Numerical Investigation of Flow and Heat Transfer in a Serpentine-Oval-Cell Composite Heat Transfer Tube

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Inspired by the surface-guiding characteristics of snake skin and the fluid-directing features of oval cells, a novel composite heat exchange tube integrating a snake-like wavy inner rib and an elliptical T-cell structure was developed. Numerical simulations were conducted to investigate the effects of different rib arrangements, rib numbers, and spacings on the heat transfer characteristics of the tube over a Reynolds number range of 8,000–18,000. The results indicate that variations in rib configuration, number, and spacing have a significant impact on heat transfer performance. Under the condition of Re = 8,000, the optimal configuration achieved a maximum overall heat transfer performance (PEC) of 1.21, with the average Nusselt number (Nu) enhanced by 89% compared to a smooth tube. Moreover, at the same Reynolds number, the wavy inner rib T-cell tube exhibited lower pressure loss than other types of composite heat exchange tubes while maintaining comparable PEC, and demonstrated better flow resistance characteristics than both single rib and T-cell tubes. These findings confirm that the proposed structure effectively reduces energy loss while sustaining efficient heat transfer. Finally, field synergy analysis revealed the intrinsic mechanism by which the composite structure enhances heat transfer through improved coordination between the velocity and temperature fields. This study provides a theoretical foundation for the design and optimization of advanced composite internally ribbed heat exchanger structures. Wavy inner ribs Elliptical cells Composite structure Enhanced heat transfer Structural optimization Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 1. Introduction With the growing challenges of energy shortages and increasing environmental protection requirements, the application of enhanced heat exchanger tube technologies has become increasingly important[1]. In recent years, improving heat transfer efficiency while reducing pressure loss has been a key focus in processes such as hot-water dewaxing of oil and gas pipelines and thermal exchange in industrial equipment.Xie Shuai et al. [2] numerically investigated the flow and heat transfer performance of teardrop-shaped grooved enhanced tubes, finding that the streamlined grooves not only improved heat transfer efficiency but also effectively reduced pressure drop by suppressing flow separation. Wang Yu and He Yaling et al. [3] proposed and experimentally validated a novel elliptical grooved tube, demonstrating that it significantly enhanced heat transfer with only a slight increase in pressure drop, highlighting the influence of surface cavities on flow adhesion behavior. Ding Liang and Tang Songzhen et al. [4] numerically analyzed a Variable Direction Twisted Oval Tube (VDTOT) and found that periodically changing the twisting direction effectively improved overall heat transfer performance by promoting fluid disturbance. Hu Qixuan and Fan Zhonglei et al. [5] conducted a systematic numerical optimization of the sinusoidal channel in a Printed Circuit Heat Exchanger (PCHE), confirming that wavy channel structures can further reduce pressure loss. In the study of composite and multi-structure heat exchangers, Songzhen Tang et al. [6] and Zhen Tian et al. [7] performed numerical simulations on double-pipe heat exchangers with elliptical inner tubes having alternating torsion directions and phase angles, achieving improved thermal performance through coordinated flow disturbance. Tao Wang et al. [8] numerically studied the thermohydraulic characteristics of a combined structure featuring triple helical twisted tubes and elliptical pits, demonstrating that multi-angle perturbations can significantly enhance heat transfer. Similarly, Gong Quanyu et al. [9] and Song Kewei et al. [10] showed that multi-structural configurations and periodic flow disturbances can further improve comprehensive heat exchange performance. Previous studies have often faced the challenge of simultaneously enhancing heat transfer and minimizing pressure drop, as increasing heat transfer through intensified fluid disturbance typically leads to a substantial rise in flow resistance. To overcome this limitation, the present study proposes a novel heat exchange tube featuring a serpentine wavy inner-ribbed cellular composite structure. By integrating the flow-disturbing effect of the serpentine wavy ribs with the flow-guiding capability of the cellular cavities, this design achieves enhanced heat transfer performance while effectively reducing pressure loss. 2. Numerical simulation 2.1. Physical Model This study investigates a composite heat exchange tube structure that integrates elliptical cells with serpentine corrugated ribs, as illustrated in Fig. 1 . The tube has an inner diameter (D) of 20 mm, and the total length (L) of the computational domain is 800 mm. The domain consists of three sections: an inlet section, a test section, and an outlet section, with respective lengths of 200 mm, 500 mm, and 100 mm. This configuration ensures that the fluid flow entering the test section is fully developed and prevents the outlet boundary from influencing the flow field within the test region. To investigate the effects of the serpentine wavy internal rib cells and their geometric parameters on the flow and heat transfer characteristics of the composite enhanced tube, the parameters of the elliptical rib cells were kept constant, with a major axis (a) of 7.2 mm, a minor axis (b) of 3.6 mm, and a depth (h) of 3.6 mm. The variables considered include the rib depth (H), the radii of the semicircular crests (Rₚ) and troughs (R v ), the crest-to-trough radius ratio (Rₐ = Rₚ / R v ), the rib spacing (P), and the number of circumferential rib cells (N). The specific parameter values are listed in Table 1 . Since the numerical simulations focus on the internal flow and heat transfer characteristics of the composite tube, the influence of the tube wall thickness was neglected. Table 1 Geometric parameters of wave rib composite tube Parameter Size/mm Overall length of the pipe L 800 Length of the inlet area Lin 200 Length of the exit area Lout 100 Test area length Ltest 500 Rib depth H 0.9、1、1.1 The ratio of crest radius to trough radius Ra 1、1.25、1.5 Number of D cells N 4、5、6 2.2. Selection of Turbulence Model To further minimize errors and improve the accuracy of the numerical simulations, different turbulence models were employed to validate and compare the results for smooth tubes under identical geometric and operating conditions. The turbulence models evaluated are presented in Fig. 2 . As shown in the figure, for the Nusselt number (Nu), the deviation ranges were 15.1%–19.3% for the SST k–ω model, 26.12%–29.43% for the RNG k–ε model, 6.34%–11.3% for the Standard k–ε model, and 4.73%–9.1% for the Realizable k–ε model. In terms of the friction factor (f), the corresponding deviation ranges were 5.6%–9.3% for the SST k–ω model, 2.12%–3.1% for the RNG k–ε model, 2.34%–3.3% for the Standard k–ε model, and 1.73%–3.1% for the Realizable k–ε model. Among the models considered, the Realizable k–ε model exhibited the best overall agreement with empirical correlations, providing higher accuracy in predicting both heat transfer and flow resistance. Therefore, the Realizable k–ε model was selected for subsequent analyses of the flow and heat transfer characteristics under different structural parameters[11–13]. 2.3. Mesh division and grid independence test The mesh generation was carried out using Fluent Meshing, with enhanced wall functions applied in the near-wall region. A total of 12 boundary layers were generated with a growth rate of 1.2 to accurately resolve the velocity and temperature gradients near the wall. Additionally, local mesh refinement was applied to the rib and cell regions to ensure computational accuracy and capture the complex flow behavior. A schematic of the computational mesh is presented in Fig. 3 . Mesh independence was verified using a model with geometric parameters of H = 1.1 mm, Rₐ = 1.5, N = 6, and P = 20 mm under a Reynolds number (Re) of 8000. Five computational models with different mesh densities were tested, and the results are summarized in the corresponding table. When the total mesh count reached 2,037,341, the relative deviations of the Nusselt number (Nu) and friction factor ( f ) were 0.56% and 0.65%, respectively, indicating that the results had stabilized. Considering both computational cost and numerical accuracy, the third mesh configuration was selected for subsequent simulations. 2.4. Simulation method verification In order to ensure the accuracy of numerical simulation, the smooth tube was simulated and compared with the empirical formula[14–15], and the results are shown in Fig. 5 . As shown in the figure, the simulated Nusselt number (Nu) deviates from the Dittus–Boelter correlation by 8.09%, while the simulated friction factor ( f ) deviates from the Filonenko correlation by 5.41%. The close agreement between the theoretical and simulated results indicates that the numerical simulation method is reliable, with deviations remaining within an acceptable range[16]. 3. Analysis of flow and heat transfer characteristics 3.1 Effects of different arrangement methods on heat transfer and flow characteristics inside the tube Figure 6 presents the velocity gradient and temperature contour maps of heat exchanger tubes with different internal structures. From left to right, the configurations correspond to a ring-shaped inner rib tube, a corrugated inner rib tube, and a serpentine corrugated inner rib T-cell tube. The high-velocity region within the tube is primarily concentrated in the core flow area, where a boundary layer is formed near the wall. As observed from left to right, the size of the high-velocity region first decreases and then increases. This behavior indicates that the serpentine corrugated inner rib induces large-scale flow separation, resulting in a reduction of the central high-velocity zone. Meanwhile, the stable T-cell vortices generated by the elliptical T-cell structure not only disturb the flow but also segment and reorganize the large-scale separation region downstream of the corrugated ribs, thereby guiding and restoring the core flow and enlarging the high-velocity region again.This phenomenon demonstrates that a pronounced synergistic effect exists between the serpentine corrugated inner rib and the elliptical T-cell structure, rather than a simple additive effect of flow disturbances. As shown in the temperature contour maps, the near-wall high-temperature region of the serpentine corrugated inner rib T-cell tube is the smallest, exhibiting the highest degree of temperature field fragmentation and the largest overall temperature gradient, which together indicate a stronger heat transfer driving potential. Consequently, under the synergistic action of the serpentine corrugated inner rib and the elliptical T-cell structure, the overall heat transfer performance (PEC) is significantly enhanced. Figure 7 illustrates the variations in the average Nusselt number (Nu) and the average friction factor ( f ) for heat exchange tubes with different structural configurations. As shown, Nu increases with increasing Reynolds number (Re). This occurs because higher Re values correspond to greater fluid velocity and turbulence intensity, which in turn reduce the thickness of the thermal boundary layer and enhance radial mixing. Both effects lead to intensified convective heat transfer, thereby increasing Nu.Specifically, the Nu of the serpentine corrugated inner ribbed T-cell tube is 89.9% higher than that of the smooth tube, and 39.6% and 4.2% higher than those of the annular inner ribbed tube and the wavy inner ribbed tube, respectively. In contrast, the average friction factor ( f ) exhibits a gradual decreasing trend as Re increases, since the inertial effects dominate over viscous forces at higher flow velocities. Notably, the f value of the serpentine corrugated inner ribbed T-cell tube is 81.8% higher than that of the annular inner ribbed tube, yet lower than that of the wavy inner ribbed tube.This finding indicates that the synergistic interaction between the serpentine corrugated ribs and the elliptical T-cell structure improves the internal pressure distribution and effectively mitigates flow resistance, enabling the tube to maintain enhanced heat transfer performance with a relatively lower pressure drop. As shown in Fig. 8 , within the Reynolds number (Re) range of 8000–18000, the performance evaluation criterion (PEC) of the annular inner-ribbed tube ranges from 0.94 to 1.05, that of the serpentine corrugated inner-ribbed tube ranges from 0.97 to 1.16, and that of the serpentine corrugated inner-ribbed T-cell tube reaches 1.02–1.22. Under identical Re conditions, the overall heat transfer performance of the serpentine corrugated inner-ribbed T-cell tube is markedly superior to that of the other heat exchanger tube configurations.The results presented in Figs. 5 and 6 further verify that the synergistic interaction between the corrugated inner ribs and the elliptical T-cell structures not only enhances both the Nusselt number (Nu) and the friction factor ( f ), but also significantly improves the comprehensive heat transfer performance of the tube. 3.2 Effect of different cell numbers on heat transfer and flow characteristics inside the tube Figure 9 presents the velocity and temperature distribution contours of the serpentine wave-shaped internally ribbed T-cell tube at the cross-section of x = 200 mm for different numbers of T-cells. As shown in the velocity contour maps, the high-velocity region at the tube center expands with an increasing number of T-cells. However, for the configuration with N = 5 T-cells, the flow field exhibits noticeable asymmetry along the longitudinal direction due to the complex geometric interaction of the T-cell structures.By examining both the cross-sectional and longitudinal temperature contours, it can be observed that the flow disturbance intensity within the tube reaches its maximum when N = 4. Furthermore, the temperature distribution contour reveals that the overall temperature gradient is also the largest at N = 4, indicating a stronger convective heat transfer capability under this configuration. Figure 10 illustrates the variations of the average Nusselt number (Nu) and average friction coefficient ( f ) for heat exchanger tubes with different numbers of T-cells. In serpentine corrugated inner-ribbed tubes with varying cell numbers, Nu generally increases with increasing Reynolds number (Re), while f exhibits a gradual decreasing trend. However, a “jump” phenomenon in f is occasionally observed. This can be attributed to the increased flow disorder induced by the T-cell structures, which alters the local pressure distribution and reduces the overall pressure drop at higher flow velocities. Compared with the annular and corrugated inner-ribbed tubes, the serpentine corrugated inner-ribbed tubes exhibit higher heat transfer performance, with Nu values increasing by approximately 4.1%–4.5% relative to the corrugated inner-ribbed tubes. Moreover, when N = 5 and 6, the friction coefficient decreases by 2.8%–3.4% compared with the corrugated inner-ribbed configuration, indicating that an appropriate number of T-cells can improve heat transfer efficiency while mitigating pressure losses. Figure 11 illustrates the influence of different numbers of T-cells on the heat transfer performance of the pseudo-serpentine corrugated inner-ribbed tube. As shown in Fig. 10 , the PEC decreases gradually with increasing Reynolds number, reaching its maximum value of 1.21 when N = 5. This indicates that selecting an appropriate number of T-cells is crucial for optimizing the overall heat transfer performance.Compared with the annular inner-ribbed tube, the average PEC of the pseudo-serpentine corrugated inner-ribbed tube increases by approximately 9.6%–15%. Relative to the corrugated inner-ribbed tube, the improvement ranges from 2.36% to 6.2%. As the number of T-cells increases from N = 4 to N = 5, the total heat transfer area expands, the convective heat transfer capacity is enhanced, and the synergistic effect between the serpentine corrugated ribs and the elliptical T-cell structures reaches its optimal state. This improves flow uniformity, reduces pressure losses, and results in the maximum PEC value.However, further increasing the number of T-cells (from N = 5 to N = 6) leads to a more complex flow path, higher turbulence intensity, and increased wall contact frequency. Although this enhances fluid mixing, it simultaneously raises flow resistance and pressure loss, thereby offsetting the benefits of heat transfer enhancement. Therefore, the number of T-cells should be optimized rather than maximized, as excessive structural complexity can deteriorate overall heat transfer performance. 3.3. Effect of the number of T cells on the heat exchange and flow characteristics in the tube Figure 12 presents the velocity distribution and turbulent kinetic energy (TKE) contours at the cross-section (x = 200 mm) of the serpentine wave-shaped internally ribbed tube under different rib spacings (P). As shown in the figure, with increasing rib spacing, the velocity magnitude in the central high-speed region decreases, and the velocity gradient between the core and near-wall regions becomes less pronounced.When P = 20 mm, the central flow velocity is high, and a distinct low-velocity region forms near the wall, accompanied by a significant velocity gradient. This indicates strong flow disturbance, generating evident secondary flow and vortex structures that enhance momentum and energy exchange between the core and near-wall regions. Simultaneously, the turbulent kinetic energy near the wall increases markedly, demonstrating intensified local flow activity and enhanced fluid mixing capability.As the rib spacing increases to P = 40 mm, the central velocity decreases and becomes more evenly distributed, while the velocity gradient diminishes slightly. This suggests that flow disturbance weakens and TKE near the wall decreases, leading to reduced radial mixing intensity. When the rib spacing is further enlarged to P = 60 mm, the velocity distribution in the core region becomes nearly uniform, the velocity gradient variation is minimal, and the flow disturbance is significantly weakened. Consequently, the TKE near the wall drops further, and the radial mixing ability of the fluid deteriorates sharply, resulting in the poorest overall convective performance. Figure 13 illustrates the variation trends of the average Nusselt number (Nu) and friction coefficient ( f ) under different rib spacings (P). As shown in the figure, Nu increases consistently with increasing Reynolds number (Re). At a constant Re, the heat transfer coefficient for P = 20 mm is higher than that for other rib spacings, indicating the strongest convective heat transfer intensity and the most effective thermal enhancement.The variation in the friction coefficient ( f ) reveals that at P = 20 mm, f is greater than that at P = 40 mm and P = 60 mm, but lower than that of the conventional corrugated inner-finned tube. This demonstrates that the synergistic interaction between the serpentine corrugated inner ribs and the elliptical cell structure effectively enhances flow uniformity and suppresses excessive flow separation, thereby achieving a favorable balance between heat transfer enhancement and drag reduction. Figure 14 presents the variation of the performance evaluation criterion (PEC) for heat exchange tubes with different rib spacings (P). As shown in the figure, the PEC of all ribbed tubes decreases with increasing Reynolds number (Re), but remains higher than that of the smooth tube across the entire Re range. This confirms that the rib structures play an important role in enhancing the overall heat transfer capability. Notably, the serpentine corrugated inner-ribbed tube with P = 20 mm exhibits a significantly higher PEC compared with the conventional corrugated inner-ribbed tube, indicating that the composite configuration of the serpentine corrugated ribs and elliptical fins effectively strengthens the overall heat transfer performance. The pronounced synergistic interaction between the serpentine corrugated ribs and the elliptical fin cells enables an optimal balance between heat transfer enhancement and flow resistance, thereby improving thermal–hydraulic performance comprehensively. 3.4 field collaborative analysis To elucidate the mechanism by which the wavy, internally ribbed composite tube enhances heat transfer, the field synergy theory (FST) is introduced to analyze the interaction between the velocity and temperature fields in different structures. The field synergy angle (FSA) is employed to quantitatively evaluate the degree of coordination between these two fields. It is defined as the angle between the velocity vector and the temperature gradient vector. A smaller FSA indicates a closer alignment between the flow direction and the temperature gradient, representing stronger synergy between the velocity and temperature fields and, consequently, more effective heat transfer performance. Figure 15 illustrates the variation of the field synergy angle (FSA) for heat exchange tubes with different structures, numbers of cells, and rib spacings within the Reynolds number range of 8,000–18,000. As shown in the figure, the FSA of the smooth tube remains above 86°, indicating a weak synergistic interaction between the velocity and temperature fields and, consequently, poor heat transfer performance. In contrast, the introduction of internal rib structures significantly reduces the FSA to 80°–83°, with the wavy ribbed T-cell tube exhibiting the lowest value. This demonstrates that structural perturbations effectively enhance the synergy between the velocity and temperature fields.Among the various geometric parameters, the FSA reaches its minimum when the rib spacing P = 20 mm and the number of cells N = 5, indicating the most favorable synergistic condition. Under this configuration, the multi-scale vortices generated within the tube effectively disrupt the near-wall thermal boundary layer and strengthen energy exchange between the core flow region and the wall, thereby maximizing convective heat transfer capability.In summary, the serpentine corrugated inner-ribbed T-cell tube achieves the strongest field synergy among all configurations. The combined influence of flow disturbances and secondary vortices generated by the corrugated ribs and elliptical T-cells facilitates more efficient thermal interaction from the near-wall region to the core flow region. This enhanced velocity–temperature field coordination is the fundamental mechanism responsible for the superior overall heat transfer performance (PEC) of the composite tube compared to conventional structures. 4. Summary This paper innovatively proposes and verifies an affine serpentine wave rib-ovoid cell composite heat exchange tube. By designing a composite structure of affine serpentine wave inner rib and ovoid cell, the interference and radial mixing ability of fluid flow in the heat exchange tube are improved, a stronger longitudinal vortex structure is formed, and the fluid convection heat transfer ability is enhanced. The effects of different structural parameters on flow and heat transfer were studied. The best heat transfer performance was achieved when N = 5 and = 20 mm. However, the pressure also increased, resulting in greater resistance. This indicates that there is an optimal balance between heat transfer and resistance. The composite structure provides the same heat exchange efficiency at the same Reynolds number, but the pressure loss of the heat exchange tube is smaller than that of other types of structures. This is because the wave ribs reduce the degree of separation while maintaining the disturbance, and reduce the frictional resistance to effectively suppress the increase of pressure drop. This means lower energy consumption. Its structural parameters provide theoretical reference for parameter optimization and energy-saving design of chemical processes. It has application value for hot wax removal of oil and gas pipelines and energy saving in chemical processes. The study revealed the intrinsic mechanism by which the composite structure enhances heat transfer through the synergistic improvement of the velocity and temperature fields. The results provide a theoretical basis for the design optimization of novel composite internal rib heat exchanger tube structures. Declarations Author Contribution Zhimiao Li reviewed the manuscript.Zhouyang Wang wrote the main manuscript text. Lin Zheng,Sizhe Zhang and Qi Zhang prepared the figures. Data Availability The datasets generated and/or analysed during the current study are available from the corresponding author on reasonable request. Declarations Conflict of interest The authors declare that they have no known com peting financial interests or personal relationships that could have ap peared to influence the work reported in this paper. References Ali MR, Al-Khaled K, Hussain M et al (2023) Effect of design parameters on passive control of heat transfer enhancement phenomenon in heat exchangers–A brief review[J]. Case Stud Therm Eng 43:102674 Xie S, Zhu X, Zeng G et al (2025) Numerical simulation study of flow and heat transfer characteristics of the spiral ribbed tube with elliptical dimples[J]. Numer Heat Transf Part A-Applications 86(3):551–568 Wang Y, He YL, Lei YG et al (2010) Heat transfer and hydrodynamics analysis of a novel dimpled tube[J]. Exp Thermal Fluid Sci 34(8):1273–1281 Ding L, Tang S, Qiu T et al (2025) Analysis of heat transfer characteristics and optimization of variable-direction twisted oval tubes with inserts[J]. Int J Therm Sci 210:109661 Hu Q, Fan Z, Zhang Z et al (2023) Analysis of flow and heat transfer characteristics and multi-objective optimization for sinusoidal PCHE[J]. Energies 16(15):5763 Tang S, Ding L, Sheng R et al (2024) Parametric analysis on thermal-hydraulic characteristics in variable-direction twisted-oval tube bundle in cross-flow[J]. Int J Therm Sci 197:108761 Tian Z, Song KW, Sun K et al (2024) Numerical investigation of thermal characteristics of double-tube heat exchangers with alternate twist direction and different phase angles of the inner oval tube[J]. Appl Therm Eng 255:123979 Wang T, Zhang Q, Song KW et al (2022) Thermodynamic characteristics of a novel combination of three-start twisted tube and oval dimples[J]. Case Stud Therm Eng 37:102284 Gong Q, Yu C, Wang W et al (2023) Experimental and numerical exploration on improved heat transfer by continuous spiral flow in shell of spiral wound corrugated tube heat exchanger[J]. Case Stud Therm Eng 51:103483 Song KW, Tian Z, Wu X et al (2025) Thermal characteristics of a double-tube heat exchanger with different twist directions of the inner oval tube[J]. Int J Therm Sci 208:109481 Assoudi A, Habli S, Saïd NM et al (2015) Experimental and numerical study of an offset jet with different velocity and offset ratios[J]. Eng Appl Comput Fluid Mech 9(1):490–512 Kumar R, Dewan A (2013) Assessment of buoyancy-corrected turbulence models for thermal plumes[J]. Eng Appl Comput Fluid Mech 7(2):239–249 Patil PS, Dhande KK, Borse SL (2023) Experimental investigation of heat transfer and pressure drop using combination of ribs and dimples[J]. Australian J Mech Eng 21(2):628–640 Chow PM (1993) Y. Control volume unstructured mesh procedure for convection-diffusion solidification processes[D]. University of Greenwich, Ozceyhan V, Gunes S, Buyukalaca O et al (2008) Heat transfer enhancement in a tube using circular cross sectional rings separated from wall[J]. Appl Energy 85(10):988–1001 Naphon P, Nuchjapo M, Kurujareon J (2006) Tube side heat transfer coefficient and friction factor characteristics of horizontal tubes with helical rib[J]. Energy Conv Manag 47(18–19):3031–3044 Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 10 Feb, 2026 Reviews received at journal 08 Feb, 2026 Reviews received at journal 05 Feb, 2026 Reviewers agreed at journal 02 Feb, 2026 Reviewers agreed at journal 31 Jan, 2026 Reviewers agreed at journal 31 Jan, 2026 Reviews received at journal 30 Jan, 2026 Reviewers agreed at journal 10 Jan, 2026 Reviewers invited by journal 08 Jan, 2026 Editor assigned by journal 07 Jan, 2026 Submission checks completed at journal 07 Jan, 2026 First submitted to journal 07 Jan, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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16:39:32","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":120873,"visible":true,"origin":"","legend":"\u003cp\u003ePEC heat exchange tubes with different numbers of cells.\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-8536966/v1/53d382581b5e4f5c26b75693.png"},{"id":100364409,"identity":"5db5c4b4-e04e-4e22-b6bb-8deee5369568","added_by":"auto","created_at":"2026-01-16 07:53:38","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":341343,"visible":true,"origin":"","legend":"\u003cp\u003eVelocity distribution contour map and TKE distribution contour map at the x=200mm section\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-8536966/v1/97b6c22ebcf48e1869e0aef9.png"},{"id":100364595,"identity":"244c73eb-d6fa-4696-aff7-b61612cbc3c5","added_by":"auto","created_at":"2026-01-16 07:53:59","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":245436,"visible":true,"origin":"","legend":"\u003cp\u003eAverage Nusselt number Nu and average friction factor f for heat exchange tube structures with different rib spacings\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-8536966/v1/244179c8e3267161caab1c22.png"},{"id":100364448,"identity":"5ae0118f-ce33-4e64-9feb-58986f5aa6ed","added_by":"auto","created_at":"2026-01-16 07:53:43","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":127446,"visible":true,"origin":"","legend":"\u003cp\u003eHeat exchanger tubes PEC with different fin spacings\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-8536966/v1/8339a95fcbf87b4e4486636a.png"},{"id":100073146,"identity":"d2c09fdb-09e2-41d0-b27f-bbe2b7b22aad","added_by":"auto","created_at":"2026-01-12 16:39:32","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":78799,"visible":true,"origin":"","legend":"\u003cp\u003eInfluence of different structural parameters on the field coordination angle\u003c/p\u003e","description":"","filename":"15.png","url":"https://assets-eu.researchsquare.com/files/rs-8536966/v1/54c6dabbb8607055e54028b7.png"},{"id":100405714,"identity":"ec0176fd-68e7-4bcc-9e5d-402c8e2b646e","added_by":"auto","created_at":"2026-01-16 12:17:10","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2246821,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8536966/v1/438b79f7-19b4-4c98-8ad4-52d64e0c3b59.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Numerical Investigation of Flow and Heat Transfer in a Serpentine-Oval-Cell Composite Heat Transfer Tube","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eWith the growing challenges of energy shortages and increasing environmental protection requirements, the application of enhanced heat exchanger tube technologies has become increasingly important[1]. In recent years, improving heat transfer efficiency while reducing pressure loss has been a key focus in processes such as hot-water dewaxing of oil and gas pipelines and thermal exchange in industrial equipment.Xie Shuai et al. [2] numerically investigated the flow and heat transfer performance of teardrop-shaped grooved enhanced tubes, finding that the streamlined grooves not only improved heat transfer efficiency but also effectively reduced pressure drop by suppressing flow separation. Wang Yu and He Yaling et al. [3] proposed and experimentally validated a novel elliptical grooved tube, demonstrating that it significantly enhanced heat transfer with only a slight increase in pressure drop, highlighting the influence of surface cavities on flow adhesion behavior. Ding Liang and Tang Songzhen et al. [4] numerically analyzed a Variable Direction Twisted Oval Tube (VDTOT) and found that periodically changing the twisting direction effectively improved overall heat transfer performance by promoting fluid disturbance.\u003c/p\u003e \u003cp\u003eHu Qixuan and Fan Zhonglei et al. [5] conducted a systematic numerical optimization of the sinusoidal channel in a Printed Circuit Heat Exchanger (PCHE), confirming that wavy channel structures can further reduce pressure loss. In the study of composite and multi-structure heat exchangers, Songzhen Tang et al. [6] and Zhen Tian et al. [7] performed numerical simulations on double-pipe heat exchangers with elliptical inner tubes having alternating torsion directions and phase angles, achieving improved thermal performance through coordinated flow disturbance. Tao Wang et al. [8] numerically studied the thermohydraulic characteristics of a combined structure featuring triple helical twisted tubes and elliptical pits, demonstrating that multi-angle perturbations can significantly enhance heat transfer. Similarly, Gong Quanyu et al. [9] and Song Kewei et al. [10] showed that multi-structural configurations and periodic flow disturbances can further improve comprehensive heat exchange performance.\u003c/p\u003e \u003cp\u003ePrevious studies have often faced the challenge of simultaneously enhancing heat transfer and minimizing pressure drop, as increasing heat transfer through intensified fluid disturbance typically leads to a substantial rise in flow resistance. To overcome this limitation, the present study proposes a novel heat exchange tube featuring a serpentine wavy inner-ribbed cellular composite structure. By integrating the flow-disturbing effect of the serpentine wavy ribs with the flow-guiding capability of the cellular cavities, this design achieves enhanced heat transfer performance while effectively reducing pressure loss.\u003c/p\u003e"},{"header":"2. Numerical simulation","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Physical Model\u003c/h2\u003e \u003cp\u003eThis study investigates a composite heat exchange tube structure that integrates elliptical cells with serpentine corrugated ribs, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The tube has an inner diameter (D) of 20 mm, and the total length (L) of the computational domain is 800 mm. The domain consists of three sections: an inlet section, a test section, and an outlet section, with respective lengths of 200 mm, 500 mm, and 100 mm. This configuration ensures that the fluid flow entering the test section is fully developed and prevents the outlet boundary from influencing the flow field within the test region.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo investigate the effects of the serpentine wavy internal rib cells and their geometric parameters on the flow and heat transfer characteristics of the composite enhanced tube, the parameters of the elliptical rib cells were kept constant, with a major axis (a) of 7.2 mm, a minor axis (b) of 3.6 mm, and a depth (h) of 3.6 mm. The variables considered include the rib depth (H), the radii of the semicircular crests (Rₚ) and troughs (R\u003csub\u003ev\u003c/sub\u003e), the crest-to-trough radius ratio (Rₐ = Rₚ / R\u003csub\u003ev\u003c/sub\u003e), the rib spacing (P), and the number of circumferential rib cells (N). The specific parameter values are listed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Since the numerical simulations focus on the internal flow and heat transfer characteristics of the composite tube, the influence of the tube wall thickness was neglected.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eGeometric parameters of wave rib composite tube\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSize/mm\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOverall length of the pipe L\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e800\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLength of the inlet area Lin\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLength of the exit area Lout\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTest area length Ltest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRib depth H\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9、1、1.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThe ratio of crest radius to trough radius Ra\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1、1.25、1.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNumber of D cells N\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4、5、6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Selection of Turbulence Model\u003c/h2\u003e \u003cp\u003eTo further minimize errors and improve the accuracy of the numerical simulations, different turbulence models were employed to validate and compare the results for smooth tubes under identical geometric and operating conditions. The turbulence models evaluated are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. As shown in the figure, for the Nusselt number (Nu), the deviation ranges were 15.1%\u0026ndash;19.3% for the SST k\u0026ndash;ω model, 26.12%\u0026ndash;29.43% for the RNG k\u0026ndash;ε model, 6.34%\u0026ndash;11.3% for the Standard k\u0026ndash;ε model, and 4.73%\u0026ndash;9.1% for the Realizable k\u0026ndash;ε model. In terms of the friction factor (f), the corresponding deviation ranges were 5.6%\u0026ndash;9.3% for the SST k\u0026ndash;ω model, 2.12%\u0026ndash;3.1% for the RNG k\u0026ndash;ε model, 2.34%\u0026ndash;3.3% for the Standard k\u0026ndash;ε model, and 1.73%\u0026ndash;3.1% for the Realizable k\u0026ndash;ε model. Among the models considered, the Realizable k\u0026ndash;ε model exhibited the best overall agreement with empirical correlations, providing higher accuracy in predicting both heat transfer and flow resistance. Therefore, the Realizable k\u0026ndash;ε model was selected for subsequent analyses of the flow and heat transfer characteristics under different structural parameters[11\u0026ndash;13].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3. Mesh division and grid independence test\u003c/h2\u003e \u003cp\u003eThe mesh generation was carried out using Fluent Meshing, with enhanced wall functions applied in the near-wall region. A total of 12 boundary layers were generated with a growth rate of 1.2 to accurately resolve the velocity and temperature gradients near the wall. Additionally, local mesh refinement was applied to the rib and cell regions to ensure computational accuracy and capture the complex flow behavior. A schematic of the computational mesh is presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eMesh independence was verified using a model with geometric parameters of H\u0026thinsp;=\u0026thinsp;1.1 mm, Rₐ = 1.5, N\u0026thinsp;=\u0026thinsp;6, and P\u0026thinsp;=\u0026thinsp;20 mm under a Reynolds number (Re) of 8000. Five computational models with different mesh densities were tested, and the results are summarized in the corresponding table. When the total mesh count reached 2,037,341, the relative deviations of the Nusselt number (Nu) and friction factor (\u003cem\u003ef\u003c/em\u003e) were 0.56% and 0.65%, respectively, indicating that the results had stabilized. Considering both computational cost and numerical accuracy, the third mesh configuration was selected for subsequent simulations.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4. Simulation method verification\u003c/h2\u003e \u003cp\u003eIn order to ensure the accuracy of numerical simulation, the smooth tube was simulated and compared with the empirical formula[14\u0026ndash;15], and the results are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs shown in the figure, the simulated Nusselt number (Nu) deviates from the Dittus\u0026ndash;Boelter correlation by 8.09%, while the simulated friction factor (\u003cem\u003ef\u003c/em\u003e) deviates from the Filonenko correlation by 5.41%. The close agreement between the theoretical and simulated results indicates that the numerical simulation method is reliable, with deviations remaining within an acceptable range[16].\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Analysis of flow and heat transfer characteristics","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\n \u003ch2\u003e3.1 Effects of different arrangement methods on heat transfer and flow characteristics inside the tube\u003c/h2\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e presents the velocity gradient and temperature contour maps of heat exchanger tubes with different internal structures. From left to right, the configurations correspond to a ring-shaped inner rib tube, a corrugated inner rib tube, and a serpentine corrugated inner rib T-cell tube. The high-velocity region within the tube is primarily concentrated in the core flow area, where a boundary layer is formed near the wall. As observed from left to right, the size of the high-velocity region first decreases and then increases. This behavior indicates that the serpentine corrugated inner rib induces large-scale flow separation, resulting in a reduction of the central high-velocity zone. Meanwhile, the stable T-cell vortices generated by the elliptical T-cell structure not only disturb the flow but also segment and reorganize the large-scale separation region downstream of the corrugated ribs, thereby guiding and restoring the core flow and enlarging the high-velocity region again.This phenomenon demonstrates that a pronounced synergistic effect exists between the serpentine corrugated inner rib and the elliptical T-cell structure, rather than a simple additive effect of flow disturbances. As shown in the temperature contour maps, the near-wall high-temperature region of the serpentine corrugated inner rib T-cell tube is the smallest, exhibiting the highest degree of temperature field fragmentation and the largest overall temperature gradient, which together indicate a stronger heat transfer driving potential. Consequently, under the synergistic action of the serpentine corrugated inner rib and the elliptical T-cell structure, the overall heat transfer performance (PEC) is significantly enhanced.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e7\u003c/span\u003e illustrates the variations in the average Nusselt number (Nu) and the average friction factor (\u003cem\u003ef\u003c/em\u003e) for heat exchange tubes with different structural configurations. As shown, Nu increases with increasing Reynolds number (Re). This occurs because higher Re values correspond to greater fluid velocity and turbulence intensity, which in turn reduce the thickness of the thermal boundary layer and enhance radial mixing. Both effects lead to intensified convective heat transfer, thereby increasing Nu.Specifically, the Nu of the serpentine corrugated inner ribbed T-cell tube is 89.9% higher than that of the smooth tube, and 39.6% and 4.2% higher than those of the annular inner ribbed tube and the wavy inner ribbed tube, respectively. In contrast, the average friction factor (\u003cem\u003ef\u003c/em\u003e) exhibits a gradual decreasing trend as Re increases, since the inertial effects dominate over viscous forces at higher flow velocities. Notably, the f value of the serpentine corrugated inner ribbed T-cell tube is 81.8% higher than that of the annular inner ribbed tube, yet lower than that of the wavy inner ribbed tube.This finding indicates that the synergistic interaction between the serpentine corrugated ribs and the elliptical T-cell structure improves the internal pressure distribution and effectively mitigates flow resistance, enabling the tube to maintain enhanced heat transfer performance with a relatively lower pressure drop.\u003c/p\u003e\n \u003cp\u003eAs shown in Fig. \u003cspan class=\"InternalRef\"\u003e8\u003c/span\u003e, within the Reynolds number (Re) range of 8000\u0026ndash;18000, the performance evaluation criterion (PEC) of the annular inner-ribbed tube ranges from 0.94 to 1.05, that of the serpentine corrugated inner-ribbed tube ranges from 0.97 to 1.16, and that of the serpentine corrugated inner-ribbed T-cell tube reaches 1.02\u0026ndash;1.22. Under identical Re conditions, the overall heat transfer performance of the serpentine corrugated inner-ribbed T-cell tube is markedly superior to that of the other heat exchanger tube configurations.The results presented in Figs. \u003cspan class=\"InternalRef\"\u003e5\u003c/span\u003e and \u003cspan class=\"InternalRef\"\u003e6\u003c/span\u003e further verify that the synergistic interaction between the corrugated inner ribs and the elliptical T-cell structures not only enhances both the Nusselt number (Nu) and the friction factor (\u003cem\u003ef\u003c/em\u003e), but also significantly improves the comprehensive heat transfer performance of the tube.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\n \u003ch2\u003e3.2 Effect of different cell numbers on heat transfer and flow characteristics inside the tube\u003c/h2\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e9\u003c/span\u003e presents the velocity and temperature distribution contours of the serpentine wave-shaped internally ribbed T-cell tube at the cross-section of x\u0026thinsp;=\u0026thinsp;200 mm for different numbers of T-cells. As shown in the velocity contour maps, the high-velocity region at the tube center expands with an increasing number of T-cells. However, for the configuration with N\u0026thinsp;=\u0026thinsp;5 T-cells, the flow field exhibits noticeable asymmetry along the longitudinal direction due to the complex geometric interaction of the T-cell structures.By examining both the cross-sectional and longitudinal temperature contours, it can be observed that the flow disturbance intensity within the tube reaches its maximum when N\u0026thinsp;=\u0026thinsp;4. Furthermore, the temperature distribution contour reveals that the overall temperature gradient is also the largest at N\u0026thinsp;=\u0026thinsp;4, indicating a stronger convective heat transfer capability under this configuration.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e illustrates the variations of the average Nusselt number (Nu) and average friction coefficient (\u003cem\u003ef\u003c/em\u003e) for heat exchanger tubes with different numbers of T-cells. In serpentine corrugated inner-ribbed tubes with varying cell numbers, Nu generally increases with increasing Reynolds number (Re), while f exhibits a gradual decreasing trend. However, a \u0026ldquo;jump\u0026rdquo; phenomenon in f is occasionally observed. This can be attributed to the increased flow disorder induced by the T-cell structures, which alters the local pressure distribution and reduces the overall pressure drop at higher flow velocities.\u003c/p\u003e\n \u003cp\u003eCompared with the annular and corrugated inner-ribbed tubes, the serpentine corrugated inner-ribbed tubes exhibit higher heat transfer performance, with Nu values increasing by approximately 4.1%\u0026ndash;4.5% relative to the corrugated inner-ribbed tubes. Moreover, when N\u0026thinsp;=\u0026thinsp;5 and 6, the friction coefficient decreases by 2.8%\u0026ndash;3.4% compared with the corrugated inner-ribbed configuration, indicating that an appropriate number of T-cells can improve heat transfer efficiency while mitigating pressure losses.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e11\u003c/span\u003e illustrates the influence of different numbers of T-cells on the heat transfer performance of the pseudo-serpentine corrugated inner-ribbed tube. As shown in Fig. \u003cspan class=\"InternalRef\"\u003e10\u003c/span\u003e, the PEC decreases gradually with increasing Reynolds number, reaching its maximum value of 1.21 when N\u0026thinsp;=\u0026thinsp;5. This indicates that selecting an appropriate number of T-cells is crucial for optimizing the overall heat transfer performance.Compared with the annular inner-ribbed tube, the average PEC of the pseudo-serpentine corrugated inner-ribbed tube increases by approximately 9.6%\u0026ndash;15%. Relative to the corrugated inner-ribbed tube, the improvement ranges from 2.36% to 6.2%. As the number of T-cells increases from N\u0026thinsp;=\u0026thinsp;4 to N\u0026thinsp;=\u0026thinsp;5, the total heat transfer area expands, the convective heat transfer capacity is enhanced, and the synergistic effect between the serpentine corrugated ribs and the elliptical T-cell structures reaches its optimal state. This improves flow uniformity, reduces pressure losses, and results in the maximum PEC value.However, further increasing the number of T-cells (from N\u0026thinsp;=\u0026thinsp;5 to N\u0026thinsp;=\u0026thinsp;6) leads to a more complex flow path, higher turbulence intensity, and increased wall contact frequency. Although this enhances fluid mixing, it simultaneously raises flow resistance and pressure loss, thereby offsetting the benefits of heat transfer enhancement. Therefore, the number of T-cells should be optimized rather than maximized, as excessive structural complexity can deteriorate overall heat transfer performance.\u003c/p\u003e\u003cspan\u003e\n \u003cp\u003e\u003cstrong\u003e3.3. Effect of the number of T cells on the heat exchange and flow characteristics in the tube\u003c/strong\u003e\u003c/p\u003e\n \u003c/span\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e12\u003c/span\u003e presents the velocity distribution and turbulent kinetic energy (TKE) contours at the cross-section (x\u0026thinsp;=\u0026thinsp;200 mm) of the serpentine wave-shaped internally ribbed tube under different rib spacings (P). As shown in the figure, with increasing rib spacing, the velocity magnitude in the central high-speed region decreases, and the velocity gradient between the core and near-wall regions becomes less pronounced.When P\u0026thinsp;=\u0026thinsp;20 mm, the central flow velocity is high, and a distinct low-velocity region forms near the wall, accompanied by a significant velocity gradient. This indicates strong flow disturbance, generating evident secondary flow and vortex structures that enhance momentum and energy exchange between the core and near-wall regions. Simultaneously, the turbulent kinetic energy near the wall increases markedly, demonstrating intensified local flow activity and enhanced fluid mixing capability.As the rib spacing increases to P\u0026thinsp;=\u0026thinsp;40 mm, the central velocity decreases and becomes more evenly distributed, while the velocity gradient diminishes slightly. This suggests that flow disturbance weakens and TKE near the wall decreases, leading to reduced radial mixing intensity. When the rib spacing is further enlarged to P\u0026thinsp;=\u0026thinsp;60 mm, the velocity distribution in the core region becomes nearly uniform, the velocity gradient variation is minimal, and the flow disturbance is significantly weakened. Consequently, the TKE near the wall drops further, and the radial mixing ability of the fluid deteriorates sharply, resulting in the poorest overall convective performance.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e13\u003c/span\u003e illustrates the variation trends of the average Nusselt number (Nu) and friction coefficient (\u003cem\u003ef\u003c/em\u003e) under different rib spacings (P). As shown in the figure, Nu increases consistently with increasing Reynolds number (Re). At a constant Re, the heat transfer coefficient for P\u0026thinsp;=\u0026thinsp;20 mm is higher than that for other rib spacings, indicating the strongest convective heat transfer intensity and the most effective thermal enhancement.The variation in the friction coefficient (\u003cem\u003ef\u003c/em\u003e) reveals that at P\u0026thinsp;=\u0026thinsp;20 mm, f is greater than that at P\u0026thinsp;=\u0026thinsp;40 mm and P\u0026thinsp;=\u0026thinsp;60 mm, but lower than that of the conventional corrugated inner-finned tube. This demonstrates that the synergistic interaction between the serpentine corrugated inner ribs and the elliptical cell structure effectively enhances flow uniformity and suppresses excessive flow separation, thereby achieving a favorable balance between heat transfer enhancement and drag reduction.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e14\u003c/span\u003e presents the variation of the performance evaluation criterion (PEC) for heat exchange tubes with different rib spacings (P). As shown in the figure, the PEC of all ribbed tubes decreases with increasing Reynolds number (Re), but remains higher than that of the smooth tube across the entire Re range. This confirms that the rib structures play an important role in enhancing the overall heat transfer capability.\u003c/p\u003e\n \u003cp\u003eNotably, the serpentine corrugated inner-ribbed tube with P\u0026thinsp;=\u0026thinsp;20 mm exhibits a significantly higher PEC compared with the conventional corrugated inner-ribbed tube, indicating that the composite configuration of the serpentine corrugated ribs and elliptical fins effectively strengthens the overall heat transfer performance. The pronounced synergistic interaction between the serpentine corrugated ribs and the elliptical fin cells enables an optimal balance between heat transfer enhancement and flow resistance, thereby improving thermal\u0026ndash;hydraulic performance comprehensively.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\n \u003ch2\u003e3.4 field collaborative analysis\u003c/h2\u003e\n \u003cp\u003eTo elucidate the mechanism by which the wavy, internally ribbed composite tube enhances heat transfer, the field synergy theory (FST) is introduced to analyze the interaction between the velocity and temperature fields in different structures. The field synergy angle (FSA) is employed to quantitatively evaluate the degree of coordination between these two fields. It is defined as the angle between the velocity vector and the temperature gradient vector. A smaller FSA indicates a closer alignment between the flow direction and the temperature gradient, representing stronger synergy between the velocity and temperature fields and, consequently, more effective heat transfer performance.\u003c/p\u003e\n \u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e15\u003c/span\u003e illustrates the variation of the field synergy angle (FSA) for heat exchange tubes with different structures, numbers of cells, and rib spacings within the Reynolds number range of 8,000\u0026ndash;18,000. As shown in the figure, the FSA of the smooth tube remains above 86\u0026deg;, indicating a weak synergistic interaction between the velocity and temperature fields and, consequently, poor heat transfer performance. In contrast, the introduction of internal rib structures significantly reduces the FSA to 80\u0026deg;\u0026ndash;83\u0026deg;, with the wavy ribbed T-cell tube exhibiting the lowest value. This demonstrates that structural perturbations effectively enhance the synergy between the velocity and temperature fields.Among the various geometric parameters, the FSA reaches its minimum when the rib spacing P\u0026thinsp;=\u0026thinsp;20 mm and the number of cells N\u0026thinsp;=\u0026thinsp;5, indicating the most favorable synergistic condition. Under this configuration, the multi-scale vortices generated within the tube effectively disrupt the near-wall thermal boundary layer and strengthen energy exchange between the core flow region and the wall, thereby maximizing convective heat transfer capability.In summary, the serpentine corrugated inner-ribbed T-cell tube achieves the strongest field synergy among all configurations. The combined influence of flow disturbances and secondary vortices generated by the corrugated ribs and elliptical T-cells facilitates more efficient thermal interaction from the near-wall region to the core flow region. This enhanced velocity\u0026ndash;temperature field coordination is the fundamental mechanism responsible for the superior overall heat transfer performance (PEC) of the composite tube compared to conventional structures.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"4. Summary","content":"\u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eThis paper innovatively proposes and verifies an affine serpentine wave rib-ovoid cell composite heat exchange tube. By designing a composite structure of affine serpentine wave inner rib and ovoid cell, the interference and radial mixing ability of fluid flow in the heat exchange tube are improved, a stronger longitudinal vortex structure is formed, and the fluid convection heat transfer ability is enhanced.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe effects of different structural parameters on flow and heat transfer were studied. The best heat transfer performance was achieved when N\u0026thinsp;=\u0026thinsp;5 and =\u0026thinsp;20 mm. However, the pressure also increased, resulting in greater resistance. This indicates that there is an optimal balance between heat transfer and resistance.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe composite structure provides the same heat exchange efficiency at the same Reynolds number, but the pressure loss of the heat exchange tube is smaller than that of other types of structures. This is because the wave ribs reduce the degree of separation while maintaining the disturbance, and reduce the frictional resistance to effectively suppress the increase of pressure drop. This means lower energy consumption. Its structural parameters provide theoretical reference for parameter optimization and energy-saving design of chemical processes. It has application value for hot wax removal of oil and gas pipelines and energy saving in chemical processes.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe study revealed the intrinsic mechanism by which the composite structure enhances heat transfer through the synergistic improvement of the velocity and temperature fields. The results provide a theoretical basis for the design optimization of novel composite internal rib heat exchanger tube structures.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eZhimiao Li reviewed the manuscript.Zhouyang Wang wrote the main manuscript text. Lin Zheng,Sizhe Zhang and Qi Zhang prepared the figures.\u003c/p\u003e\u003cp\u003e\u003cstrong\u003eData Availability\u003c/strong\u003e The datasets generated and/or analysed during the current study are available from the corresponding author on reasonable request.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDeclarations Conflict of interest\u003c/strong\u003e The authors declare that they have no known com peting financial interests or personal relationships that could have ap peared to influence the work reported in this paper.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAli MR, Al-Khaled K, Hussain M et al (2023) Effect of design parameters on passive control of heat transfer enhancement phenomenon in heat exchangers\u0026ndash;A brief review[J]. Case Stud Therm Eng 43:102674\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eXie S, Zhu X, Zeng G et al (2025) Numerical simulation study of flow and heat transfer characteristics of the spiral ribbed tube with elliptical dimples[J]. Numer Heat Transf Part A-Applications 86(3):551\u0026ndash;568\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang Y, He YL, Lei YG et al (2010) Heat transfer and hydrodynamics analysis of a novel dimpled tube[J]. Exp Thermal Fluid Sci 34(8):1273\u0026ndash;1281\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDing L, Tang S, Qiu T et al (2025) Analysis of heat transfer characteristics and optimization of variable-direction twisted oval tubes with inserts[J]. Int J Therm Sci 210:109661\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHu Q, Fan Z, Zhang Z et al (2023) Analysis of flow and heat transfer characteristics and multi-objective optimization for sinusoidal PCHE[J]. Energies 16(15):5763\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTang S, Ding L, Sheng R et al (2024) Parametric analysis on thermal-hydraulic characteristics in variable-direction twisted-oval tube bundle in cross-flow[J]. Int J Therm Sci 197:108761\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTian Z, Song KW, Sun K et al (2024) Numerical investigation of thermal characteristics of double-tube heat exchangers with alternate twist direction and different phase angles of the inner oval tube[J]. Appl Therm Eng 255:123979\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang T, Zhang Q, Song KW et al (2022) Thermodynamic characteristics of a novel combination of three-start twisted tube and oval dimples[J]. Case Stud Therm Eng 37:102284\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGong Q, Yu C, Wang W et al (2023) Experimental and numerical exploration on improved heat transfer by continuous spiral flow in shell of spiral wound corrugated tube heat exchanger[J]. Case Stud Therm Eng 51:103483\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSong KW, Tian Z, Wu X et al (2025) Thermal characteristics of a double-tube heat exchanger with different twist directions of the inner oval tube[J]. Int J Therm Sci 208:109481\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAssoudi A, Habli S, Sa\u0026iuml;d NM et al (2015) Experimental and numerical study of an offset jet with different velocity and offset ratios[J]. Eng Appl Comput Fluid Mech 9(1):490\u0026ndash;512\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKumar R, Dewan A (2013) Assessment of buoyancy-corrected turbulence models for thermal plumes[J]. Eng Appl Comput Fluid Mech 7(2):239\u0026ndash;249\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePatil PS, Dhande KK, Borse SL (2023) Experimental investigation of heat transfer and pressure drop using combination of ribs and dimples[J]. Australian J Mech Eng 21(2):628\u0026ndash;640\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChow PM (1993) Y. Control volume unstructured mesh procedure for convection-diffusion solidification processes[D]. University of Greenwich,\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eOzceyhan V, Gunes S, Buyukalaca O et al (2008) Heat transfer enhancement in a tube using circular cross sectional rings separated from wall[J]. Appl Energy 85(10):988\u0026ndash;1001\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNaphon P, Nuchjapo M, Kurujareon J (2006) Tube side heat transfer coefficient and friction factor characteristics of horizontal tubes with helical rib[J]. Energy Conv Manag 47(18\u0026ndash;19):3031\u0026ndash;3044\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"iranian-journal-of-science-and-technology-transactions-of-mechanical-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"istm","sideBox":"Learn more about [Iranian Journal of Science and Technology, Transactions of Mechanical Engineering](https://link.springer.com/journal/40997)","snPcode":"40997","submissionUrl":"https://submission.springernature.com/new-submission/40997/3","title":"Iranian Journal of Science and Technology, Transactions of Mechanical Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Wavy inner ribs, Elliptical cells, Composite structure, Enhanced heat transfer, Structural optimization","lastPublishedDoi":"10.21203/rs.3.rs-8536966/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8536966/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study tackles the issue of low heat transfer efficiency in conventional heat exchange tubes through a biomimetic design approach. Inspired by the surface-guiding characteristics of snake skin and the fluid-directing features of oval cells, a novel composite heat exchange tube integrating a snake-like wavy inner rib and an elliptical T-cell structure was developed. Numerical simulations were conducted to investigate the effects of different rib arrangements, rib numbers, and spacings on the heat transfer characteristics of the tube over a Reynolds number range of 8,000\u0026ndash;18,000. The results indicate that variations in rib configuration, number, and spacing have a significant impact on heat transfer performance. Under the condition of Re\u0026thinsp;=\u0026thinsp;8,000, the optimal configuration achieved a maximum overall heat transfer performance (PEC) of 1.21, with the average Nusselt number (Nu) enhanced by 89% compared to a smooth tube. Moreover, at the same Reynolds number, the wavy inner rib T-cell tube exhibited lower pressure loss than other types of composite heat exchange tubes while maintaining comparable PEC, and demonstrated better flow resistance characteristics than both single rib and T-cell tubes. These findings confirm that the proposed structure effectively reduces energy loss while sustaining efficient heat transfer. Finally, field synergy analysis revealed the intrinsic mechanism by which the composite structure enhances heat transfer through improved coordination between the velocity and temperature fields. This study provides a theoretical foundation for the design and optimization of advanced composite internally ribbed heat exchanger structures.\u003c/p\u003e","manuscriptTitle":"Numerical Investigation of Flow and Heat Transfer in a Serpentine-Oval-Cell Composite Heat Transfer Tube","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-12 16:39:27","doi":"10.21203/rs.3.rs-8536966/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-02-10T14:43:36+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-09T04:39:17+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-02-05T13:58:27+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"298004799849782945242450867214116646901","date":"2026-02-02T14:02:18+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"135904460345517123843067627768055623661","date":"2026-02-01T03:52:25+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"326347653968772550630869837007656674657","date":"2026-01-31T13:31:27+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-01-30T20:11:07+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"161037352285458990891285708403322063198","date":"2026-01-10T10:51:48+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-01-08T07:52:35+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-01-07T14:58:30+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-01-07T14:57:28+00:00","index":"","fulltext":""},{"type":"submitted","content":"Iranian Journal of Science and Technology, Transactions of Mechanical Engineering","date":"2026-01-07T05:06:33+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"iranian-journal-of-science-and-technology-transactions-of-mechanical-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"istm","sideBox":"Learn more about [Iranian Journal of Science and Technology, Transactions of Mechanical Engineering](https://link.springer.com/journal/40997)","snPcode":"40997","submissionUrl":"https://submission.springernature.com/new-submission/40997/3","title":"Iranian Journal of Science and Technology, Transactions of Mechanical Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"560953f4-92de-4069-b38a-41ea702f5f8e","owner":[],"postedDate":"January 12th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-01T03:09:17+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-12 16:39:27","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8536966","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8536966","identity":"rs-8536966","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}