expected due to the fluid becoming more distributed and less confined in the larger diameter heat exchanger.Despite the flow remaining in the turbulent flow regime, the decrease in flow velocity may affect the convective heat transfer coefficients within the heat exchanger.Lower flow velocities can lead to reduced heat transfer coefficients, impacting the overall heat transfer efficiency.Table 1 indicates the flow velocity on different diameters of spiral heat exchanger.Although the increased surface area allowed for more contact opportunities between the hot and cold fluids, the reduction in convective heat transfer coefficients due to the lower flow velocity offset some of these advantages.As a result, the overall heat transfer efficiency decreased, as evidenced by the observed decline in the heat transfer coefficient and heat transfer rate in Figure 2.This finding clearly agrees with the findings of Xing Lu et al., who explain that the proportional relationship between heat transfer rate and heat transfer coefficient leads to a logical drop in the overall heat transfer coefficient (UA) as the tube diameter increases.Figure 2 illustrates the relationship between the diameter and the heat transfer rate (Q) as well as the heat transfer coefficient (UA).

Figure 2.
The effect of diameter against the heat transfer rate, Q and heat transfer coefficient, UA

Effect of windings on STHE
The data presented in Figure 3 reveals the heat transfer rates and heat transfer coefficients for spiral heat exchangers with different numbers of windings.Winding 5 demonstrated the highest heat transfer rate of 2073.91 W, indicating efficient heat dissipation and a higher capacity to transfer heat from the hot fluid to the cold fluid.On the other hand, winding 7 displayed the highest heat transfer coefficient of 58.4 W/m²°C, suggesting that it was the most efficient in transferring heat per unit of surface area.The results suggest that the number of windings plays a significant role in the heat transfer performance of the spiral heat exchanger.The superior performance of winding 5 in terms of heat transfer rate can be attributed to its larger surface area available for heat transfer, which allows for more extensive contact between the hot and cold fluids, leading to enhanced heat exchange.Additionally, the increased number of windings in winding 5 might have facilitated enhanced turbulent flow within the heat exchanger, promoting better mixing and further improving the heat transfer efficiency.On the other hand, winding 7, with more windings, had a larger surface area and theoretically more opportunities for efficient heat exchange [18].However, the comparison suggests that the additional windings may have introduced complexities in the flow path, possibly resulting in non-uniform flow distribution and impacting the overall heat transfer performance when compared to winding 5.The data presented imply that, despite having a high heat transfer coefficient, winding 7 might not dissipate heat as quickly as winding 5, within the specific experimental setup or cooling conditions provided in the data.

Simulation Convergence Validation
The table compares the results of Computational Fluid Dynamics (CFD) analysis and an Analytical Solution for a heat transfer system with different numbers of windings.The key parameters studied are the heat transfer rate (Q) and the overall heat transfer coefficient (UA).For the case with 3 windings, both CFD analysis and the Analytical Solution provide very close results for Q and UA, with negligible differences of 0.00% and 0.04% respectively.This indicates strong agreement between the two methods, suggesting accurate predictions for the heat transfer system with 3 windings.In the case with 5 windings, there are slightly larger differences between CFD analysis and the Analytical Solution.The percentage difference in Q is 0.18%, indicating reasonably consistent predictions.However, the percentage difference in UA is 6.73%, which suggests some discrepancies in predicting the overall heat transfer coefficient for this specific configuration with 5 windings.These differences could be attributed to the complexity of the system and the challenges in accurately capturing the fluid flow and heat transfer phenomena.For the case with 7 windings, CFD analysis and the Analytical Solution yield nearly identical results for both Q and UA, with differences of 0.00%.This implies good agreement between the two methods, indicating accurate predictions for the heat transfer system with 7 windings.The data presented in the table indeed shows that the heat transfer rates (Q) and overall heat transfer coefficients (UA) obtained from the CFD analysis and the analytical solution are very close for all three diameters.The small percentage differences (ranging from 0.00% to 6.73%) indicate a high level of agreement between the two methods.This level of agreement is essential because it demonstrates that the CFD analysis is providing reliable and accurate results for heat transfer in the given system with varying diameters.When the CFD results closely align with the simpler analytical approach, it adds confidence to the validity of the CFD model and its ability to capture the heat transfer behaviour.The data form Table 2 and 3, suggests that the accuracy of the CFD analysis is generally high, as indicated by the close agreement with the analytical solution for heat transfer rates and overall heat transfer coefficients.This confirms the reliability of CFD as a valuable tool for heat transfer analysis and engineering design, particularly for systems with simpler configurations.

Conclusions
In conclusion, this study utilized Computer Aided Design (CAD) Computational Fluid Dynamics (CFD) simulation to investigate the heat transfer performance of a STHE.The dimensions of the STHE were based on a previous study, with specific variations in the internal diameter of the copper tube and the number of spiral coil windings as parameters.The results indicated that changes in the diameter of the spiral heat exchanger had a notable impact on heat transfer efficiency.Larger diameters led to a decrease in heat transfer rate and coefficient due to reduced convective heat transfer coefficients resulting from lower flow velocities.Additionally, the number of windings significantly affected heat transfer performance, with winding 5 demonstrating the highest heat transfer rate and winding 7 showing the highest heat transfer coefficient.The convergence validation between CFD and analytical solutions exhibited a high level of agreement for all cases, confirming the reliability of the CFD analysis for heat transfer simulations with varying diameters and windings.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Figure 1 .
Figure 1.I Design of STHE

Figure 3 .
Figure 3.The amount of flat spiral winding (stroke) against the heat transfer rate, Q and heat transfer coefficient, UA

6 .
Credit authorship contribution statement Z.Michael: Conceptualization, Methodology, Writing -Review & Editing, Supervision.M.F.A.Hamid: Data collection, Data analysis, Writing -Original draft preparation, Visualization.M.Khairulmaini: Writing -Review & Editing, Assistance in completing the report.N.A.Z.Abidin: Writing -Review & Editing, Assistance in completing the report, A.Roslan: Writing -Review & Editing, Assistance in completing the report.

Table 1 .
Flow Characteristics at Different Diameters.

Table 2 .
Percent accuracy between CFD analysis and analytical solution at different number of stroke

Table 3 .
Percent accuracy between CFD analysis and analytical solution at different diameter