Enhanced Heat Transfer in Plate-Fin Heat Exchangers Using Offset Triangular Fins with Vortex Generators: A Numerical Study

Figure 1 illustrates the basic OTF and VG geometry. Key dimensions are:

• Fin height, h = 10.25 mm.
• Fin spacing, S = 4 mm.
• Fin thickness, t = 0.25 mm.
• Interrupted fin length, L = 8 mm.
• Hydraulic diameter, $D_h=4 A_c / P=3.557$ mm.

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Figure 1. Classification of plate fins and rationale for selecting OTF based on previous work [10]

2.1 Configurations

Table 1 summarizes the four PFHE cases investigated. All VG cases use an optimum height ($\mathrm{h}_{V G}$) of 1.25 mm and entrance length ($\mathrm{L}_{V G}$) of 0.5 mm at β = 45°.

Table 1. Geometric parameters for proposed PFHE configurations

2.2 Computational domain and boundary conditions

The 3D computational domain for each case is shown in Figure 2. Air enters at $T_{i n}=300 \mathrm{~K}$ with Reynolds number $\operatorname{Re}=600-1400$. Boundary conditions are:

• Inlet: uniform velocity (corresponding to Re range), $T=300 \mathrm{~K}$.
• Outlet: zero-gauge pressure.
• Top/bottom plates: constant heat flux $q^{\prime \prime}=3000 \mathrm{~W} / \mathrm{m}^2$.
• Side faces: periodic to mimic an infinite fin array.
• Solid surfaces: no-slip, conjugate heat transfer with constant properties.
• The wall thickness is neglected.

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Figure 2. Frontal view of the computational domain for baseline and VG-mounted cases

Note that preliminary conduction analysis indicates that the thermal resistance due to conduction through the fin base is less than 1% of the convective resistance under all tested operating conditions. This was determined by comparing the conduction resistance Rcond = t_wall/(k_wall A) with the convective resistance R_conv = 1/(hA) and finding R_cond/R_conv < 0.01. Therefore, neglecting wall conduction introduces a negligible error in the heat transfer predictions and justifies the thin-wall assumption.

The steady-state, incompressible Navier–Stokes and energy equations are solved using ANSYS Fluent 2021 R1 with:

Finite-volume discretization, second-order upwind for momentum and energy.

SIMPLE algorithm for pressure–velocity coupling.

Mesh independence: residual variation < 1% in friction factor; final cell counts of 186 213 (RWP), 151 214 (DWP), 182 214 (TWP).

Convergence criteria: residuals < 10⁻⁶ for continuity/momentum, < 10⁻⁸ for energy.

2.2.1 Special considerations for vortex and boundary‐layer modeling

No-slip on VG surfaces captures flow separation and longitudinal vortex formation, which intensifies near-wall mixing and disrupts thermal boundary layers [12-14]. This detailed capture of vortical structures is critical to predict the enhanced heat-transfer mechanisms induced by each VG shape.

2.2.2 Numerical implementation

Simulations employed the finite-volume approach with second-order upwind discretization for momentum and energy, and the SIMPLE algorithm for pressure–velocity coupling. Computations ran on a 32-core workstation, averaging 6 h per case to reach converged solutions.

2.3 Governing equations

For fluid motion in the plate fin heat exchanger under laminar conditions, by integrating the average differential equations of continuity, momentum, and energy, the laminar incompressible stable equations can be employed as:

Continuity equation [35]:

$\frac{\delta U}{\delta x}+\frac{\delta V}{\delta y}+\frac{\delta W}{\delta z}=0$     (1)

$\frac{\delta u}{\delta x}+\frac{\delta v}{\delta y}+\frac{\delta w}{\delta z}=0$         (2)

Momentum equations:

The momentum equations were developed using Newton's second rule of motion to address the conservation of fluid momentum over the x, y, and z axes in fluid dynamics [34, 36]. These equations are the Navier-Stokes equations (NSE).

Momentum equation in x-direction:

$\rho\left(u \frac{\delta u}{\delta x}+v \frac{\delta u}{\delta y}+w \frac{\delta u}{\delta z}\right)=-\frac{\delta p}{\delta x}+\left(\frac{\delta^2 u}{\delta x^2}\right)+\left(\frac{\delta^2 u}{\delta y^2}\right)+\left(\frac{\delta^2 u}{\delta z^2}\right)$                (3)

Momentum equation in y-direction:

$\rho\left(u \frac{\delta v}{\delta x}+v \frac{\delta v}{\delta y}+w \frac{\delta v}{\delta z}\right)=-\frac{\delta p}{\delta x}+\left(\frac{\delta^2 v}{\delta x^2}\right)+\left(\frac{\delta^2 v}{\delta y^2}\right)+\left(\frac{\delta^2 v}{\delta z^2}\right)$     (4)

Momentum equation in z-direction:

$u \frac{\delta w}{\delta x}+v \frac{\delta w}{\delta y}+w \frac{\delta w}{\delta z}=-\frac{\delta p}{\delta x}+\left(\frac{\delta^2 w}{\delta x^2}\right)+\left(\frac{\delta^2 w}{\delta y^2}\right)+\left(\frac{\delta^2 w}{\delta z^2}\right)$       (5)

Energy equation:

$\begin{aligned} & u \frac{\delta T}{\delta x}+v \frac{\delta T}{\delta y}+w \frac{\delta T}{\delta z}=  -\frac{k}{\rho C_p}+\left(\frac{\delta^2 T}{\delta x^2}\right)+\left(\frac{\delta^2 T}{\delta y^2}\right)+\left(\frac{\delta^2 T}{\delta z^2}\right)\end{aligned}$      (6)

2.4 Computational methods

Numerical simulations are conducted utilizing ANSYS Fluent 2021 R1. The governing equations, comprising continuity, momentum (Navier-Stokes), and energy equations, are resolved via the finite volume approach. A double-precision pressure-based solver is utilized for numerical calculation. The SIMPLE algorithm is employed for pressure-velocity coupling. The spatial discretization of all words is accomplished by a second-order upwind method.

Hydrodynamic parameters:

$P_{\text {in }}-P_{\text {out }}=\Delta P$               (7)

Hydraulic diameter (Dh) [37] as recorded in Eq. (8):

$D_h=\frac{4 A}{P}$             (8)

For Re number [6] as shown in Eq. (9) below:

$R e=\frac{\rho U_{i n} D_h}{\mu}$             (9)

While for Nu number [8] as illustrated in Eq. (10):

$N u=\frac{h D_h}{k}$           (10)

For hydraulic features, including f calculation as in Eq. (11):

$C_f=\tau_w / \frac{1}{2} \rho U^2$              （11）

And for the fanning fraction factor as in Eq. (12):

$C_f=\frac{f}{4}$           (12)

2.5 Grid independence study

Figure 3 presents the mesh convergence analysis demonstrating how the friction factor (f) and Nusselt number (Nu) stabilize with increasing cell count for each VG configuration at Re = 600. The convergence trends reveal that both parameters show significant variation at lower mesh densities but progressively stabilize as refinement increases. For the RWP configuration, f varies by approximately 8.5% between 50,000 and 100,000 cells, but this variation decreases to less than 0.7% between 150,000 and 186,213 cells. Similarly, Nu changes by 6.3% in the coarser range but by only 0.4% in the finer region. The DWP configuration achieves stability earlier, with variations in f falling below 0.6% and Nu below 0.5% beyond 151,214 cells. The TWP configuration required 182,214 cells to reach similar stability thresholds. These convergence patterns reflect the different geometric complexities of each VG shape, with the more complex RWP geometry requiring higher cell counts to accurately capture the flow physics and heat transfer characteristics, particularly in the wake regions where longitudinal vortices form. The final mesh densities used in this study (186,213 for RWP, 151,214 for DWP, and 182,214 for TWP) ensure that numerical uncertainty related to spatial discretization is minimal.

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Figure 3. Mesh independence

2.6 Validation

The numerical model was confirmed by comparing Colburn j-factor results to Yang et al. [38] experimental data on offset strip fins in PFHEs. Averaging 3% variation between numerical and experimental data spanning the Re 600–1400 showed remarkable agreement. This validation shows that the numerical technique accurately predicts PFHE heat transfer across fin and vortex generator configurations, as illustrated in Figure 4.

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Figure 4. Validation for numerical work compared to experimental work

4.1 Temperature

The temperature contours along the tested domain are depicted in Figures 9-15. These figures also include cross-sectional slices that were obtained at 4, 8, and 12 millimeters to demonstrate the differences in temperature that occur for various VGX shapes. Because of the heat absorption from the heated fin surfaces (3,000 W/m²), the outlet air temperature rises gradually as one moves downstream. This is consistent with what was anticipated. In order to visualize this trend, the color transition from dark blue at the entrance to lighter hues (light blue, yellow, and green) toward the outlet indicates a continual rise in air temperature. This transition is depicted by the color transition.

Because of the interaction between the entering cold air and the heated fins, the boundary layer that is close to the walls gets thinner, which results in an increase in the amount of energy that is transmitted to the airflow. As a consequence of this, the outlet temperature at the 12 mm segment is the greatest, which is evidence of the cumulative heat gain that occurs while the channel is being extended. This is because there is less direct contact with hot surfaces in the center region, which results in moderate temperature levels. The highest temperatures are found along the interface between the fin and the wall, which is where convection is at its fiercest.

Quantitatively analyzed, the fins that have rectangular VGX cause the greatest temperature increase in the core region, which is an indication of improved heat transfer ability. The sharp-edged geometry of these structures causes stronger longitudinal vortices to be generated, which in turn intensifies mixing between the core and wall areas. This, in turn, causes the thermal boundary layer to be disrupted, which in turn increases the amount of heat that is transferred through convection. The T-shaped VGX is responsible for a modest boost, but the delta VGX is responsible for the least temperature rise. This is because the delta VGX has a smoother shape and a reduced vortex intensity.

The cut design of OSF fins and the addition of VGX elements generate recurrent boundary-layer disruptions and enhanced flow penetration into the fin base, which ultimately results in greater local heat transfer coefficients. This finding is in line with the findings of prior studies [10, 38, 44]. When taken as a whole, the cause–effect relationship between VGX shape, flow behavior, and temperature distribution makes it abundantly evident that stronger vortex generation results in more thermal enhancement. The rectangular VGX displays the most effective performance in this regard.

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Figure 9. 3D view of triangle VGX mounted on OT fins

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Figure 10. 3D view of rectangular VGX mounted on OT fins

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Figure 11. 3D view of delta VGX mounted on OT fins

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Figure 12. 3D view for temperature contours OTF with various VGX geos

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Figure 13. 2D front view temp of rectangular VGX mounted on OT fins through various locations (4, 8, and 12) mm

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Figure 14. 2D front view temp of triangular VGS mounted on OT fins through various locations (4, 8, and 12) mm

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Figure 15. 2D front view temp of Delta VGS mounted on OT fins through various locations (4, 8, and 12) mm

4.2 Velocity

As shown in Figures 16-19, the velocity vectors and temperature fields that highlight the air-side heat transfer and pressure drop characteristics of the fin-tube heat exchanger (FTHEX) are presented. All of the VGX geometries have their contours displayed for three different places along the domain: four, eight, and twelve millimeters. It has been found that the incorporation of VGX elements results in the generation of longitudinal vortices that interact with the main flow. This interaction ultimately results in the formation of swirl zones and a temporary slowdown of the flow in the vicinity of the VGX surfaces. When compared to the darker zones, which correlate to higher flow speeds away from the VGX, these regions appear as lighter colors, which indicates a decrease in velocity.

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Figure 16. 2D Velocity front view of rectangular VGS mounted on OT fins through various locations (4, 8, and 12) mm

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Figure 17. 2D Velocity front view of delta VGS mounted on OT fins through various locations (4, 8, and 12) mm

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Figure 18. 2D Velocity front view of triangle VGS mounted on OT fins through various locations (4, 8, and 12) mm

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Figure 19. streamlines for the three proposed VGX (rectangular, delta, and triangle)

Due to the fact that the flow slows down near the VGX as a result of the produced vortices, it stays in touch with the heated surfaces for a longer period of time, which ultimately results in increased local heat transfer rates. In contrast, sections of accelerated flow that are further away from the VGX have a lower level of heat exchange. This is because the reduced residence time restricts the influence of thermal contact. In comparison to other geometries, the rectangular VGX exhibits the fewest areas of low velocity, often known as light zones. This indicates that there is less flow separation and more stable vortex formations overall. On account of this, it displays the most efficient enhancement of heat transport when compared to the delta and triangular VGX designs.

Furthermore, the rectangular VGX demonstrates a 10–15% higher average outlet temperature and a commensurate rise in local Nusselt number in comparison to the delta VGX when the Reynolds number is the same. This substantiates the fact that the rectangular VGX has superior thermal performance. Due to the fact that the delta VGX has a profile that is smoother and narrower, it results in the development of weaker vortices and bigger wake zones, which ultimately makes the heat transfer efficiency less effective.

When compared to the 4 mm segment, the velocity contours at 12 mm indicate higher flow resistance along the flow direction. This is due to the fact that the cumulative pressure losses and the interaction between many vortices worsen downstream. This tendency is further confirmed by the streamline plots that are shown in Figure 19. As shown by the red zones in the temperature field, flow recirculation in the vicinity of the VGX corners, particularly in the triangular arrangement, results in the formation of localized regions of slower heat transport. However, matching and aligning VGX near these corner regions improves mixing and increases the local temperature gradient through amplified vortex motion. This is accomplished by increasing the amount of vortex motion.

As a whole, the investigation reveals that the shape of the VGX is directly responsible for determining the intensity of the vortex, the disruption of the boundary layer, and the rates of local heat transfer. The best balance between strong swirl formation and little flow separation is provided by rectangular VGX. This allows for the maximum amount of convective heat transfer while simultaneously minimizing the amount of pressure loss that occurs.

4.3 Pressure

Pressure drop characteristics for proposed VGX configurations are shown in Figures 20-22. The results show that pressure loss is directly related to VGX shape, which controls flow blockage, vortices, and wakes downstream of each element.

When referring to the RWP, the abrupt and perpendicular shape results in a significant flow impingement on the leading face, which in turn results in the formation of a prominent high-pressure area upstream. The winglet experiences a significant pressure drop. This happens when the fluid abruptly breaks from the surface, creating a wide wake region with low pressure. This structure creates massive downstream recirculation zones with high-intensity longitudinal vortices. Figure 20's elongated high–low pressure bands show this. Due to this, the RWP design has the highest pressure drop, 18–22% higher than the triangle and delta designs. RWP design creates a powerful vortex and increases drag.

Flow separation is less abrupt with the TWP due to its streamlined leading edge. Due to the lower pressure differential between the front and rear surfaces, the wake region is smaller, and pressure recovers faster downstream. This causes a 10–12% pressure drop below RWP. However, the effective creation of vortices that promote high thermal mixing is still maintained, as demonstrated in Figure 21. The design of the TWP provides a good balance between increased heat transfer and reduced pressure loss, which is a significant advantage.

To achieve the highest level of aerodynamic efficiency, the DWP is the optimal configuration. The gradual flow dissociation that occurs as a result of its smooth and tapered edges also results in the generation of only minor low-pressure zones that quickly dissipate into the main stream. As a consequence of this, DWP displays the lowest overall pressure difference, typically between 25 and 30 percent lower than RWP. On the other hand, in comparison to the other VGX geometries, this design has a decreased heat transfer enhancement because the vortex intensity associated with it is lower.

In general, the comparison findings indicate that there is a direct cause-and-effect relationship: as the shape of the VGX becomes more streamlined (from rectangular to delta), the produced vortex strength and flow disturbance decrease. This leads to smaller pressure drops, but it also results in a reduction in the performance of heat transfer. As a result, the RWP arrangement gives the greatest improvement in heat transfer, but at the expense of a greater loss of pressure. On the other hand, the DWP configuration delivers the least amount of drag, but only a modest improvement in thermal efficiency.

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Figure 20. 2D pressure front view of rectangular VGS mounted on OT fins through various locations (4, 8, and 12) mm

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Figure 21. 2D pressure front view of delta VGS mounted on OT fins through various locations (4, 8, and 12) mm

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Figure 22. 2D pressure front view of triangular VGX mounted on OT fins through various locations (4, 8, and 12) mm

Future research can improve vortex generator PFHE performance in several ways. First, examine how VGX materials and surface treatments affect heat transmission, friction, and durability. They impact thermal and hydraulic performance. Real-world experiments are needed to validate numerical results and ensure practical implementation. Third, try curved, wavy, helical, or hybrid VGX shapes for thermal enhancement and vortex production. Multi-objective optimization can find the best VGX shape, size, orientation, and position across Reynolds numbers to maximize heat transfer and reduce pressure loss. Study compact or micro-scale PFHE designs with flow limits, transient or high Reynolds flows, and multi-fluid systems using nanofluids or phase-change materials. These studies will improve industrial heat exchanger VGX and personalize them.