Thermal–Fluid Behavior and Heat-Transfer Enhancement in PEMFC Cooling Plates Using Multi-Fin Zigzag Channels Under Variable Slope Angles

Abstract

Effective thermal management is critical for sustaining the performance, durability, and stability of a proton exchange membrane fuel cell (PEMFC). A thorough numerical investigation of six multi-fin zigzag cooling-channel geometries operating under three slope angles (75°, 90°, and 120°) is presented to monitor the combined impact of geometric complexity and channel inclination on cooling performance. In addition, temperature fields, velocity distributions, localized heat flow, total heat removal, and cooling efficiency were reviewed to characterize thermal–fluid behavior of the individual configuration. The results showed that geometric refinement had the strongest influence on cooling performance, with Type 5 (a = 2, b = 4, h = 2) and Type 6 (a = 4, b = 4, h = 2) progressively achieving declining temperature distributions, greater outlet velocities, and modified coolant mixing. Slope angles also affected flow behavior, where reduced inclination extended coolant residence time and elevated inclination intensified secondary flows, although the influence was secondary to geometry. Total heat flow, area-specific heat extraction, and cooling efficiency were highest in Type 5 (a = 2, b = 4, h = 2) and Type 6 (a = 4, b = 4, h = 2), with Type 5 exhibiting an optimal balance between flow disturbance and hydraulic resistance. This study generally presented practical design guidance for next-generation PEMFC cooling systems, proving that optimized multi-fin zigzag channels significantly advanced thermal uniformity and heat-transfer effectiveness under diverse operating conditions.

1. Introduction

Proton exchange membrane fuel cells (PEMFCs) are among the most promising clean energy technologies due to their high efficiency, fast start-up capability, and low environmental impact [1,2,3]. However, PEMFCs are also susceptible to performance degradation during long-term operation. This degradation arises from multiple interacting mechanisms, including catalyst dissolution and agglomeration, electrode material degradation, mechanical damage to the membrane electrode assembly, and fluctuations in operating conditions. Thermal non-uniformity and excessive local temperatures are recognized as key accelerating factors for these degradation processes, as they intensify material aging, promote membrane dehydration, and reduce electrochemical stability. Consequently, effective thermal management plays a critical role not only in enhancing PEMFC performance but also in prolonging durability, reducing maintenance requirements, and lowering lifecycle costs [4]. Despite these advantages, maintaining stable thermal conditions in the PEMFC stack remains a critical challenge [5,6,7]. Irregular or elevated temperatures can deteriorate the membrane, accelerate catalyst degradation, and cause ohmic losses, as well as reduce overall system durability [8,9,10]. Furthermore, temperature inhomogeneity of the cooling plate may affect the liquid water transport behavior of adjacent gas diffusion layers (GDLs) through the thermal conduction gradient, thereby inducing local flooding and exacerbating membrane electrode degradation. This coupling effect needs to be optimized synergistically in the system design. An effective cooling strategy is essential to ensure uniform temperature distribution, safeguard material integrity, and enhance long-term operational reliability [11,12,13]. Among the various thermal management strategies for PEMFCs, air cooling, liquid cooling, phase-change-material-based cooling, and heat-pipe-assisted systems have been widely investigated. Air cooling offers structural simplicity but is limited by its low heat removal capacity, while phase-change and heat-pipe-based approaches can improve thermal buffering but often introduce additional system complexity and volume. In contrast, liquid-cooled plates integrated with optimized flow channels provide a compact and efficient solution capable of achieving high heat removal rates and uniform temperature control, making them particularly suitable for high-power-density PEMFC applications [14,15,16]. Numerous studies have explored temperature management strategies in PEMFC systems. For instance, air cooling has been investigated for low-power applications due to its simplicity, while liquid cooling with serpentine, wavy, or straight channels has been widely used for higher heat flux conditions. Phase-change materials and heat-pipe-assisted cooling were also proposed to address transient thermal loads and improve heat spreading. Recent works have examined variations in cooling-channel geometry, such as sawtooth, zigzag, and multi-fin designs, demonstrating that geometric modification can enhance heat transfer by promoting flow mixing and boundary-layer disruption. However, most of these studies focus on fixed-orientation layouts or single geometric parameters, and do not systematically assess the combined effects of geometric refinement and channel inclination. This gap motivates the present investigation, which examines how slope angle interacts with multi-fin zigzag geometry to influence thermal–fluid performance in PEMFC cooling plates [17].

Following the description above, channel geometry plays a decisive role in determining the heat-transfer capability of cooling plates [18,19,20]. Furthermore, temperature non-uniformity and localized hot spots were caused by the inability of conventional straight or serpentine channels to produce strong coolant mixing [21,22,23]. These limitations were tackled by studying modified channel designs such as wavy, baffled, and zigzag configurations, responsible for boosting greater disturbance-induced mixing and secondary flows [24,25,26]. Compared with wavy channels, zigzag configurations introduce sharper flow redirection that more effectively disrupts the thermal boundary layer and promotes transverse mixing, leading to improved heat transfer uniformity. In contrast to baffled channels, zigzag designs can enhance convective heat transfer without introducing severe flow blockage, thereby achieving a more favorable balance between thermal performance and pressure drop. These characteristics make zigzag channels particularly suitable for compact PEMFC cooling plates, where both efficient heat removal and hydraulic efficiency are critical. Although various zigzag and sawtooth cooling-channel configurations have been widely reported to enhance heat transfer in PEMFC cooling plates [27,28,29], most existing studies primarily focus on geometric modification under a fixed installation orientation. In these works, performance improvement is generally attributed to flow disturbance induced by channel shape, while the effect of channel inclination is either neglected or treated independently. The adoption of multi-fin structures, known to raise surface area, intensify flow disturbances, and heighten coolant–wall interaction, prompted further improvements [30,31,32]. These geometric enhancements were individually reevaluated by innumerable studies, but the combined effect with structural parameters, namely slope angles, had not been carefully reviewed.

Another main factor that regulates coolant behavior in the channel is slope angle. The variations detected in channel inclination changed coolant momentum and adjusted flow direction. This also included the formation of vortices and secondary flows [33,34,35]. Low slope angles raised coolant residence time and heat absorption. However, high slope angles reinforced directional forcing and introduced extra hydraulic resistance [36]. The slope angles of 75°, 90°, and 120° were selected to represent distinct channel inclination regimes. The 90° configuration serves as a baseline reference, while the reduced slope angle (75°) is intended to extend flow residence time and enhance heat exchange. In contrast, the increased slope angle (120°) intensifies flow redirection and secondary flow generation, enabling assessment of the trade-off between enhanced heat transfer and hydraulic resistance. The interaction between channel inclination and multi-fin zigzag geometry was unsatisfactorily revised in existing literature, regardless of the relevance [37]. This research investigated zigzag-based cooling channels without considering how changes in slope angle interact with geometric complexity to influence coolant residence time, secondary flow formation, and heat-transfer uniformity. As a result, the coupling effect between channel geometry and tilt angle remains insufficiently explored, despite its practical relevance for PEMFC stacks installed under non-horizontal conditions. The understanding of this coupled effect played an essential role in the design of next-generation cooling plates that could sustain high performance under differing operating conditions in PEMFC [38,39,40]. Recent research further emphasizes that the coordinated control of cooling plate geometry, such as fin or channel combinations and slope angle, is crucial for overcoming thermal management bottlenecks [41]. The serrated multi-fin structure designed in this paper is a practical exploration of this paradigm. When operated without an active cooling system, PEMFCs can experience a significant temperature rise due to electrochemical heat generation and ohmic losses. Previous studies have reported that cell temperatures may exceed 340–360 K under moderate to high current densities, leading to membrane dehydration, non-uniform reaction rates, and accelerated material degradation. In practical PEMFC operation, an optimal temperature range of approximately 333–353 K is generally recommended to balance proton conductivity, water management, and overall durability. Based on the authors’ experimental observations, operating temperatures above this range result in noticeable thermal non-uniformity and performance deterioration, underscoring the importance of effective thermal management. When a PEMFC operates without an effective cooling system, the cell temperature can increase significantly due to reaction heat generation and ohmic losses. Several studies have reported that PEMFC temperatures may exceed 330–350 K under high current density operation in the absence of adequate cooling, which can accelerate membrane dehydration, catalyst degradation, and overall performance decay. In contrast, the optimal operating temperature range for PEMFCs is generally reported to be approximately 333–353 K, where favorable electrochemical kinetics, membrane hydration stability, and durability can be maintained. Therefore, maintaining the cell temperature within this optimal range through an appropriate cooling strategy is essential for ensuring stable performance and long-term reliability of PEMFC systems.

This study engaged in a systematic numerical investigation of six multi-fin cooling-channel geometries reviewed under three representative slope angles (75°, 90°, and 120°), to bridge the knowledge gap. The key thermal–fluid characteristics, including temperature distribution, velocity field development, localized and total heat flow, alongside the total cooling efficiency, were mainly explored. The assessment of geometric complexity and inclination angle initiated the identification of the design features that greatly induced coolant mixing, temperature uniformity, and heat-removal effectiveness. The applied method incorporated exhaustive CFD simulations to monitor the flow dynamics in zigzag channels, as well as to evaluate the performance of the specific configuration. The results offered constructive insights into advancing PEMFC cooling-plate design. It also showed that geometric refinement predominantly in Types 5 and 6 intensely supported coolant mixing, modifying thermal uniformity across the channel. Additionally, the influence of slope angle was observed to differ depending on geometric complexity, with optimal heat-transfer performance realized when both parameters were adequately combined. A comprehensive framework was fabricated to advance PEMFC thermal management as well as support the promotion of practical design guidelines. The essence was to advance high-efficiency cooling channels capable of reinforcing long-term, stable PEMFC operation.

Despite extensive research on zigzag and multi-fin cooling channels for enhancing heat transfer in PEMFC applications, the combined influence of channel geometry and slope angle on thermal behavior has not been sufficiently explored. Most existing studies focus on planar geometries or fixed channel orientations, while the effect of channel inclination relative to gravity is often neglected despite its potential impact on flow redistribution, secondary flow formation, and heat removal effectiveness. Consequently, the interaction between geometric refinement and slope angle remains insufficiently understood, particularly for compact PEMFC thermal management systems. To address this gap, the present study systematically evaluates the combined influence of multi-fin zigzag geometry and variable slope angles (75°, 90°, and 120°). Six channel configurations with increasing geometric refinement are analyzed to quantify their marginal contribution to temperature uniformity, heat removal rate, and flow behavior under different inclinations. This approach enables a direct assessment of how slope-induced secondary flows interact with geometric disturbances, thereby extending previous sawtooth-channel studies toward a more comprehensive and application-oriented cooling design strategy.

2. Materials and Methods

2.1. PEMFC Stack Architecture and Cooling Channel Arrangement

The cooling configuration fitted into the PEMFC stack is shown in Figure 1. The system consisted of anode and cathode plates, including a multilayer membrane assembly. In addition, the assembly comprised the catalyst and gas diffusion layers alongside the central proton-conducting membrane. A reserved cooling plate was placed adjacent to the anode and cathode plates to monitor the temperature that evolved during electrochemical reactions. The specific cooling plate featured a zigzag channel pattern devised to augment convective heat transfer. This was realized by stimulating secondary flow structures and flow mixing along the coolant path. Furthermore, the geometric configuration prompted the elimination of heat from the active reaction zone. The essence was to manage the operational temperature in the anticipated range, which enabled the sustenance of stable PEMFC performance.

2.2. Experimental Setup

The essence of the experimental setup was to monitor the thermal behavior of a single PEMFC featuring a zigzag cooling system. Additionally, the fundamental test unit constituted the compact PEMFC with an active area of 20.25 cm². Graphite-based bipolar plates, a Nafion^® 212 membrane (DuPoint, Wilmington, DE, USA), and Pt/C catalyst layers at the electrodes comprised the cell components. The heat evolved during fuel cell operation was regulated by a reserved cooling plate characterized by multi-fin zigzag channels screwed on each side. The preference of this geometric arrangement was a result of improved coolant mixing and heat transfer performance.

The whole cooling plate assembly was fixed at varying inclination angles to detect the impact of the slope angle on cooling efficiency. The delivery of coolant through zigzag channels at regulated flow velocities inspired the examination of the flow rate and gravity-induced redistribution impact. The temperature was further regulated with a set of calibrated K-type thermocouples fixed at strategic inlet and outlet locations. This simplified the assessment of axial temperature variations along the coolant path. Meanwhile, the gas flow rates, system pressure, and electrical output used during the entire experiment were detected with supplementary sensors. The entire measurements were gathered through an integrated data acquisition system to ascertain reliable and synchronized recording. This setup presented a controlled environment for reevaluating the joint effect of coolant velocity and channel slope on heat removal. Furthermore, the setup certified that the acquired data was associated with numerical predictions from the CFD model.

All experimental data were recorded after the PEMFC reached steady-state operating conditions. Temperature, pressure, and electrical output were continuously monitored, and the reported values represent time-averaged measurements obtained under stable conditions rather than instantaneous single-point readings. Measurement uncertainty was evaluated using standard error propagation methods. The combined uncertainties were estimated to be ±2% for flow rate, ±0.5 K for temperature measurement, and ±3% for calculated efficiency. Thermocouple measurements were used as reference data to assess the reliability of the numerical temperature predictions.

2.3. Calculation for Heat Transfer in Cooling System

The heat transfer pattern detected across the cooling plate of PEMFC is shown in Figure 2. In this context, the heat from the membrane electrode assembly was directed outward toward both sides of the cell. The heat was further delivered to cooling channels, where thermal energy passing through the zigzag passage was absorbed by the coolant. Figure 2 shows the manner in which the heat flux penetrated the cooling system from the active avenue of the fuel cell, migrating toward the coolant stream. Subsequently, coolant moves from the inlet, continuing to the outlet, as it progressively eliminates heat from the plate, leading to the establishment of a temperature gradient in the flow direction. The distribution process exhibited the significance of the geometry of the channel, including coolant flow rate, in sustaining steady temperature control and prohibiting the formation of hot spots in PEMFC.

2.3.1. Cooling System Heat (${\dot{Q}}_{cooling system}$)

The quantity of $Q_{thermal}$ transferred from the fluid to the cooling system was calculated using Equation (1):

$${\dot{Q}}_{cooling system}=\dot{m} C_p ∆T$$

(1)

where ${\dot{Q}}_{cooling system}$ is thermal energy transferred to the cooling system [W], $\dot{m}$ refers to the mass flow rate outlet [kg/s], $C_p$ denotes the heating capacity of fluid [kJ/kg·K], and $∆T$ depicts the temperature difference between outlet and inlet fluid [K]. In this circumstance, the following were applied: inlet velocity is 3 m/s; T₁ = 293 K; outlet temperature, $T_{out}$, is obtained from the result of the simulation, $\dot{m}$ (the mass flow rate for each cell calculated from outlet velocity, surface area of cooling system, and density); and $C_p$ is determined depending on the average temperature of the cooling system.

2.3.2. Convective Heat Transfer (${\dot{Q}}_{convection}$)

The convection heat transfer was calculated using Equation (2):

$${\dot{Q}}_{convection}=h A ∆T$$

(2)

where ${\dot{Q}}_{convection}$ is convection heat transfer [W], $h$ depicts the heat convection coefficient [W/m²·k], $A$ refers to the area of the cooling system [m²], $∆T$ represents the temperature difference between the surface of the cooling system and fluid [K]. For fluid velocity 3 m/s, T₁ = 328.13 K, T₂ = 293 K, $h$ = 120 W/m²·k (for gas), and $A$ = 0.002025 m²; as a result, ${\dot{Q}}_{convection}$ = 8.54 W.

2.3.3. Cooling System Efficiency

Cooling system efficiency was used to determine its functionality in reducing the high temperature of the PEMFC. Furthermore, the efficiency could be increased depending on the lower temperature. The efficiency $\left(\eta \right)$ was determined using Equation (3).

$$\eta ={\displaystyle \frac{{\dot{Q}}_{cooling system}}{{\dot{Q}}_{convection}}}\times 100\%$$

(3)

2.4. Parameter of Manifold and Cooling Channel

The main geometric and operating parameters of the manifold and cooling channels were defined prior to running the simulations. The dimensions of cooling passages and the manifold configuration used to maintain uniformity across all test conditions are shown in

Table 1. Parameters for cooling system.

Parameter	Value
Channels per cell	5–9
Channel length (representative)	45 mm
Coolant	Air
Coolant density	1.165 kg/m3
Coolant viscosity	1.86 × 10−5 Pa·s
Coolant cp	1.04 kJ/kg·K
Velocity Inlet	3 m/s
Mean channel velocity	≈2.86 m/s
Reynolds number	≈2.45
Estimated ΔP (per channel, L = 45 mm)	≈2.5 kPa

. The preference for a parallel-flow layout, uniting 5 to 9 identical square channels in each cell, eased fabrication, certifying stable flow distribution. These geometric specifications, including the associated fluid properties, were applied uniformly in CFD boundary settings and experimental arrangements.

The geometric and flow parameters used for the cooling system are shown in Table 1. The individual PEMFC united 5 to 9 square cooling channels, using a representative channel with a length of 45 mm. However, air served as the working fluid, with its thermophysical properties, namely density, viscosity, and specific heat capacity, expressed according to standard conditions. The inlet velocity was set at 3 m/s, which led to an average velocity of roughly 2.86 m/s detected in cooling passages. Under the diverse reported conditions, the corresponding Reynolds number was 2.45, representing laminar flow in the channels. The decline in pressure was estimated to be 2.5 kPa per channel over the 45 mm length. The distinct parameters served as the basis for the numerical simulation and experimental evaluation of cooling performance.

2.5. Numerical Method

Preliminary studies on PEMFC cooling stated that numerical analysis concentrated on the adoption of computational procedures. The essence was to certify that the present model was reliably compared with existing validated results. Meanwhile, the three-dimensional model geometry was introduced into ANSYS Fluent Workbench 2024 R2, equipped with the PEMFC add-on module. The SIMPLE algorithm was adopted for the pressure–velocity coupling because of its strength in steady-state simulations, including incompressible flow. The pressure field was resolved with the aid of a semi-implicit formulation, and all equations, including momentum, energy, and species transport discretized using second-order schemes to advance accuracy.

The multigrid strategy, in conjunction with the F-cycle acceleration procedure, enriched numerical stability and lowered computation time. Bi-Conjugate Gradient Stabilized (BCGSTAB) solver triggered iterative convergence for the species equations and the prospective electrochemical fields on the anode and cathode. Moreover, the numerical framework and solver settings closely adhered to initially verified CFD studies, as well as those reported by Fahruddin et al. [41], which served as a reference for validating the accuracy of the formulated simulation approach. The complete numerical parameters and operating conditions used are shown in

Table 2. Simulation result of PEMFC without a cooling system.

Information	Value
Initial velocity	3 m/s
Initial temperature of cathode	333.33 K
Average temperature after reaction	340.41 K
Minimum temperature	332.88 K
Maximum temperature	378.57 K
Current density	8723.41 A/m2
Power density	5670.21 W/m2

.

PEMFC refers to an energy-conversion device known to utilize a proton-conducting membrane to create electricity through the hydrogen and oxygen electrochemical reaction. A series of operating and structural parameters were monitored during numerical simulations of PEMFC to offer deeper insight into the general performance of the cell.

2.5.1. Geometry Model

Cooling plate geometry was obtained from a zigzag multi-fin, multi-channel configuration fabricated to enrich coolant mixing and heat transfer, with the schematic layout shown in Figure 3. In addition, the active cooling region had a size of 45 mm × 45 mm, with a respective flow channel possessing a width of 1.0 mm. The zigzag pattern with an angle of 45° stimulated flow disturbances, which led to heightened convection effectiveness in the channels. The outer corners of the plate featured a 4 mm radius, responsible for reducing mechanical stress concentrations and aiding manufacturing ease. Moreover, the inlet and outlet manifolds were situated at the edges of the plate to confirm homogeneous coolant distribution across the zigzag channel network. A detailed compilation of geometric parameters in conjunction with dimensions a, b, and c is shown in

Table 3. Geometric parameters of zigzag multi-fin/multi-channel cooling plate.

Parameter	Value
Plate length	45 mm
Plate high	45 mm
Corner radius	4 mm
Channel width	1.0 mm
Zigzag variation	a	b	h	c
Type 1	1	1	2	45°	90°	120°
Type 2	1	2	2	45°	90°	120°
Type 3	1	4	2	45°	90°	120°
Type 4	2	2	2	45°	90°	120°
Type 5	2	4	2	45°	90°	120°
Type 6	4	4	2	45°	90°	120°
Material	Aluminum
Fabrication process	CNC milling

.

The base material used was aluminum, considering the high thermal conductivity, low weight, and machinability, which made it ideal for PEMFC cooling applications. Furthermore, the plate was factory-made with CNC milling to certify reliable channel dimensions. A brief analysis of zigzag multi-fin/multi-channel plate geometric parameters is shown in Table 3. The cooling plate was characterized by a 45 mm × 45 mm active area with 4 mm rounded corners, to improve manufacturability and stimulate easier flow distribution. The individual channel possessed an even width of 1.0 mm, permitting the cooling system to deliver steady airflow across all configurations. Meanwhile, six zigzag variations were fabricated by changing the amplitude (a), fin spacing (b), and zigzag height (h), presumed to regulate the quantity of flow disturbance and thermal augmentation in the channels. The three slope angles (c = 45°, 90°, and 120°) of the individual configuration were studied to monitor how channel inclination affected the heat-removal performance of the cooling system. Aluminum, characterized by its high thermal conductivity, was selected as the plate material, and all components were machined with CNC milling to certify dimensional accuracy.

2.5.2. CFD Method System

A structured hexahedral mesh was generated for the cooling plate domain, with finer grid spacing applied around the channel walls and fin surfaces to ideally capture thermal and velocity gradients. Mesh-independence testing was performed using three grid densities: approximately 200,000 cells (coarse), 400,000 cells (medium), and 800,000 cells (fine), which were evaluated by comparing average plate temperature and pressure drop. The medium mesh was selected for subsequent simulations because its predicted temperature and pressure distributions differed by less than 2% from those of the fine mesh, while requiring significantly lower computational time. Although the Reynolds numbers considered in this study fall within the laminar regime, the complex multi-fin zigzag geometry induces strong velocity gradients, flow separation, and secondary flow structures. Therefore, the realizable k–ε model with enhanced wall treatment was employed to improve numerical robustness and capture geometry-induced flow disturbances, rather than to represent fully developed turbulence. This configuration was commonly recommended for heat-transfer analysis in PEMFC cooling channels. A uniform coolant velocity and an initial temperature of 3 m/s and 293 K, respectively, were imposed at the inlet. In this context, the outlet boundary was defined as a pressure outlet. Additionally, all solid boundaries were treated as no-slip surfaces, and material properties were assumed to be constant throughout the computation.

In this research, A uniform inlet velocity of 3 m/s and an inlet temperature of 293 K were imposed [37]. The outlet was defined as a pressure outlet, and a constant heat flux was applied at the cooling plate wall. In the present study, a uniform heat flux boundary condition was applied at the cooling plate wall to represent the average heat generation from the PEMFC active area. Although heat generation in an operating PEMFC is inherently non-uniform, with localized peaks in the catalyst reaction zones, the use of a constant heat flux is a commonly adopted simplification in cooling-plate-focused numerical studies. This assumption allows for a consistent and fair comparison of different cooling channel geometries and slope angles under identical thermal loading conditions. The objective of this work is to evaluate the relative cooling performance and thermal uniformity associated with geometric refinement and channel inclination, rather than to reproduce detailed electrochemical heat generation. The influence of spatially non-uniform heat sources and fully coupled electrochemical–thermal modeling is therefore identified as an important direction for future work.

Although the experimental geometry in ref. [41] differs from the present zigzag multi-fin design, the validation focuses on the consistency of global thermal parameters, such as temperature distribution trends and pressure drop, under comparable operating conditions. Although the Reynolds numbers considered in this study fall within the laminar regime, the complex multi-fin zigzag geometry introduces strong velocity gradients, flow separation, and secondary flow structures that significantly enhance fluid mixing and heat transfer. In this context, the realizable k–ε model was employed to improve numerical robustness and capture disturbed flow behavior induced by geometric complexity, rather than to represent fully developed turbulence. Similar modeling approaches have been adopted in previous PEMFC cooling studies involving complex channel geometries operating at low Reynolds numbers.

A simulation was considered converged once the residuals for momentum, continuity, energy, and turbulence equations decreased below 10⁻⁶, as well as when monitored outputs, particularly pressure drop and outlet temperature, varied by less than 0.1% over the last 100 iterations. The reliability of the numerical approach was ensured by cross-checking the modeling strategy with the experimental and numerical data presented by Fahruddin et al. [41], who examined flow structures in PEMFC cooling plates with internal baffles. The results showed similar patterns of coolant temperature rise and pressure loss, with deviations in ±5%, thereby confirming the adequacy of the CFD method used. The validation focuses on temperature trends and pressure drop consistency rather than exact geometric replication. In addition, the role of thermocouple measurements as reference data for assessing numerical temperature predictions has been emphasized.

2.5.3. Model Validation Using Experimental Results

The key performance indicators derived from the numerical model were paralleled with corresponding experimental data, as shown in

Table 4. Validation of simulation and experiment results of PEMFC.

PEMFC Model	Parameter	Flow Rate	Simulation	Experiment	Error (%)
PEMFC (Without Cooling System)	Cathode temperature of bipolar plates	3 m/s	340.41 K	342.10 K	0.494
	Power density		5670.21 W/m2	5853.54 W/m2	3.131
PEMFC and Triple Channel Cooling System	Cathode temperature of bipolar plates	3 m/s	326.96 K	327.3 K	0.104
	Power density		7564.38 W/m2	7440.24 W/m2	−1.668
	Efficiency of cooling system		55.33%	54.51%	−1.498
PEMFC and Multiple Fin Channel Cooling System	Cathode temperature of bipolar plates	5 m/s	328.75 K	326.58 K	−0.664
	Power density		7954.19 W/m2	7942.15 W/m2	−0.152
	Efficiency of cooling system		67.04%	65.77%	1.931
PEMFC and Cooling System	Outlet temperature	5 m/s	314.8 K	316.0 K	−0.38
	Average temperature		312.2 K	313.5 K	−0.41
	Cooling efficiency		82.70%	83.50%	−0.96
	Pressure drop		68.4 Pa	70.2 Pa	−2.56

, to certify the validation process. The simulation for PEMFC featuring a triple-channel cooling system using a 20% ethylene-glycol working fluid at an inlet velocity of 3 m/s forecasted a power density of 7564.39 W/m². Meanwhile, PEMFC operating without any cooling system produced roughly 5853.54 W/m². This depicted a performance increase of about 1710.85 W/m², which proved that the integration of a flow-based cooling system at 3 m/s effortlessly eliminated excess heat and maintained elevated electrochemical output. In addition, the cooling system greatly dropped the cathode-side temperature. The bipolar plate temperature measured in the no-cooling condition reached 340.41 K, while the cooled configuration had a temperature of 326.96 K, implying a reduction of roughly 13.45 K. The advancement was a result of the heat-removal capability of the ethylene-glycol-based cooling system. This aided in regulating stable thermal conditions, decreased thermal loading on the materials, thereby contributing to upgraded operational efficiency.

Further validation was performed at an elevated cooling system flow velocity of 5 m/s, using experimental data reported by Fahruddin et al. [41]. Under the innumerable conditions, the simulation presumed an outlet and average plate temperatures of 314.8 K and 312.2 K, respectively, with a cooling efficiency and pressure drop of 82.7% and 68.4 Pa. The simulated values fell within ±3% of the experimental results, implying an ideal correlation between the numerical model and reference measurements. These results proved that the cooling system supported firm thermal performance at heightened flow velocities, advancing heat removal, and aiding in stabilizing the operating temperatures. The validation outcomes generally showed that the application of a liquid-based cooling system with flow rates between 3 and 5 m/s greatly raised PEMFC thermal and electrical performances. The decline in temperature (typically around ±20 K) and efficiency upgrade of 40–55% were in line with formerly published work. This certified that the proposed cooling strategy, reinforced by numerical analysis and experimental comparison, effortlessly upgraded PEMFC performance while sustaining stable cathode operation for future fuel cell applications.

3. Results and Discussion

3.1. Temperature, Velocity, and Heat Flow Under Baseline Condition (Slope Angle c = 90°)

This subsection performed a thorough review of the temperature distribution, velocity field, and heat-flow characteristics obtained under the baseline configuration, with a slope angle of 90°. The baseline results instituted a reference condition that permitted thermal–fluid behavior of the cooling system to be monitored prior to exploring the channel inclination effects or executing geometric modifications. In Figure 4, the temperature distribution for the six cooling-plate configurations was in a relatively narrow range of 293–328 K, implying that the entire system supported a homogenous thermal environment under the given operating conditions. The internal geometric dissimilarity among the configurations triggered discrete temperature patterns across the cooling surface, irrespective of the relationship in the entire temperature range. Types 1 and 2 represented significant even gradients, implying that respective fin arrangements triggered the spreading of heat with fewer localized temperature variations.

The heightened geometric complexity in Types 3 and 4 led to the detection of more pronounced regions of localized cooling. These were depicted by the enlarging blue zones in the temperature contours. The areas with improved heat transport as a coolant are efficiently related to the channel walls. The trend was plainly observed in Types 5 and 6, where larger portions of the cooling surface experienced a drop in temperature values. This reduction replicated heat-removal capability advancement from sharper zigzag transitions and occasional directional alterations in coolant flow. Meanwhile, Type 6 was characterized by the most compelling cooling performance under the baseline slope angle, as represented by the prevalent low-temperature regions across the domain. This showed that the aggressive geometric features triggered superior coolant mixing and thermal extraction, leading to the consideration as the most effective design for heat dissipation under the baseline condition. The average temperature of outlets is 308.82 °C, 309.99 °C, 309.75 °C, 305.87 °C, 306.35 °C and 300.06 °C for Types 1, 2, 3, 4, 5, and 6, respectively.

Velocity fields in Figure 5 expressed that the individual zigzag configuration formulated a distinct flow pattern in cooling channels. However, in the simpler layouts (Types 1 and 2), coolant chiefly progressed at lower velocities, implying decreased internal mixing and a smoother, homogenous flow path. The designs stimulated fewer disturbances along the channel walls, which restricted interaction between the fluid and fin surfaces. The increase in fin spacing and zigzag amplitude in Types 3 through 5 led to the varying nature of velocity contours. The result showed firmer flow disturbances and heightened active coolant–wall engagement. This behavior was linked to recurrent directional alterations imposed by the channel geometry, responsible for inducing localized acceleration zones and modest recirculation regions that contribute to the mixing process.

A more pronounced shift was observed in the Type 6 configuration, with innumerable high-velocity streaks detected in the coolant path. The sharper bends and firmer fin spacing deepened secondary flows, namely vortices and rotational motion, which raised disturbance-induced mixing in the channels. The flow features were beneficial for heat transfer, permitting the breakdown of thermal boundary layers, including the even distribution of coolant across the heated surfaces. Based on this perspective, Type 6 disseminated the most effective convective heat transfer and coolant circulation among the analyzed configurations. The average velocity of outlets is 2.64 m/s, 2.85 m/s, 3.22 m/s, 3.45 m/s, 3.79 m/s, and 4.81 m/s for Types 1, 2, 3, 4, 5, and 6, respectively.

Figure 6 shows the relationship between the outlet temperature and velocity, in conjunction with the channel-wise heat transfer characteristics for the six multi-fin geometries at the baseline slope angle of c = 90°. The outlet temperature profiles in Figure 6a showed noticeable variation across the varying configurations, exhibiting the effect of fin spacing and zigzag intensity on convection strength. Types 1 and 2 had relatively stable temperature values with slight fluctuations detected between channels, signifying delicate heat extraction capability. However, Types 5 and 6 exhibited reduced outlet temperatures across virtually all channels, with Type 6 obtaining the maximum pronounced reduction. This behavior depicted that sharper zigzag transitions and restricted fin spacing fostered firmer coolant–wall interactions, permitting an enormous portion of the heat generated in PEMFC to be expelled before exiting the system.

The outlet velocity distributions in Figure 6b further elaborated on the interpretation process. Types 3 through 6 depicted an increase in flow velocities compared to 1 and 2. Type 6 showed peak velocities across several outlet channels. Additionally, elevated exit velocities improved flow acceleration caused by channel constriction and amplified mixing in zigzag paths. This behavior promoted heat-transfer performance, as raised disturbance induced mixing and secondary flow structures interrupted thermal boundary layers established along cooling-plate walls. As a result, the coolant monitored hotter core regions, permitting excessive heat to be conveyed downstream. The trend was in line with the results of the channel-wise heat flow in Figure 6c, where Type 6 obtained the maximum heat-transfer rates for the entire outlet channels. An upgraded performance was exhibited by Types 4 and 5 compared to the easier geometries. However, Type 6 gradually showed superior thermal extraction. The enormous heat flow in this configuration was associated with the ability to generate more uniform flow distribution, reduce velocity dead zones, and maintain stronger shear interaction along fin surfaces. The three subfigures jointly clarified that extreme geometric complexity with sharper zigzag angles and lowered fin spacing boosted the cooling system fluid-dynamic and thermal behavior. This progress prompted PEMFC applications to sustain steady temperature, as well as led to the prohibition of localized hot spots directly affecting membrane hydration, catalyst durability, and total power output.

This section reviewed the effect of the six zigzag multi-fin configurations on thermal and flow characteristics under the baseline slope angle of 90°. The results proved that the entire temperature range was the same across all types. Geometric complexity also changed the distribution of local heat. Simpler geometries (Types 1 and 2) reproduced steady but less effective cooling. The intermediate types (Types 3 and 4) improved heat spreading caused by stronger flow disturbances. The most complex designs (Types 5 and 6) steadily promoted coolant mixing, elevated flow velocity, and channel-wise heat flow. Furthermore, Type 6 represented the strongest performance, offering the fewest temperature zones and the most vigorous internal flow. This certified that fin complexity advanced thermal management under baseline conditions.

3.2. Effect of Low and High Slope Angle on Temperature, Velocity, and Heat Flow Distribution

Cooling channel slope angle enabled the determination of coolant mixing intensity and the entire thermal–fluid performance of the PEMFC system. The adjustment of the channel inclination modified coolant direction, centrifugal forces acting in zigzag passages, and the formation of secondary flow structures. The innumerable effects were explored by performing simulations at two representative slope angles: namely, the low (c = 75°) and high-angle configurations (c = 120°). Regarding this perspective, the low-angle configuration led to the triggering of extended flow paths and milder redirection of the fluid. The high-angle configuration initiated sharper turns that built up flow disturbance, which affected heat removal in a different way. This section studied the impact of several geometric variations on the resulting temperature distributions, velocity fields, and channel-wise heat transfer.

The temperature contours for the six zigzag multi-fin configurations at the lower slope angle of 75° are shown in Figure 7. The entire values were in the range of 293 to 328 K. However, the spatial distribution was extremely sensitive to the geometric details. In Types 1 and 2, the contours remained stable, implying that modest zigzag profiles generated restricted advancement of heat extraction under reduced inclination. The designs sustained vast regions of moderate temperature with slight gradient fluctuations, indicating that coolant flow was largely undisturbed. When transitioning to Types 3 and 4, it was observed that more pronounced cooling regions started to evolve. The stretched blue contours signal modified thermal transport because of heightened directional changes in the coolant path. This deteriorated thermal boundary layer, as well as elevated interaction between coolant and channel walls. The modification process was evident in Types 5 and 6, where cooling zones greatly extended across the entire domain. In Type 6, the intensified zigzag geometry propelled coolant through occasional accelerations and firmer directional shifts, which led to vigorous mixing and effective heat removal. The extensive dark-blue temperature regions showed that Type 6 monitored the lowest and most stable temperature field among all configurations under the 75° slope angle. These observations proved that a decline in slope angle amplified the influence of fin geometry, allowing sharper zigzag patterns to more effectively drive coolant–wall interaction. Accordingly, the Type 6 design implied excellent thermal performance, which certified channel inclination and geometric complexity as essential factors in realizing effective PEMFC cooling.

The temperature field across the cooling plate was subjected to greater changes than the lower-angle configuration when the slope angle was increased to 120°. In Figure 8, Types 1 and 2 gradually depicted relatively even temperature gradients, despite the slight drop in cooling effect compared to the 75° case. This decline was caused by the steeper channel inclination, which drove coolant to undergo abrupt directional changes. The procedure further deteriorated the stability of the thermal boundary layer, affecting the distribution of coolant flow across the fins.

In Types 3 and 4, a well-defined contrast was detected between warmer and cooler regions, suggesting that the sharper zigzag profile firmly correlated with the intensified flow redirection. The contours extended regions of moderate cooling. This implied that while the mixing procedure progressed relative to simpler geometries, the maximum slope angle initiated extra flow resistance that affected uniform heat dispersion. A distinctive development was detected in Types 5 and 6, where the temperature contours displayed enormous and more continuous regions with lesser values. In the Type 6 configuration, the elevated geometric complexity functioned synergistically with the steep slope angle, resulting in the most robust cooling performance among all designs. The more aggressive zigzag features drove dynamic coolant agitation, which escalated coolant–wall interaction, as well as causing a drop in thermal buildup across the fin surfaces. The extensive blue areas in the Type 6 contour showed steady elimination of heat. This configuration countered the extra flow resistance triggered by the higher slope angle. The results certified that although a 120° slope angle enforced firmer directional changes on the coolant, it can still enhance thermal performance when paired with an optimized multi-fin geometry. For that reason, Type 6 evolved as the most capable design in driving steady cooling, causing a drop in temperature gradients at heightened channel inclination.

Velocity contours in Figure 9 showed that reducing the slope angle to 75° changed coolant motion in zigzag channels, with well-defined distinctions among the six geometric types. In this context, Types 1 and 2 showed relatively low and stable velocity magnitudes across the domain, which reflected the simpler fin arrangements that presented limited disturbance to the coolant path. The designs generated smoother flow trajectories with slight acceleration zones, which led to insubstantial secondary flow structures and a drop in disturbance-induced mixing. As the geometry transitioned to Types 3 and 4, velocity contours exhibited a rise in small-scale variations, reflecting deeper interactions between coolant and channel walls.

The modified zigzag pattern suggested recurrent directional changes, which confined acceleration, resulting in moderate mixing in the channel. The effects disturbed flow uniformity and upgraded coolant distribution than the easier configurations. The impact of geometry was greatly pronounced in Types 5 and 6, where remarkably higher velocity regions were observed in the cooling domain. Type 6 represented extensive zones of heightened velocity magnitudes linked to intensified flow disturbances and secondary motion. These features emanated from the firmer fin spacing and sharper zigzag curvature, which drove coolant to repeatedly speed up as it navigated the channel turns. The resulting disturbance induced mixing triggered coolant mixing as well as lowered stagnant regions, sustaining the steady flow supply in the entire cooling plate. Additionally, the presence of innumerable high-velocity streaks in Type 6 proved that this configuration triggered fluid agitation and momentum transport under low-angle conditions. The trends in Figure 9 showed that complexity and channel inclination firmly governed the development of internal flow structures, with Type 6 geometry achieving the most effective coolant circulation among the examined designs.

The coolant pathway was steeper when the slope angle was increased to 120°, and this caused abrupt directional shifts and tighter momentum redistribution in the channels. Velocity fields in Figure 10 depicted that Types 1 and 2 generated relatively modest velocity magnitudes, with the majority of the regions exhibiting low to moderate flow intensity. The simpler zigzag patterns in the configurations reproduced inadequate disturbances, and this led to the inability to induce substantial secondary flows, thereby causing smoother trajectories and reduced mixing. Several pronounced velocity variations evolved from the channel domain, as the geometric complexity heightened in Types 3 and 4. The sharper zigzag angles subjected the coolant to recurrent accelerations, resulting in the formulation of localized higher velocity pockets. The diverse flow behaviors improved interaction between coolant and channel walls, which tended to strengthen internal mixing than the low-angle case. Substantial improvement in flow activity was observed in Types 5 and 6. In addition, the Type 6 configuration built extensive regions of heightened velocity magnitudes, evidenced by consistent high-intensity bands across the cooling plate. The integration of aggressive zigzag geometry and steep slope angle drove fluid agitation, advancing firm vortex formation and secondary flow structures reported to improve turbulence. The features aided in disintegrating low-velocity stagnant zones to certify even distribution of coolant momentum. The high-velocity streaks evident in Type 6 proved that the geometry sped up coolant flow under the 120° slope condition. Consequently, Type 6 showed the greatest potential for upgrading convective heat transfer. This ascertained that the synergistic effect of steep inclination and increased geometric complexity was critical in amplifying cooling-channel performance.

The trends of the outlet temperature in Figure 11a showed typical distinctions among the six configurations under the low-angle condition. Types 1 and 2 upheld relatively high and stable temperatures across all outlet channels, representing restricted thermal extraction capability caused by simpler zigzag patterns. The gentle turns led to feeble coolant–wall interaction, leading to modest cooling effectiveness. Types 3 and 4 exhibited slightly improved thermal behavior, with a drop recorded in outlet temperatures across the channels. This improvement arose from elevated zigzag amplitude, responsible for initiating robust coolant motion and advanced local heat transport. The most outstanding temperature decline was reported in Types 5 and 6. Based on this perspective, in Type 6, the outlet temperatures were gradually reduced across the channel range. The result proved that sharper geometric variations at a 75° inclination boosted stronger heat elimination. This was achieved by intensifying coolant mixing as well as raising the convective heat transfer. The observation was further reinforced by the outlet velocity distributions in Figure 11b. Types 1 and 2 had the least exit velocities, certifying that the respective geometries prompted reduced flow acceleration. However, Types 3 and 4 showed outstanding velocity rise triggered by enhanced directional forcing in the channels. The main improvement was detected in Types 5 and 6, with Type 6 obtaining the maximum velocity peaks across the outlets. The increased velocities represented intensified internal mixing and lowered flow stagnation, responsible for modifying the entire heat-transfer process. The heat-flow trends in Figure 11c reflected the outlet temperature and velocity distributions. Furthermore, Types 1 and 2 featured minimum heat-flow outputs, implying that the restricted coolant agitation declined convective energy transport to the exits. As geometric complexity heightened, Types 3 and 4 showed moderate improvements, with heat flow rising in the numerous channels. This reportedly showed that homogenous moderate zigzag enhancements supported coolant–wall interactions, resulting in effective thermal extraction. The most pronounced heat-flow performance was evident in Type 5, specifically Type 6. This configuration steadily delivered maximum heat-flow values, verifying that the sharper fins and intensified zigzag pattern adequately modified coolant mixing and energy dissipation. Moreover, under the low slope angle condition, Type 6 reproduced the most exceptional combination of cooling uniformity, flow acceleration, and thermal transport.

The outlet temperature distributions in Figure 12a exhibited noticeable changes when the slope angle was raised to 120°. Types 1 and 2 sustained relatively high temperatures in most outlet channels. This showed that respective moderate zigzag patterns were inadequate to overcome the extra flow resistance introduced by the steeper inclination. Coolant felt firmer directional shifts at the high slope angle, which tended to disrupt heat elimination in simpler geometries. Types 3 and 4 had reduced outlet temperatures compared to 1 and 2, proving that heightened geometric complexity modified heat dissipation despite the steeper channel orientation. The most outstanding improvement was evident in Types 5 and 6, where outlet temperatures remained lower in the channel. Type 6 specifically had the firmest cooling capability, with the temperature decline more pronounced compared to the low-angle case. This showed that the sharper zigzag pattern conformed with a high slope angle, thereby upgrading the coolant–wall interaction.

The results of the outlet velocity in Figure 12b were in line with these observations. Types 1 and 2 featured the minimum exit velocities, which certified the restricted ability to accelerate coolant flow under steep inclination. The modification of geometric complexity enabled Types 3 and 4 to present noticeably higher velocities, thereby showing improved flow agitation and lowered stagnation. The maximum velocity peaks were evident in Types 5 and 6, with Type 6 achieving adequate flow enhancement. The tighter velocity distribution reflected intensified internal mixing, which managed low outlet temperatures by raising convective heat transfer. The heat-flow patterns in Figure 12c adhered to a similar trend evident in the values of the temperature and velocity. Types 1 and 2 had the least heat-flow values across all outlet channels, showcasing restricted thermal transport and deteriorating convective performance. Meanwhile, Types 3 and 4 showed moderate improvement, with heat flow rising in conjunction with the modified coolant acceleration made by respective sharper geometric profiles. The most considerable heat-flow enhancement was detected in Types 5 and 6, representing the exceptional ability to dissipate heat under the high-angle setting. In Type 6, the progressively raised heat-flow values in all channels certified that the integration of steep slope angle and aggressive zigzag geometry exploited coolant mixing and energy removal. The results implied that while a high slope angle triggered flow resistance, it greatly modified cooling performance when paired with adequately complex fin geometry. This made Type 6 the most productive configuration for high-angle operation.

The shallow channel orientation fostered the formation of reverse-flow regions in a zigzag pathway, at a low slope angle of 75°. The recirculation zones triggered hydraulic resistance, leading to a notable pressure drop in the cooling channel. Moreover, as coolant flow decelerated and felt greater opposition, the ability to expel heat deteriorated, and this led to heightened outlet temperatures. The process proved that excessively low slope angles compromised cooling effectiveness by lowering velocity and raising pressure losses.

Although the thermal performance of the Type 5 and Type 6 configurations is commonly evaluated in terms of temperature reduction and cooling efficiency, their superior behavior can be attributed to enhanced secondary flow structures induced by the multi-fin zigzag geometry. The presence of closely spaced fins combined with abrupt directional changes generates strong velocity gradients near the channel walls, which intensify shear layers and promote the formation of streamwise vortical structures. These secondary flows enhance fluid mixing by continuously disrupting the thermal boundary layer and increasing local flow intensity, particularly in regions downstream of fin junctions and zigzag turns. As a result, heat transfer between the cooling-channel walls and the working fluid is significantly improved, leading to enhanced thermal uniformity and heat removal in the Type 5 and Type 6 configurations. Compared to simpler geometries, the increased geometric complexity sustains stronger flow recirculation zones and more uniform heat extraction along the channel length, explaining their optimal cooling performance despite a moderate increase in hydraulic resistance. Overall, the results of this section demonstrate that geometric refinement through multi-fin zigzag structures plays a dominant role in enhancing PEMFC cooling performance, while providing a clear physical basis for selecting Type 5 and Type 6 configurations as optimal designs.

3.3. Total Heat Flow, Heat Flow of Each Area, and Efficiency of Cooling System

The previous subsections centered on the temperature field, velocity distribution, and channel-wise heat transfer behavior under varying slope angles and geometric configurations. Considering that these local thermal–fluid characteristics offered valuable insight into coolant movement and heat removal at certain cooling plate regions, a thorough analysis should explore the entire heat-transfer capacity of the system. This subsection concentrated on three main performance indicators, namely (i) the entire heat flow expelled from the cooling plate, (ii) the heat flow supplied by the individual surface region, and (iii) the resulting cooling efficiency of the respective configuration.

The total heat flow portrayed the cumulative thermal energy delivered by the coolant from the whole domain. This presented a direct assessment of the global cooling performance. The heat flow distribution in diverse areas (e.g., central region, zigzag fin surfaces, and inlet/outlet zones) presented insight into how effectively the individual geometric type monitored localized thermal loads. This was essential for evading hotspots in PEMFC. Additionally, the cooling efficiency metric quantified the effectiveness of each configuration in converting coolant motion into useful thermal removal. The process served as a practical indicator for design optimization. The following analyses compared the six geometric types with respect to various slope angles. The essence was to discover the combinations that produced the most favorable cooling performance.

The total heat flow distributions in Figure 13 pinpointed an upward trend as the geometric complexity rose from Type 1 to 6. For the three slope angles, Types 1 and 2 had the minimum heat-flow values, depicting that the relatively simple zigzag arrangements offered restricted coolant agitation and feeble convective performance. As the fin geometry transitioned to Types 3 and 4, the overall heat flow was raised considerably. This represented the positive impact of modified zigzag amplitude on coolant mixing and thermal extraction. The sharper channel transition and reinforced surface area fostered stronger coolant–wall interactions, allowing excessive heat to be conveyed from the cooling plate to the flowing fluid. The improvement was consistently monitored across the entire slope angles, showing the important role of geometric refinement in improving cooling capacity.

The most pronounced performance gains were detected in Types 5 and 6, under the 90° and 120° slope angles. Type 5 realized the maximum total heat flow, specifically at the baseline condition (c = 90°). Additionally, thermal-extraction capability reached its peak due to balanced mixing intensity and flow resistance. Type 6 also exhibited a strong performance, although it slightly declined at 120° compared to 90°, due to heightened flow resistance. This was caused by the incorporation of steep inclination and extremely intricate geometry. However, both Types 5 and 6 consistently surpassed the simpler designs, confirming that enhanced fin complexity dramatically improved global heat-transfer efficiency. The results depicted that the geometric shape had a more dominant effect on total heat flow than slope angle. In this context, the slope angle could either reinforce or slightly reduce cooling performance depending on the degree of flow redirection introduced.

The area-wise heat-flow trends in Figure 14 showed a consistent increase in heat-removal capability as the geometric complexity intensified from Types 1 to 6. Furthermore, in Types 1 and 2, the heat flow from each surface area remained relatively low across all slope angles, reflecting the limited coolant mixing and lower interaction between the fluid and fin surfaces. The easy zigzag patterns failed to generate the strong flow disruptions needed to activate effective convective heat transfer. As the geometry transitioned to Types 3 and 4, the contributions made by the heat flow from the individual area increased noticeably. The improvement was attributed to the modified zigzag amplitude and extended fin surface, which triggered firmer directional changes in the coolant path and raised the shear interaction with cooling walls. Furthermore, the localized modifications in heat flow across these configurations reported that moderate geometric refinement boosted the capacity of the system to extract heat from the PEMFC cooling plate. The highest area-specific heat flows were monitored in Types 5 and 6, under the 90° slope angle condition. Type 5 progressively showed the highest values, representing an optimal balance between coolant acceleration, geometric sharpness, and flow resistance. The sharper zigzag patterns established intensified secondary flows that swept heat away from the fin surfaces. Type 6 further delivered strong thermal performance, although the heat flow gradually declined at the 120° slope angle. This was caused by the integrated impact of steep inclination and extremely intricate geometry, responsible for introducing extra flow losses. Types 5 and 6 outperformed the easier geometries in all operating angles, certifying that localized heat removal was firmly managed by fin complexity. These results proved that the design of fin geometry played a dominant role in modifying area-specific heat flow than merely slope angle alone. Optimal performance was reported when the factors acted synergistically.

As shown in Figure 15, cooling efficiency rose progressively alongside geometric complexity. This followed a similar trend detected in the entire heat and area-specific heat flows. Meanwhile, Types 1 and 2 demonstrated the least efficiency in all slope angles, with the remaining being less than 15%. The limited zigzag features achieved insufficient internal mixing. This fostered the weak coolant–wall interaction and lowered convective heat transfer. Types 3 and 4 showed an outstanding modification, with efficiencies rising in the range of 20–35% depending on the slope angle. The rise depicted the advanced coolant acceleration and directional changes introduced by the more pronounced zigzag geometry, lowered thermal resistance, and enhanced heat extraction. The moderate enhancements showed that incremental geometric adjustments greatly supported cooling performance. Meanwhile, the maximum cooling efficiencies were found in Types 5 and 6, with Type 5 exhibiting the total optimum performance, specifically under the baseline slope angle (c = 90°), where efficiency was greater than 50%. The result proved that Type 5 reached an effective balance between flow mixing intensity and hydraulic resistance. Type 6 also performed strongly, although it felt a gradual decline in efficiency at the highest slope angle of 120°. The decrease was caused by elevated flow losses linked to the steeper redirection of coolant, combined with the extremely complex fin pattern. Both configurations delivered greater efficiencies compared to the easier types, certifying that geometric refinement was the dominant factor regulating cooling effectiveness. The results reflected that while slope angle modified the strength of secondary flows, optimized multi-fin geometry was the main driver of high cooling efficiency in PEMFC systems.

This section concentrated on reviewing the global performance metrics of the cooling system, namely total heat flow, area-specific heat removal, and cooling efficiency. Elevating geometric complexity generated clear gains in all metrics, with Types 5 and 6 outperforming the easier designs with respect to all slope angles. Type 5 delivered the maximum total heat flow and efficiency, specifically at the 90° slope angle. This was attributed to the firm balance existing between coolant mixing and flow resistance. Type 6 exhibited the same absolute performance, and the efficiency gradually reduced at the steepest angle (120°), caused by added hydraulic losses. The results confirmed that geometric refinement had a greater impact on global cooling performance than slope angle. The synergy of fin shape and inclination was essential for realizing optimal PEMFC thermal management. From a stack-level perspective, the improved cooling performance observed in this study has important implications for PEMFC operation. A more uniform temperature distribution across the cooling plate helps maintain stable membrane hydration, which is critical for sustaining proton conductivity and minimizing local voltage losses. In addition, reduced temperature gradients lower the risk of thermal stress and material degradation, contributing to improved durability and long-term reliability of PEMFC stacks. Although the present work focuses on single-cell cooling behavior, the demonstrated enhancements in heat removal and thermal uniformity are directly applicable to multi-cell stack configurations, where effective thermal management is essential for achieving uniform voltage output and stable operation. The summary of the results is shown in

Table 5. Summary of thermal fluid performance of multi-fin zigzag cooling channels under different slope angles.

Type	Geometry (a–b–h)	Slope Angle (°)	Temperature Distribution	Flow Behavior	Heat Transfer and Cooling Performance	Overall Assessment
Type 1	a = 1, b = 1, h = 2	75/90/120	Relatively high and non-uniform temperature	Low velocity, weak disturbance	Lowest heat flow and cooling efficiency	Least effective design
Type 2	a = 1, b = 2, h = 2	75/90/120	Slightly improved uniformity vs. Type 1	Mild flow redirection	Marginal heat-transfer improvement	Limited enhancement
Type 3	a = 1, b = 4, h = 2	75/90/120	Moderate temperature reduction	Increased velocity and mixing	Moderate increase in heat flow	Transitional performance
Type 4	a = 2, b = 2, h = 2	75/90/120	Improved thermal uniformity	Stronger secondary flows	Higher area-specific heat removal	Good balance
Type 5	a = 2, b = 4, h = 2	75/90/120	Low and uniform temperature field	Strong mixing, stable velocity	Highest total heat flow and peak efficiency (especially at 90°)	Optimal configuration
Type 6	a = 4, b = 4, h = 2	75/90/120	Lowest temperature but locally sensitive	Very high velocity, intense vortices	High heat transfer but increased pressure drops	High performance with higher hydraulic loss

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4. Conclusions

In conclusion, the thermal and flow behavior of PEMFC cooling systems was explored by adopting six multi-fin channel geometries under diverse slope angles. The main findings gathered from temperature distribution, velocity profiles, and heat-transfer performance were summarized as follows. These presented practical guidance for optimizing PEMFC cooling-channel design.

• Increasing fin complexity enormously modified thermal–fluid behavior of the cooling system. Types 5 and 6 produced stronger coolant mixing and greater velocity magnitudes, which translated into superior heat-transfer performance. The results showed that geometric design played the major role in certifying cooling effectiveness.
• Complex zigzag configurations gradually reproduced lower and more homogeneous temperature distributions in the cooling plate. This uniformity suppressed the formation of hot spots, which were responsible for stable PEMFC operation. Types 5 and 6 represented the most gradual temperature decline in all slope angles.
• Sharper zigzag paths triggered occasional coolant redirection, which led to maximum velocities and intensified secondary flow structures. The flow patterns triggered internal mixing and lowered stagnant regions in the channels. Type 6 layout exhibited the strongest capability for accelerating coolant flow.
• At a low slope angle of 75°, reverse-flow regions started to build up in the zigzag channel, raising pressure drop and deteriorating coolant velocity, which led to increased outlet temperatures. However, the 120° configuration fostered stronger forward flow and better mixing, advancing heat removal compared to the 75° case. The influence of slope angle was still secondary compared to the effect of channel geometric complexity.
• Types 5 and 6 delivered the peak heat flow, area-specific heat expulsion, and cooling efficiency in all operating conditions. In addition, Type 5 exhibited the most balanced performance, particularly at the 90° slope angle, where efficiency reached its peak. The results showed that advanced multi-fin channels were the most effective configurations for improving PEMFC cooling performance.

From an engineering perspective, the temperature reduction achieved by the optimized zigzag multi-fin cooling configurations has important implications for PEMFC durability and system efficiency. The literature indicates that a 10–15 K decrease in operating temperature can significantly slow membrane degradation and potentially extend membrane lifetime by approximately 1.5–2 times. In this study, temperature reductions of about 13–20 K were obtained, suggesting a meaningful contribution to long-term operational stability. Although geometric refinement increases pressure drop, the maximum value of approximately 2.5 kPa results in an estimated pumping power penalty of less than 1–2% of the net electrical output, indicating a favorable trade-off between thermal enhancement and auxiliary power consumption. Overall, the proposed multi-fin zigzag cooling design, particularly Types 5 and 6, provides improved temperature uniformity, enhanced heat transfer, and acceptable hydraulic losses, offering practical design guidance for efficient and durable PEMFC thermal management systems.