Impact of Corrugated Fins on Flow and Heat Transfer Performance in Medium-Deep Coaxial Underground Heat Exchangers

Abstract

To enhance the efficient development of geothermal energy, this study investigates the heat transfer enhancement mechanisms in medium-depth coaxial underground heat exchangers (CUHEs) integrated with corrugated fins, using computational fluid dynamics (CFD) simulations. Nine distinct corrugated fin geometries were modeled, and the streamlines, velocity fields, temperature fields, and turbulent kinetic energy were analyzed across Reynolds numbers (Re) ranging from 12,000 to 42,000. The results demonstrate that corrugated fins significantly promote fluid turbulence and mixing, thereby augmenting convective heat transfer. Compared to smooth inner tubes, the Nusselt number (Nu) is enhanced by a factor of 1.43–2.19, while the friction factor (f) increases by a factor of 2.94–6.79. The performance evaluation criterion (PEC) improves with increasing fin width and decreasing fin spacing. The optimal configuration, featuring a fin width of 15 mm, a spacing of 60 mm, and a thickness of 15 mm, achieves a maximum PEC value of 1.34 at Re = 12,000, indicating a substantial improvement in heat transfer performance within acceptable pressure drop limits. This research innovatively explores the performance enhancement of CUHEs at high Re, systematically elucidates the influence of geometric parameters on heat transfer and flow resistance, and employs the PEC index to optimize the structural design. This provides significant theoretical support for the efficient engineering application of CUHEs in geothermal utilization.

1. Introduction

With the growing challenge of global energy consumption and climate change, energy conservation and emission reduction have become global strategic priorities. China’s proposed “dual carbon” goals [1,2] further underscore the necessity of a global transition to a sustainable energy system. As a clean and sustainable resource, geothermal energy has garnered significant attention [3,4,5,6,7]. Coaxial underground heat exchangers (CUHEs) for medium and deep geothermal resources, with their advantages of high efficiency, stability, and environmental friendliness, hold significant potential in the field of geothermal development. Given the considerable potential of CUHEs, improving their heat transfer performance is crucial. This has driven extensive research into heat transfer enhancement technologies (HTETs) [8,9]. Among these, passive HTETs have attracted considerable attention due to their merits, such as requiring no external energy input, simple structure, and cost-effectiveness [10,11]. Passive HTETs mainly enhance convective heat transfer by modifying the internal geometry of heat exchangers, disturbing fluid flow, and disrupting thermal boundary layers. Within this field, many scholars are dedicated to exploring their applications and effects in various aspects [12]. Typical passive heat transfer enhancement techniques include incorporating grooves [13], twisted tapes [14], corrugated surfaces [15], and fins [16] into heat exchanger channels. Although passive HTETs have shown progress, further improving the heat transfer performance of CUHEs remains a key research focus.

To further enhance the heat transfer performance of CUHEs, research has focused on optimizing existing technologies and exploring novel structures. For example, Samad Jafarmadar et al. [17] significantly improved the Nusselt number (Nu) and overall heat transfer performance by introducing specific flow channel designs and adjusting geometric parameters. Similarly, Kim Leong Liaw et al. [18] investigated helically coiled tubes with twisted tape inserts and determined the optimal twist ratio. Furthermore, K. Kazerani et al. [19] found that baffles at specific angles can improve the heat transfer performance of baffled heat exchangers. Additionally, Himadri Chattopadhyay et al. [20] verified the effectiveness of twisted tape inserts. In other research directions, Li et al. [21] pointed out that asymmetric corrugated tube designs can improve heat transfer performance. Muhannad A. R. Muhammed et al. [22] experimentally confirmed that rectangular fins provide the most effective heat transfer in geothermal heat exchangers. Zafar Iqbal et al.’s [23] study showed that introducing a tip-to-base angle ratio can improve both Nu and the j-factor. Finally, M.S. Kumar et al. [24] enhanced the heat transfer performance of double pipe heat exchangers by adding circular ribs to the outer surface of the inner tube. These studies demonstrate that optimizing geometric structures and flow conditions can significantly improve the heat transfer performance of heat exchangers [25,26].

Researchers have also focused on heat exchangers with novel corrugated structures to explore their potential for further enhancing heat transfer performance. Mouza et al. [27] studied the flow and heat transfer characteristics of corrugated wall heat exchangers and found that corrugated walls significantly improved flow and heat exchange efficiency. Additionally, Samad Jafarmadar et al. [28] explored the performance impact of different corrugated tube arrangements on novel underground heat exchangers. Moreover, Iman Bashtani et al. [29] analyzed the effect of different corrugation amplitudes on the performance of corrugated tube heat exchangers under turbulent conditions. Furthermore, Mousa Farhadi et al. [30] experimentally investigated the enhanced heat transfer effect of nanofluids in tubes with different corrugated structures.

Researchers have conducted in-depth studies on the specific impact of corrugation geometric parameters and flow conditions on heat transfer performance from multiple perspectives. Jose Fernandez-Seara et al. [31] investigated the influence of corrugation height and spacing on heat transfer. Similarly, Pethkool et al. [32] pointed out the importance of optimizing corrugated fin spacing and height-to-diameter ratio for improving heat transfer performance. Jassim Alhamid et al. [33] emphasized that increasing the geometric complexity of corrugations can effectively enhance the heat transfer coefficient. Liu Q et al. [34] showed that different fin widths and rotation directions have a significant impact on heat transfer and flow behavior. Gong Q et al. [35] revealed the influence of corrugation geometric parameters on the overall performance of heat exchangers through experiments and numerical simulations. Other studies include the following: Hasan et al. [36] confirmed that helically coiled heat exchangers with uniform pitch have superior thermal performance compared to traditional designs; Zhang et al. [37] found that larger heat exchanger diameters and longitudinal spacing are beneficial for enhancing heat transfer performance.

Despite numerous studies on heat transfer enhancement technologies for CUHEs, there is a scarcity of research systematically investigating the heat transfer performance of CUHEs with different corrugated fins at high Reynolds numbers (Re = 12,000–42,000), while high Re flows are prevalent in industrial applications. Therefore, filling this research gap is crucial for improving heat transfer efficiency. In this study, we systematically analyze the heat transfer and flow characteristics of CUHEs with different corrugated fin inner tube structures and geometric parameters in the high Reynolds number range through numerical simulations. We evaluate the impact of a range of fin widths and spacings on heat transfer performance (Nu, f, and PEC) and reveal the heat transfer enhancement mechanism of corrugated fin inner tubes. This study aims to provide valuable references for the design and optimization of high-performance CUHEs.

2. Working Principle and Evaluation Metrics of CUHEs

This chapter aims to introduce the working principle of the CUHE under investigation and define the key performance evaluation metrics. This will lay the groundwork for the numerical simulations and subsequent analysis of the results presented in later chapters.

2.1. Working Principle

The working principle of the studied CUHE is depicted in Figure 1, illustrating the overall flow path of the working fluid within the annulus and the placement of the corrugated fins. Working fluid is injected into the annular space between the inner and outer tubes. The corrugated fins on the outer wall of the inner tube modify the fluid flow regime, enhancing fluid turbulence and disrupting the fluid boundary layer. This disruption reduces the boundary layer thickness and improves the mixing between the fluid in the core region and the fluid near the tube wall. Consequently, heat absorption from the surrounding hot wellbore is intensified, achieving enhanced heat transfer. Driven by the bottom hole pressure, the fluid is extracted from the inner cavity of the inner tube. The primary function of the inner tube is to convey the heated fluid upwards.

2.2. Evaluation Metrics

To quantitatively assess the effects of corrugated fins on both the heat transfer performance and flow resistance of the coaxial heat exchanger, this study utilizes the Nu, f, and PEC as performance evaluation metrics. The definitions and calculation methodologies for these metrics will serve as the basis for the subsequent analysis of the numerical simulation results [33,35].

The Nu is expressed as:

$$\mathrm{N}\mathrm{u}={\displaystyle \frac{\mathsf{\alpha }\mathrm{D}}{\mathsf{\lambda }}}$$

(1)

where λ is the thermal conductivity of the fluid, D is the hydraulic diameter of the CUHE.

The heat transfer coefficient is determined by:

$$\mathsf{\alpha }={\displaystyle \frac{\mathrm{q}}{{\mathrm{T}}_{\mathrm{W}}-{\mathrm{T}}_{\mathrm{a}}}}$$

(2)

where q is the inner surface heat flux; T_w is the temperature of the heat pipe wall; T_a is the average fluid temperature.

$${\mathrm{T}}_{\mathrm{a}}={\displaystyle \frac{{\mathrm{T}}_{\mathrm{i}\mathrm{n}}+{\mathrm{T}}_{\mathrm{o}\mathrm{u}\mathrm{t}}}{2}}$$

(3)

where T_in is the inlet temperature of the enhanced heat transfer section, T_out is the outlet temperature of the enhanced heat transfer section.

The friction coefficient is expressed as:

$$\mathrm{f}={\displaystyle \frac{2\mathrm{D}\mathsf{\Delta }\mathrm{P}}{\mathrm{L}\mathsf{\rho }{\mathrm{u}}^2}}$$

(4)

where ΔP is the inlet-to-outlet pressure difference, $\mathrm{u}$ is the average flow speed, ρ is the fluid density, and L is the length of the enhanced heat transfer section.

$$\mathrm{P}\mathrm{E}\mathrm{C}={\displaystyle \frac{(\mathrm{N}\mathrm{u}/{\mathrm{N}\mathrm{u}}_{\mathrm{s}})}{{(\mathrm{f}/{\mathrm{f}}_{\mathrm{s}})}^{1/3}}}$$

(5)

where Nu_s and f_s are the Nu and f of the smooth inner tube at the same Re.

3. Numerical Model

3.1. Physical Model

Figure 2 illustrates the physical model of a CUHE featuring corrugated fins on the outer surface of the inner tube. Given the study’s focus on the effect of corrugated fins with varying pitches (P_c) and widths (H_c) on the heat transfer performance of medium-deep CUHEs, and considering computational constraints, the model length (L) was set to 4.5 m. Specifically, the enhanced heat transfer section (L_e), where the fins are located, measures 4 m, while the inlet (L_in) and outlet (L_out) sections are 0.1 m and 0.4 m, respectively.

Detailed geometric parameters for the CUHE and corrugated fins are provided in

Table 1. Model parameters.

Geometric Parameters	Unit	Numerical Value
Inner pipe outer diameter	mm	D0 = 134.6
Outer pipe inner diameter	mm	D1 = 177.8
Outer pipe outer diameter	mm	D2 = 193.8
Enhanced Heat Transfer Section	mm	Le = 4000
Width of Corrugated Fins	mm	Hc = 5, 10, 15
Pitch of Corrugated Fins	mm	Pc = 60, 120, 180
Thickness of Corrugated Fins	mm	Wc = 5

. These dimensions were chosen to adhere to similarity theory, ensuring representative geometric scaling for practical applications.

3.2. Boundary Conditions and Numerical Methods

The boundary conditions for the numerical model are defined as follows:

(1)

Inlet: A velocity inlet boundary condition is specified, with inlet velocities set to correspond to the investigated Reynolds number range of 12,000 to 42,000. The fluid inlet temperature is set to 43 °C to represent typical operating temperatures in practical applications within the Songliao Basin, and to reflect the region’s geological and climatic characteristics.

(2)

Outlet: A pressure outlet boundary condition is applied at the outlet, with atmospheric pressure.

(3)

Walls: A constant heat flux of 600 W/m² is applied to the outer tube wall to simulate heat transfer. The inner tube wall and corrugated fins are considered adiabatic. No-slip boundary conditions are imposed on all inner and outer tube walls and fin surfaces to accurately capture the fluid-solid interaction.

Table 2. Physical parameters.

Physical Parameters/Unit	Water	Steel
$\mathsf{\rho }/\mathrm{k}\mathrm{g}·{\mathrm{m}}^{-3}$	991.04	8060
${\mathrm{C}}_{\mathrm{p}}/\mathrm{J}·{(\mathrm{k}\mathrm{g}·\mathrm{K})}^{-1}$	4179.8	400
$\mathsf{\lambda }/\mathrm{W}·{(\mathrm{m}·\mathrm{K})}^{-1}$	0.63232	40
$\mathsf{\mu }/\mathrm{k}\mathrm{g}·{(\mathrm{m}·\mathrm{s})}^{-1}$	6.1754 × 10−4	0

details the material properties used in the numerical model.

The Realizable k-ε turbulence model was employed for numerical simulations across Reynolds numbers ranging from 12,000 to 42,000. The simulation results indicate that Y+ ≤ 1, satisfying the near-wall resolution requirement of the turbulence model and thereby ensuring accurate resolution of the near-wall boundary layer flow.

In the numerical simulations, thermal radiation was neglected. The fluid was assumed to be incompressible with constant thermal properties. The SIMPLE algorithm was employed for pressure-velocity coupling to ensure solution convergence. Momentum, energy, turbulent kinetic energy, and turbulent dissipation rate equations were discretized using a second-order upwind scheme for enhanced accuracy. The governing equations include the continuity Equation (6), which describes the mass conservation of the fluid; the momentum Equation (7), based on the Navier-Stokes equations, considering the influence of viscous forces and pressure gradients; the energy Equation (8), used to calculate the energy change of the fluid; the turbulent kinetic energy Equation (9), describing the change of turbulent kinetic energy; and the turbulent dissipation rate Equation (10), used to calculate the loss of turbulent kinetic energy.

$$\nabla ·\mathbf{u}=0$$

(6)

$$\nabla ·\left(\mathsf{\rho }\mathrm{u}\mathbf{u}\right)=-\nabla \mathrm{P}+\nabla ·\left(\right(\mathsf{\mu }+{\mathsf{\mu }}_{\mathrm{t}})\nabla \mathrm{V})+\nabla ·(-\mathsf{\rho }\overline{{\mathrm{u}}^{\prime }{\mathbf{u}}^{\prime }})$$

(7)

$$\mathsf{\rho }{\mathrm{c}}_{\mathrm{p}}\mathbf{u}·\nabla \mathrm{T}=\nabla ·(\mathsf{\lambda }\nabla \mathrm{T})$$

(8)

$$\nabla ·(\mathsf{\rho }\mathbf{u}\mathrm{k})=\nabla ·((\mathsf{\mu }+{\displaystyle \frac{{\mathsf{\mu }}_{\mathrm{t}}}{{\mathsf{\sigma }}_{\mathrm{k}}}})\nabla \mathrm{k})+{\mathrm{G}}_{\mathrm{k}}+{\mathrm{G}}_{\mathrm{b}}-\mathsf{\rho }\mathsf{\epsilon }-{\mathrm{Y}}_{\mathrm{M}}$$

(9)

$$\nabla ·(\mathsf{\rho }\mathbf{u}\mathsf{\epsilon })=\nabla ·((\mathsf{\mu }+{\displaystyle \frac{{\mathsf{\mu }}_{\mathrm{t}}}{{\mathsf{\sigma }}_{\mathrm{k}}}})\nabla \mathsf{\epsilon })+{\mathrm{c}}_1\mathsf{\rho }\mathrm{S}\mathsf{\epsilon }-{\mathrm{c}}_2\mathsf{\rho }{\displaystyle \frac{{\mathsf{\epsilon }}^2}{\mathrm{k}+\sqrt{\mathsf{\nu }\mathsf{\epsilon }}}}+{\mathrm{c}}_{1\mathsf{\epsilon }}{\displaystyle \frac{\mathsf{\epsilon }}{\mathrm{k}}}{\mathrm{c}}_{3\mathsf{\epsilon }}{\mathrm{G}}_{\mathrm{b}}$$

(10)

where ${\mathrm{c}}_1=\mathrm{m}\mathrm{a}\mathrm{x}\left[0.43,{\displaystyle \frac{\mathsf{\eta }}{\mathsf{\eta }+5}}\right],\mathsf{\eta }={\displaystyle \frac{\mathrm{S}\mathrm{k}}{\mathsf{\epsilon }}},\mathrm{S}=\sqrt{2{\mathrm{S}}_{\mathrm{i}\mathrm{j}}{\mathrm{S}}_{\mathrm{i}\mathrm{j}}},{\mathrm{S}}_{\mathrm{i}\mathrm{j}}={\displaystyle \frac{1}{2}}({\displaystyle \frac{\partial {\mathrm{u}}_{\mathrm{i}}}{\partial {\mathrm{x}}_{\mathrm{j}}}}+{\displaystyle \frac{\partial {\mathrm{u}}_{\mathrm{j}}}{\partial {\mathrm{x}}_{\mathrm{i}}}}),{\mathrm{c}}_2=1.9,{\mathsf{\sigma }}_{\mathrm{k}}=1.0,{\mathsf{\sigma }}_{\mathsf{\epsilon }}=1.2,{\mathsf{\mu }}_{\mathrm{t}}={\mathrm{c}}_{\mathsf{\mu }}\mathsf{\rho }{\mathrm{k}}^2/\mathsf{\epsilon }$.

For definitions of other symbols, refer to the reference [38].

3.3. Mesh Generation and Mesh Independence Validation

High-quality structured grids were generated within the computational domain using ICEM CFD 2021 R1 software. Figure 3 presents a schematic of the mesh for the CUHE. Due to the complex flow and heat transfer phenomena in the near-wall region, mesh refinement was applied to the near-wall boundary layer and the corrugated fin surfaces.

As shown in Figure 4, a grid independence verification was performed for parameters W_c = 5 mm, H_c = 10 mm, P_c = 120 mm, and Re = 24,000. The results show that the calculated values of Nusselt number (Nu) and friction factor (f) gradually stabilize as the number of grids increases. When the number of grids exceeds 2 × 10⁶, the change of the calculated results is very minimal; in the grid number range of 2.0 × 10⁶ to 4.5 × 10⁶, the relative error of Nu is only 0.39%, and the relative error of f is 0.14%. This shows that the calculation results have converged when the number of grids reaches 2 × 10⁶.

Based on the grid independence verification and considering both computational accuracy and efficiency, a mesh with 2 × 10⁶ elements was finally selected for subsequent numerical simulations. Further increasing the grid density was found to yield only limited improvements in simulation accuracy while significantly increasing computation time. Therefore, this mesh density provides an optimal balance between accuracy and computational cost.

Grid independence verification is a crucial step in numerical simulation, as it ensures that the adopted grid density is sufficient to resolve the details of flow and heat transfer phenomena, thereby guaranteeing the reliability of the simulation results.

3.4. Model Validation

To validate the numerical model’s accuracy, the Nu obtained from simulations of a smooth inner tube coaxial heat exchanger was compared against values predicted by the Dittus-Boelter [39] and Gnielinski [40] correlations. Similarly, the simulated friction factor (f) for the smooth inner tube was compared with the Blasius [41] and Petukhov [42] correlations.

Dittus-Boelter correlation:

$$\mathrm{N}\mathrm{u}=0.023{\mathrm{R}\mathrm{e}}^{0.8}{\mathrm{P}\mathrm{r}}^{0.4}$$

(11)

Its range of applicability is: 0.7 ≤ $\mathrm{P}\mathrm{r}\le$ 120, 10⁴ ≤ $\mathrm{R}\mathrm{e}\le$ 1.2 ×10⁵.

Gnielinski correlation:

$$\mathrm{N}\mathrm{u}={\displaystyle \frac{(\mathrm{f}/8)(\mathrm{R}\mathrm{e}-1000)\mathrm{P}\mathrm{r}}{1+12.7{(\mathrm{f}/8)}^{\frac{1}{2}}({\mathrm{P}\mathrm{r}}^{\frac{2}{3}}-1)}}$$

(12)

Its range of applicability is: 0.5 ≤ $\mathrm{P}\mathrm{r}\le 2$000, 3000 ≤ $\mathrm{R}\mathrm{e}\le 1$.2 × 10⁶.

Blasius correlation:

$$\mathrm{f}=0.316{\mathrm{R}\mathrm{e}}^{-0.25}$$

(13)

Its range of applicability is: 4000 < $\mathrm{R}\mathrm{e}$ < 10⁵.

Petukhov correlation:

$$\mathrm{f}={(0.79\mathrm{l}\mathrm{n}\mathrm{R}\mathrm{e}-1.64)}^{-2}$$

(14)

Its range of applicability is: 3000 < $\mathrm{R}\mathrm{e}$ < 10⁶.

As shown in Figure 5, the mean absolute deviations of Nu from the Dittus-Boelter and Gnielinski correlations are 4.31% and 3.38%, respectively. For f, the current simulation exhibited mean absolute deviations of 0.86% and 0.50% compared to the Blasius and Petukhov correlations, respectively. The numerical results of this study are in reasonable agreement with those obtained from empirical correlations, thereby validating the numerical model.

4. Results and Discussion

4.1. Mechanism of Augmented Heat Transfer

Figure 6 illustrates the streamlines and Z-velocity distributions within representative sections of both the corrugated fin and smooth inner tube coaxial heat exchangers at Re = 24,000. As seen in Figure 6, for the smooth inner tube, the fluid streamlines are parallel straight lines, the velocity profile is smooth with no significant vortices or bypass flow, and the z-direction velocity in the near-wall region is higher than in other regions. In the CUHE, the streamlines in the mainstream area remain relatively straight. Compared to the smooth inner tube, the corrugated fins significantly disrupt and redirect the fluid flow. Some fluid bypasses the fins, flowing along the tube wall, which increases the fluid velocity in the near-wall region, enhancing the disturbance of the thermal boundary layer and reducing thermal resistance. The fins also induce the formation of vortices near the wall. As the fin width (H_c) increases, the fin spacing decreases, leading to greater flow disturbance and enhanced heat exchange between the fluid and the wall. At H_c = 15 mm, the Z-velocity distribution further clarifies the flow characteristics within the corrugated fin tube. The flow field is not characterized by a simple, uniform increase in Z-velocity. Instead, fin disturbances induce a series of local vortices in the adjacent region, promoting flow recirculation and ultimately enhancing radial mixing. In conclusion, the primary mechanism of enhanced heat transfer by corrugated fins is not direct wall surface scouring, but rather the strong mixing and disturbance generated by the induced vortices, which ultimately improve the overall heat transfer performance.

Figure 7 presents velocity contours at a section Z = −3.14 m for both the corrugated fin and smooth inner tube coaxial heat exchangers at Re = 24,000. As shown, in both types of heat exchangers, the fluid velocity near the walls is reduced due to viscous effects within the boundary layers. However, as the fluid flows through the corrugated fins, the reduced flow area caused by their presence leads to a significant increase in local velocity, enhancing mixing and turbulence downstream. With increasing fin width, this velocity increase is further amplified, promoting greater convective heat transfer between the fluid and the wall. Therefore, increasing the fin width can effectively enhance the heat transfer performance of the coaxial heat exchanger.

Figure 8 displays velocity vector fields for CUHEs of varying fin widths at Re = 24,000. As depicted, pronounced velocity gradients are observed, indicating a significantly higher degree of fluid mixing near the corrugated fins and within the annular region compared to other areas. This is attributed to the flow obstruction caused by the fins, which alters the flow regime and enhances boundary layer disruption. The fins also interact with the fluid through guidance and shearing, leading to the formation of vortices near the wall and enhancing mixing between the near-wall and core flow regions. This enhanced mixing reduces temperature differences, thins the thermal boundary layer, and enhances heat extraction from the surrounding reservoir, thereby promoting heat exchange. As the fin width increases, the fluid disturbance intensifies, the flow velocity increases significantly, and the heat transfer enhancement becomes more pronounced. The underlying mechanism involves stronger flow blockage with wider fins, generating more intense vortices and secondary flows. These phenomena more effectively disrupt both the velocity and thermal boundary layers.

Figure 9 presents turbulent kinetic energy (TKE) contours for coaxial heat exchangers with both corrugated fins and smooth inner tubes at Re = 24,000. TKE, defined as half the product of the turbulent velocity fluctuation variance and the fluid mass, quantifies the intensity and irregularity of turbulent motion, reflecting changes in heat transfer and resistance. Compared to the smooth inner tube, the TKE in the corrugated fin heat exchanger varies significantly, generally increasing with proximity to the wall, except within the viscous sublayer where TKE is minimal. The highest TKE is concentrated in the high-velocity region near the corrugated fins, with peak values at the vortex centers. The TKE remains elevated for a certain distance downstream of the fins before gradually diminishing. The coaxial heat exchanger with a fin width of H_c = 15 mm exhibits the highest TKE and, consequently, the most significant heat transfer enhancement. This is attributed to the maximized disruption of the thermal boundary layer near the inner tube wall, leading to increased heat exchange area and velocity between the fluid and the wall, thereby enhancing heat transfer.

Figure 10 illustrates temperature distribution contours at a representative cross-section (Z = −3.14 m) for both the corrugated fin (CUHE) and smooth inner tube coaxial heat exchangers at Re = 24,000. Within the CUHE, the corrugated fins are fully immersed in the fluid and maintain an approximately constant temperature at steady state. The temperature field is primarily influenced by the presence of these fins. As the width of the corrugated fins increases, the temperature gradient near the wall steepens, and the thermal boundary layer thins. This is because the fin crests accelerate the fluid, which thins the thermal boundary layer, while the troughs induce vortices or secondary flow, enhancing radial mixing. These combined effects reduce the thermal resistance of the boundary layer, thereby promoting heat transfer from the outer tube wall to the fluid. Compared to the smooth inner tube, the corrugated inner tube significantly modifies the near-wall temperature field, leading to a steeper temperature gradient and a thinner thermal boundary layer. Although the impact on the overall average fluid temperature may be modest, the corrugated fins clearly enhance heat transfer in the near-wall region. This near-wall enhancement is primarily attributed to the resulting significantly increased temperature gradient and reduced thermal boundary layer thickness. Consequently, the corrugated inner tube exhibits superior heat transfer performance compared to the smooth inner tube.

4.2. Influence of Corrugation Width

To analyze the effect of corrugation width (H_c) of the corrugated fins on heat transfer enhancement in the coaxial heat exchanger, the corrugation pitch (P_c = 120 mm) and corrugation thickness (W_c = 5 mm) were kept constant. The study then examined the variations in thermal performance parameters, including Nu, f, and PEC, as a function of H_c.

4.2.1. Effect of Different H_c on the Nusselt Number (Nu)

This section examines the variation in Nu for different corrugation widths (H_c = 5, 10, and 15 mm) across the Reynolds number range of 12,000 to 42,000. Nu reflects the intensity of convective heat transfer at the fluid boundary; higher Nu values indicate enhanced heat exchange between the fluid and the wall. As shown in Figure 11, for each H_c value, Nu increases with Re, although the rate of increase gradually diminishes. As Re increases, the resulting increase in turbulence enhances heat exchange. Consequently, the effect of the fins on heat transfer becomes more pronounced. However, at very high Re, the influence of the corrugated fins on the flow field diminishes, leading to a less pronounced heat transfer enhancement. Furthermore, at the same Re, the Nu for CUHEs is consistently higher than that of the smooth inner tube configuration. Increasing H_c alters the in-tube flow pattern, intensifying fluid disturbances and turbulence, which reduces the thermal resistance of the boundary layer, thereby enhancing heat transfer. The ratio Nu/Nu_s increases with H_c. Specifically, the heat transfer performance of the CUHEs with H_c = 5, 10, and 15 mm is 1.71–1.80, 1.86–1.96, and 1.96–2.04 times that of the smooth inner tube configuration, respectively. These results indicate that increasing H_c improves the heat transfer performance of the coaxial heat exchanger.

4.2.2. Effect of Different H_c on the Friction Coefficient (f)

This section investigates the variation of the f with Re for different corrugation widths (H_c). As shown in Figure 12, f decreases with increasing Re. However, at a given Re, CUHEs consistently exhibit a higher f compared to the smooth inner tube configuration. Increasing H_c modifies the flow characteristics within the tube. It reduces the constraint imposed by the corrugation protrusions on the fluid flow, which promotes a smoother flow path and consequently reduces the overall flow resistance. Consequently, the ratio f/f_s decreases with increasing H_c. Specifically, the f for CUHEs with H_c = 5, 10, and 15 mm is 3.94–4.09, 3.73–3.81, and 3.53–3.65 times that of the smooth inner tube configuration, respectively. This demonstrates that increasing H_c has an important impact on improving the drag performance of coaxial heat exchangers.

4.2.3. Effect of Different H_c on the Thermal Performance Coefficient (PEC)

This section examines the variation of the PEC with Re for different corrugation widths (H_c). As shown in Figure 13, the PEC generally decreases with increasing Re, eventually reaching a plateau (with a standard error of about 0.02). At a given Re, the PEC increases with increasing H_c. Specifically, the PEC for CUHEs with H_c = 5, 10, and 15 mm is 1.07–1.14, 1.19–1.26, and 1.27–1.34 times that of the smooth inner tube configuration, respectively. These values indicate that H_c = 15 mm provides the most significant enhancement in overall thermal performance. While this PEC analysis highlights the performance benefits of increasing H_c, the associated increase in manufacturing costs for the corrugated structure must also be considered for practical applications. Therefore, a comprehensive cost-benefit analysis is crucial for future research and implementation. Nevertheless, the current PEC analysis offers valuable guidance for optimizing H_c in high-performance heat exchanger designs.

4.3. Impact of Corrugation Pitch

To investigate the effect of corrugation pitch (P_c) on the enhanced heat transfer mechanism in CUHEs, the corrugation width (H_c = 5 mm) and thickness (W_c = 5 mm) were kept constant. The study analyzed the changes in thermal performance parameters, such as Nu, f, and PEC, with varying corrugation pitch.

4.3.1. Effect of Different P_c on the Nusselt Number (Nu)

This section investigates the variation of Nu with Re across the range of 12,000 to 42,000 for different corrugation pitches (P_c = 60, 120, and 180 mm). As shown in Figure 14, Nu increases with increasing Re.

This is because Re is indicative of the fluid flow velocity inside the tube. Higher flow velocity leads to increased turbulence and shear stress, which in turn reduces the thickness of the boundary layer and enhances the heat transfer coefficient. Consequently, heat transfer is significantly enhanced. The figure also indicates that the ratio Nu/Nu_s decreases as P_c increases. Specifically, the heat transfer performance for coaxial heat exchangers with P_c = 60, 120, and 180 mm is 2.17–2.19 times, 1.71–1.80 times, and 1.43–1.56 times that of the smooth inner tube configuration, respectively. This suggests that decreasing P_c is beneficial for enhancing the heat transfer performance of the coaxial heat exchanger.

4.3.2. Effect of Different P_c on the Friction Coefficient (f)

This section investigates the effect of Re on the f for different corrugation pitches (P_c). As illustrated in Figure 15, for each corrugation pitch, the f decreases with increasing Re. This behavior is attributed to the increase in both wall shear force and dynamic pressure with increasing flow velocity (reflected by Re). As the flow velocity continues to increase, the growth rates of the wall shear force and dynamic pressure tend to converge. Consequently, with increasing Re, the decreasing trend of f gradually levels off. Compared to the smooth inner tube configuration, the coaxial heat exchangers with different P_c exhibit larger f values at the same Re. Furthermore, the ratio f/f_s gradually decreases with increasing P_c. Specifically, the f values for the coaxial heat exchangers with P_c = 60, 120, and 180 mm are 5.95–6.79 times, 3.94–4.09 times, and 2.94–3.07 times that of the smooth inner tube configuration, respectively. This indicates that decreasing P_c significantly increases the f.

4.3.3. Effect of Different P_c on the Thermal Performance Coefficient (PEC)

This section examines the variation of the PEC with Re for different corrugation pitches (P_c). As shown in Figure 16, the PEC for each corrugation pitch decreases with increasing Re, and the rate of decrease diminishes until it eventually reaches a plateau.

Specifically, the PEC for CUHEs with P_c = 60, 120, and 180 mm is 1.15–1.21 times, 1.07–1.14 times, and 1.00–1.07 times that of the smooth inner tube configuration, respectively. This suggests that decreasing P_c is conducive to improving the thermal performance of the coaxial heat exchanger.

5. Conclusions

This study investigates the flow and heat transfer enhancement characteristics of CUHEs with varying widths (H_c = 5, 10, 15 mm) and pitch (P_c = 60, 120, 180 mm), and elucidates the mechanisms of heat transfer enhancement. The performance evaluation criterion (PEC), which accounts for both heat transfer augmentation and pressure drop, is utilized for assessment. A higher PEC value indicates more significant heat transfer enhancement under the same pumping power. Numerical simulation results demonstrate that the PEC values of the corrugated fin inner tubes are consistently greater than those of smooth inner tubes, thereby validating the effectiveness of the design.

Key Findings:

• The Nu, f, and PEC serve as key parameters for evaluating heat exchanger performance. The results demonstrate that as the corrugation width (H_c) is increased, the f decreases, while both the Nu and PEC increase. Specifically, compared to the smooth inner tube configuration, the CUHEs exhibit Nu values 1.71–2.04 times, f values 3.53–4.09 times, and PEC values 1.07–1.34 times higher, respectively, than those of the smooth inner tube configuration. Consequently, increasing the corrugated fin width leads to a significant enhancement in the thermal performance of the CUHE.
• With increasing pitch of the corrugated fins, both Nu and f decrease, and the PEC also decreases. Specifically, compared to the smooth tube configuration, the Nu values for various pitches are 1.43–2.19 times, the f values are 2.94–6.79 times, and the PEC values are 1.00–1.15 times that of the smooth tube configuration. This suggests that reducing pitch is beneficial for performance improvement.
• At Re = 12,000, the CUHE with a width of 5 mm, a pitch of 60 mm, and a thickness of 15 mm exhibits excellent heat transfer enhancement performance. The corrugated fins effectively promote the full mixing of hot fluid in the near-wall region and cold fluid in the core region by enhancing fluid disturbance, increasing turbulence intensity, and forming vortices. This process accelerates the heat energy transfer rate and promotes heat exchange, ultimately resulting in enhanced heat transfer. Furthermore, compared to other fin geometries, this corrugated fin structure not only significantly improves heat transfer performance but also maintains the flow resistance within an acceptable range, thereby achieving optimal overall thermal performance.

While CUHEs demonstrate significant heat transfer enhancement, further research is still necessary. This includes exploring a broader range of geometric parameters and different corrugation shapes, investigating performance under lower Re conditions, and conducting experimental validation. Such investigations are crucial for providing comprehensive guidance for heat exchanger structural design. Considering its advantages in improving heat transfer performance and potential for structural optimization, this CUHE design holds broad application prospects in industrial fields with high demands for heat exchange efficiency, such as HVAC, the chemical industry, and the power industry. It is expected to contribute to technological upgrading, energy conservation, and emission reduction in these sectors.