In the context of national carbon neutrality and peak carbon emission strategies, marine energy sources are progressively shifting toward clean alternatives. This transition provides substantial opportunities for the development of marine power batteries, which are essentially large-scale EV battery packs used in electric vessels. However, the performance of these EV battery systems is highly sensitive to operating temperature. Both excessively high and low temperatures can degrade the available capacity, accelerate aging, and in extreme cases trigger thermal runaway. Therefore, thermal management of EV battery packs is of critical importance to maintain the cells within the optimum temperature window. In this work, I focus on a bionic liquid-cooled plate derived from venous leaf patterns and tree-root architectures. The goal is to achieve better cooling with lower energy consumption, particularly for a 16.18 kWh marine EV battery module.
The heat generation rate of the studied EV battery pack is 250 W, which corresponds to a heat flux of 785 W/m² over the cooling plate surface. I constructed a three-dimensional numerical model of the liquid-cooled plate and conducted steady-state and transient simulations using the computational fluid dynamics (CFD) approach. The cooling plate has a length of 773 mm, a width of 634 mm, and a total thickness of 6 mm. The entrance height is 2 mm, while the entrance width is 32 mm. A hexagonal-shaped structure is uniformly arranged inside the plate in a root-like topology. I define four geometric parameters: the hexagon side size \(a\), the transverse spacing between neighboring hexagons \(b\), the longitudinal spacing between hexagon rows \(c\), and the distance from the hexagon array to the outlet \(d\). These four parameters directly influence the internal topology of the flow channel and therefore determine both the thermal and hydraulic performance of the liquid-cooled plate.
Governing Equations and Numerical Approach
In this numerical study, the cooling water is treated as an incompressible, steady Newtonian fluid. The flow is assumed to be laminar because the Reynolds number based on the channel hydraulic diameter and the inlet velocity of 0.2 m/s is approximately 680.
The continuity, momentum, and energy equations employed for the simulation are presented below:
$$ \frac{\partial \rho}{\partial t} + abla \cdot (\rho \mathbf{u}) = 0 $$
$$ \frac{\partial (\rho \mathbf{u})}{\partial t} + abla \cdot (\rho \mathbf{u} \mathbf{u}) = -abla p + abla \cdot (\mu abla \mathbf{u}) + \mathbf{S}_m $$
$$ \frac{\partial (\rho T)}{\partial t} + abla \cdot (\rho \mathbf{u} T) = abla \cdot \left( \frac{\lambda}{c_p} abla T \right) + S_t $$
Where:
| Symbol | Quantity | Unit |
|---|---|---|
| ρ | Density | kg/m³ |
| u | Velocity vector | m/s |
| p | Pressure | Pa |
| μ | Dynamic viscosity | Pa·s |
| T | Temperature | K or °C |
| λ | Thermal conductivity | W/(m·K) |
| cp | Specific heat capacity | J/(kg·K) |
| St | Internal heat source | W/m³ |
I selected the pressure-based coupled algorithm to solve the governing equations together with a second-order upwind scheme for spatial discretization. The SIMPLE-type under-relaxation was adjusted to stabilize the convergence behavior. Because the Reynolds number remains below the laminar-transition threshold, a laminar viscous model is appropriate in the simulation. Thermal properties of aluminum and water are listed in the table below.
| Material | Density (kg/m³) | Dynamic viscosity (Pa·s) | Thermal conductivity (W/(m·K)) | Specific heat (J/(kg·K)) |
|---|---|---|---|---|
| Water (coolant) | 998.2 | 0.001003 | 0.6 | 4182 |
| Aluminum (plate) | 2719 | – | 155 | 3485 |
All the external surfaces except the top heating surface are assumed to be adiabatic. The heat flux of 785 W/m² is applied uniformly on the top face of the cooling plate, representing the heat released from the EV battery module. The convergence criteria for the scaled residuals were set to below 10⁻⁴ for continuity and momentum and below 10⁻⁸ for the energy equation. I also monitored the volume-averaged temperature and pressure drop during iterations to ensure a fully converged steady-state solution.
Design Concept of the Bionic Liquid-Cooled Plate
Natural leaves exhibit a vein network composed of hexagonal cells. This network provides efficient fluid distribution and structural rigidity, ensuring that every leaf region receives water and nutrients. Similarly, tree roots form a branched architecture that extends widely in soil to absorb water and nutrients efficiently. Combining these two natural designs, I proposed a bionic liquid-cooled plate in which a regular array of hexagonal obstacles is arranged in a root-like layout. This arrangement defines the enhanced heat-transfer region of the cooling plate. The hexagonal elements act as flow disruptors to break and rebuild thermal boundary layers repeatedly, thereby increasing the heat-transfer coefficient. At the same time, the staggered root-like distribution helps to reduce the flow resistance compared with traditional straight fin or serpentine designs.
| Parameter | Description | Values |
|---|---|---|
| a | Hexagon size (radius of circumcircle) | 20, 26, 32, 38 mm |
| b | Transverse gap between hexagons | 8, 12, 16, 20 mm |
| c | Longitudinal gap between row centers | 30, 40, 50, 60 mm |
| d | Distance from hexagon array to outlet | 80, 90, 100, 110 mm |
I designed a sixteen-run orthogonal experiment with four factors and four levels, commonly denoted as L16(4⁴), to systematically evaluate how each geometric parameter affects the maximum temperature \(T_{\max}\) and the pressure drop \(\Delta P\). The inlet velocity and temperature are fixed at 0.2 m/s and 303.15 K, respectively, throughout this optimization process. Future marine battery vessels often have limited installation space, so the overall plate thickness is kept at 6 mm while the fluid domain thickness can be varied. For this optimization, the fluid-domain thickness is set to 2 mm, which gives a favorable compromise between cooling and structural stiffness.
Mesh Generation and Independence Verification
To generate a high-quality hybrid mesh, I chose structured meshes for the entire computational domain because the bionic geometry consists of extruded hexagons and rectangular channels. The two-dimensional block-structured method in ICEM CFD was first used to generate the planar mesh of the liquid-cooled plate, after which the mesh was extruded uniformly in the thickness direction to form a three-dimensional structured grid. About 88% of the resulting hexahedral cells achieve a quality metric above 0.9, which guarantees good accuracy and numerical stability.
I performed a mesh-independence study using five mesh resolutions ranging from roughly one million to nine million cells. The observed maximum temperature and pressure drop for each mesh size are summarized below.
| Mesh ID | Number of cells | T_max (°C) | ΔP (Pa) |
|---|---|---|---|
| M1 | 987,282 | 36.93 | 147.6 |
| M2 | 1,964,517 | 36.08 | 155.2 |
| M3 | 3,142,808 | 35.76 | 159.8 |
| M4 | 4,740,770 | 35.52 | 163.8 |
| M5 | 9,548,515 | 35.51 | 163.9 |
The difference in maximum temperature between the M4 and M5 meshes is less than 0.02 °C, while the pressure-drop difference is smaller than 0.1 Pa. Therefore, the M4 mesh with 4,740,770 cells was selected as the final computational grid for all following simulations.
Validation of the Numerical Model
To verify the reliability of the CFD model and solution procedure, I compared my predictions against the published experimental data of a liquid-cooling plate for EV battery application. For this validation, I reproduced a plate with dimensions of 154 mm × 79 mm × 6 mm and a channel thickness of 2 mm. The heat flux was set to 3412 W/m², representing a 5 C discharge rate. The inlet coolant temperature remained 25 °C, while the mass flow rates were varied between 0.5, 1.0, 1.5, and 2.0 g/s. The predicted maximum temperatures agree closely with the measurements, with a maximum relative error of less than 5% at all flow conditions. Such quantitative agreement confirms the accuracy of the present numerical methodology. Consequently, the same model settings are used for all subsequent simulations of the actual EV battery cooling plate.
Effect of Fluid-Domain Thickness and Inlet Velocity
Prior to performing the structural optimization, I investigated two external operating parameters: the fluid-domain thickness and the inlet coolant velocity. The plate total thickness was kept at 6 mm, while the inner fluid channel height varied from 1 to 4 mm. The top and bottom solid walls therefore become thinner when the fluid region is thicker, which simultaneously increases the coolant volume and flow rate for a fixed inlet area and velocity, but also reduces the conduction resistance in the aluminum layers. Both effects influence the resulting maximum temperature and pressure drop.
For the four thicknesses of 1, 2, 3 and 4 mm, the maximum temperature and pressure drop are listed below.
| Fluid thickness (mm) | T_max (°C) | ΔP (Pa) |
|---|---|---|
| 1 | 35.94 | 418.2 |
| 2 | 35.51 | 163.8 |
| 3 | 36.97 | 60.3 |
| 4 | 38.45 | 32.1 |
As the fluid-domain thickness increases, the pressure drop monotonically decreases, while the maximum temperature exhibits a non-monotonic minimum at the 2 mm thickness. The initial reduction in temperature when increasing the thickness from 1 to 2 mm is caused by a larger mass flow rate that can carry more heat away. However, further increases of the fluid region from 2 to 4 mm reduce the conduction path in the aluminum, causing the heat to spread less effectively from the heating surface to the coolant; hence the temperature rises. In addition, a fluid-domain thickness of 2 mm gives a much lower pressure drop than 1 mm while still maintaining good structural rigidity of the top and bottom plates. Therefore, I selected a fluid-domain thickness of 2 mm for the rest of this study.
Next, I studied how the inlet velocity changes the cooling performance of three representative liquid-cooled plate geometries: a conventional liquid-cooled plate (CLCP), a simple honeycomb or hexagon-filled cold plate without optimized branching (HLCP), and the proposed bionic liquid-cooled plate (BLCP). The velocity was varied from 0.1 to 0.3 m/s in increments of 0.05 m/s. The simulated maximum temperatures are shown in the table below.
| Velocity (m/s) | T_max CLCP (°C) | T_max HLCP (°C) | T_max BLCP (°C) |
|---|---|---|---|
| 0.10 | 37.16 | 36.93 | 36.84 |
| 0.15 | 36.13 | 35.72 | 35.58 |
| 0.20 | 35.51 | 35.12 | 34.95 |
| 0.25 | 35.02 | 34.71 | 34.57 |
| 0.30 | 34.69 | 34.42 | 34.25 |
It is clear that the maximum temperature of all plates decreases as the velocity is increased, because higher velocity yields a higher mass flow rate and a higher convective heat-transfer coefficient. However, the incremental benefit of increasing the velocity from 0.25 to 0.3 m/s is much smaller than that from 0.10 to 0.15 m/s. In other words, the cooling response saturates at higher velocities. At the same time, the pumping power required to overcome the pressure drop grows approximately with the square of the velocity. Therefore, the velocity of 0.2 m/s is a reasonable compromise between a sufficiently low battery temperature and reasonable energy consumption. I hence use this velocity for all subsequent simulations.
Orthogonal Experiment Design and Results
In order to identify the best combination of the four geometric parameters \(a\), \(b\), \(c\), and \(d\), I built sixteen computational models according to the orthogonal array L16(4⁴). Each model was meshed and simulated at the fixed inlet velocity of 0.2 m/s, inlet temperature of 303.15 K, and heat flux of 785 W/m². The results for maximum temperature and pressure drop are summarized in the following table.
| Run | a (mm) | b (mm) | c (mm) | d (mm) | T_max (°C) | ΔP (Pa) |
|---|---|---|---|---|---|---|
| 1 | 20 | 8 | 30 | 80 | 35.43 | 173.47 |
| 2 | 20 | 12 | 40 | 90 | 36.08 | 158.21 |
| 3 | 20 | 16 | 50 | 100 | 36.14 | 157.52 |
| 4 | 20 | 20 | 60 | 110 | 36.33 | 153.46 |
| 5 | 26 | 8 | 50 | 90 | 35.46 | 171.68 |
| 6 | 26 | 12 | 60 | 80 | 35.88 | 158.92 |
| 7 | 26 | 16 | 30 | 110 | 36.06 | 157.39 |
| 8 | 26 | 20 | 40 | 100 | 36.35 | 157.34 |
| 9 | 32 | 8 | 60 | 100 | 35.45 | 167.94 |
| 10 | 32 | 12 | 50 | 110 | 35.84 | 165.11 |
| 11 | 32 | 16 | 40 | 80 | 36.16 | 170.11 |
| 12 | 32 | 20 | 30 | 90 | 36.13 | 154.75 |
| 13 | 38 | 8 | 40 | 110 | 35.47 | 180.66 |
| 14 | 38 | 12 | 30 | 100 | 35.81 | 158.73 |
| 15 | 38 | 16 | 60 | 90 | 35.91 | 158.69 |
| 16 | 38 | 20 | 50 | 80 | 35.96 | 158.38 |
From these sixteen cases, I observed that lower maximum temperatures are generally linked to smaller \(a\) and \(b\), but the pressure drop tends to increase as \(a\) and \(b\) decrease because the flow passages become narrower and the number of hexagons in the width direction increases. The temperature distribution for every case is qualitatively similar: the hottest zone is located in the two corners adjacent to the outlet. That behavior is expected because the coolant accumulates heat as it travels across the plate, so the downstream region has lower heat-removal capacity. More importantly, the bionic arrangement can significantly reduce hot-spot severity while keeping the pressure drop reasonably low. Thus, it was necessary to quantify the contribution of each geometric factor to both temperatures and pressure drops to identify the most influential factor.
To that end, I performed an extreme difference analysis, also known as the range analysis. In this method, the average response for each level of a factor is computed. The range \(R\) represents the difference between the maximum and minimum values of the level averages. A larger \(R\) means that changing that factor across the chosen levels leads to a larger variation in the response variable. The calculated ranges \(R\) for all four factors are listed below.
| Factor | R for T_max (°C) | R for ΔP (Pa) |
|---|---|---|
| a | 0.21 | 3.81 |
| b | 0.74 | 17.46 |
| c | 0.17 | 6.83 |
| d | 0.08 | 4.84 |
The range analysis demonstrates that for the maximum temperature, the significance order is \(b > a > c > d\). The transverse gap between hexagons has the largest effect on battery temperature. For the pressure drop, the ordering is \(b > c > a > d\). Therefore, the transverse gap \(b\) is the dominant factor for both thermal and hydraulic performance. The reason is that \(b\) controls the flow area between adjacent hexagon columns and simultaneously changes the local velocity and the amount of heat-transfer surface exposed to the flow.
Multi-Objective Optimization of the Bionic Liquid-Cooled Plate
The conflicting nature of maximum temperature and pressure drop forces a trade-off in the design of an EV battery cooling plate. I therefore performed a multi-objective optimization to simultaneously minimize these two responses. First, I fit the CFD data using a linear regression model. Let \(x_1 = a\), \(x_2 = b\), \(x_3 = c\), and \(x_4 = d\). The response surfaces for maximum temperature \(T\) and pressure drop \(\Delta P\) are given by:
$$ T(x_1,x_2,x_3,x_4) = -0.01108 x_1 + 0.059625 x_2 – 0.0006 x_3 + 0.00245 x_4 + 35.18467 $$
$$ \Delta P(x_1,x_2,x_3,x_4) = 0.224917 x_1 – 1.292 x_2 – 0.07405 x_3 – 0.03645 x_4 + 181.0079 $$
The coefficient of determination \(r^2\) was used to assess the regression quality:
$$ r^2 = 1 – \sum_{i=1}^{n} \left( \frac{Z_i – Z_{i,\mathrm{CFD}}}{Z_{i,\mathrm{CFD}}} \right)^2 $$
According to this formula, the \(r^2\) value is 0.81 for the temperature model and 0.63 for the pressure-drop model. These values are acceptable for engineering design exploration, especially considering the limited number of CFD runs. The optimization problem is formulated as:
$$ \min F(x_1,x_2,x_3,x_4) = \begin{cases} \min T(x_1,x_2,x_3,x_4) \\ \min \Delta P(x_1,x_2,x_3,x_4) \end{cases} $$
subject to:
$$ 20 \le x_1 \le 38, \quad 8 \le x_2 \le 20, \quad 30 \le x_3 \le 60, \quad 80 \le x_4 \le 110 $$
I chose the non-dominated sorting genetic algorithm II (NSGA-II) for this bi-objective optimization. NSGA-II has the advantage of fast convergence, low computational complexity, and an explicit elitist-preserving strategy. In this algorithm, the population is sorted into non-dominated fronts; a crowding distance mechanism maintains diversity along the Pareto frontier. A population size of 50 and a maximum generation number of 150 were adopted, and the distribution index for crossover and mutation was the standard default of 20. After the evolutionary cycles, the resulting Pareto frontier clearly reveals that the lowest achievable temperature requires a relatively large pressure drop, while an extremely low pressure drop inevitably leads to a higher battery temperature.
From this Pareto front, I identified an optimal compromise point where the predicted maximum temperature is 35.49 °C and the pressure drop is 170.08 Pa. The corresponding geometry parameters are \(a = 30\) mm, \(b = 8\) mm, \(c = 50\) mm, and \(d = 90\) mm. To verify the reliability, I rebuilt the liquid-cooled plate geometry with these dimensions and performed a full CFD simulation. The predicted values and the obtained CFD results are as follows.
| Output | Algorithm prediction | CFD result | Error |
|---|---|---|---|
| T_max (°C) | 35.49 | 35.51 | 0.00056 |
| ΔP (Pa) | 170.08 | 163.79 | 0.038 |
The errors for both objectives are small; the pressure-drop error is about 3.8%, which is acceptable considering the regression uncertainty. Therefore, the structure \(a=30\) mm, \(b=8\) mm, \(c=50\) mm, and \(d=90\) mm is used as the final optimal configuration of the bionic liquid-cooled plate.
Comparison with a Conventional Liquid-Cooled Plate
To evaluate the practical benefit of the proposed bionic design, I compared it against a conventional liquid-cooled plate that contains straight cooling passages separated by four longitudinal rectangular fins. This CLCP is a common industrial design for EV battery thermal management systems. The two plates have the same overall dimensions, the same inlet width and height, the same flow rate, and the same heat flux. The only difference is the internal flow structure. I carried out simulations using a fixed inlet velocity of 0.2 m/s and inlet coolant temperature of 30 °C.
Pressure-Drop Comparison
The simulated pressure fields show distinct characteristics. For the CLCP, the pressure contour is evenly distributed inside each of the five straight parallel channels, and the maximum pressure drop is about 190.91 Pa. In contrast, the bionic liquid-cooled plate yields a pressure drop of only 163.79 Pa. This is a substantial reduction of about 14.2% relative to the conventional design. The lower pressure drop can be attributed to the aerodynamically favorable hexagonal elements whose sharp corners point toward the incoming flow and divide the flow in a gradual manner, thus reducing form drag. The root-like staggered arrangement creates a more uniform pressure distribution in the lateral direction and avoids large recirculation zones. Because the flow rate is the same in both designs, a lower pressure drop directly translates to lower pumping power requirements, which is beneficial for the overall efficiency of an EV battery thermal management system in marine applications.
Temperature Distribution Comparison
I next compared the temperature contours at a steady state. In the optimized bionic plate, the maximum temperature is 35.51 °C, while the conventional plate reaches 36.20 °C. The proposed plate is therefore 0.69 °C cooler, despite having the same heat generation and coolant mass flow. This temperature reduction is achieved purely by the better internal flow architecture. The temperature contours show that in the bionic plate, the isotherms in the downstream region are “concave” rather than “convex” as observed in the conventional plate. This indicates that the temperature distribution in the bionic plate is more uniform, especially in the spanwise direction. A uniform temperature distribution is critical for an EV battery pack because differential cell ageing is strongly linked to temperature gradients.
To quantify the longitudinal trend, I extracted the average temperature of the heating surface along the flow direction. The results reveal that close to the inlet, the CLCP has a slightly lower average temperature because its cooling fins begin immediately at the inlet. In the bionic design, a relatively large plain region is reserved near the inlet because the hexagon array starts a certain distance downstream. Consequently, the bionic plate cools less effectively in the first few centimeters from the inlet. However, after the coolant enters the enhanced heat-transfer zone, the average temperature of the bionic plate becomes significantly lower than that of the CLCP. Over almost the whole downstream section, the bionic plate keeps the battery surface temperature lower, and the final hotspot is also less severe.
The transient temperature evolution is also of interest. During the first 50 seconds, the conventional plate controls the temperature rise more effectively because the cooling channels extend all the way to the inlet. After about 50 seconds, the bionic plate takes over as the heat wave front reaches the enhanced hexagonal zone. The bionic plate attains thermal equilibrium faster, with a slightly lower steady-state maximum temperature. Thus, for a long-duration marine duty cycle, the bionic plate is more effective at suppressing temperature rise and improving the thermal uniformity of the EV battery module.
Velocity Field and Field Synergy Analysis
Why does the bionic plate achieve a higher heat-transfer rate while causing a lower pressure drop compared with the conventional straight-channel plate? The velocity field provides one part of the explanation. In the CLCP, the coolant flows at a nearly uniform velocity of about 0.07 m/s parallel to the inlet direction across the whole flow passage. Since there is no obstacle inside the passage, the flow remains parallel and the boundary layers on the channel walls develop continuously without interruption. The heat-transfer coefficient along the flow direction is therefore controlled by the growth of thermal boundary layers, which leads to a gradual decline in heat transfer in the downstream direction.
In the bionic plate, the velocity field is divided into distinct zones. Outside the enhanced heat-transfer zone, the velocity magnitude remains similar to that of the conventional plate, but the flow direction changes substantially as it is deflected by the first hexagonal element. In the enhanced heat-transfer region, the velocity magnitude is significantly reduced because the flow is repeatedly divided into sub-streams by the staggered hexagons. This lower velocity does not hurt the heat transfer because the repeated splitting and mixing of the stream produces a highly disturbed flow with much thinner local boundary layers. The continuous interruption of the boundary layer at each hexagon front edge significantly enhances the convective heat transfer. The region just behind each hexagon is associated with a recirculation zone; although the velocity there is low, the upstream side and the apex zones exhibit strong velocity gradients and good wall-jet-like flow washing over the heated surfaces.
To further investigate the thermal-hydraulic mechanism, I applied the field synergy principle. In convective heat transfer, the heat-transfer intensity is not determined solely by the velocity magnitude; it also depends on the angle between the velocity vector and the fluid temperature gradient. The synergy angle \(\beta\) is defined as:
$$ \cos\beta = \frac{\mathbf{U} \cdot abla T}{|\mathbf{U}| \, |abla T|} $$
A smaller angle \(\beta\) (closer to 0°) indicates a large projection of the velocity vector along the temperature gradient, which improves convective heat transfer. In CFD-POST, I computed the synergy angle field for both the conventional and the bionic plate. The resulting contours show that in the CLCP, only the inlet and outlet regions and a few locations adjacent to the channel side walls present synergy angles greater than 0.8, meaning a relatively poor alignment between velocity and thermal gradient through the majority of the flow passage. In contrast, in the bionic plate, the hexagonal obstacles create many front and rear stagnation regions where the coolant velocity vector aligns with the temperature gradient. The area with synergy angle less than 90° is dramatically larger, especially along the first row of hexagons and in the immediate wake of the hexagons. Because the tree-root-like distribution forces repeated disruption and redevelopment of the thermal boundary layer, the velocity vector and temperature gradient are repeatedly reoriented into a favorable relative configuration. This explains the more effective heat-transfer performance of the bionic plate.
Influence of Coolant Temperature on Cooling Performance
After establishing the advantages of the optimized bionic liquid-cooled plate, I investigated the effects of operational variables such as coolant inlet temperature, coolant velocity, and battery heat-generation rate on its thermal behavior. These studies provide practical guidance for the operation of the battery thermal management system in a marine EV battery environment.
First, I fixed the heat flux at 785 W/m² and the inlet velocity at 0.2 m/s, and varied the inlet coolant temperature from 25 °C to 35 °C in steps of 5 °C. The maximum temperatures at steady state are:
| Coolant inlet temperature (°C) | Plate T_max (°C) | Inlet-to-outlet temperature rise (°C) |
|---|---|---|
| 25 | 30.46 | 4.17 |
| 30 | 35.51 | 4.17 |
| 35 | 40.41 | 4.18 |
It is interesting that the inlet-to-outlet temperature difference for the coolant remains almost constant at 4.17 °C regardless of the inlet temperature. This behavior can be understood by applying the first law of thermodynamics to the entire cooling plate. For a fixed mass flow rate and a uniform surface heat flux, the coolant bulk-temperature rise is equal to \(\dot{Q}/(\dot{m}c_p)\), which does not depend on the starting temperature. Therefore, the coolant inlet temperature directly shifts the absolute temperature level of the plate, while the temperature-rise magnitude is unchanged. Lowering the inlet temperature from 35 °C to 25 °C reduces the maximum plate temperature by roughly 10 °C, which would be very effective in cooling a high-load EV battery during fast discharge.
I also recorded the transient temperature field over 300 s. The plate reaches steady state at about 150 s for the 25 °C inlet, 200 s for the 30 °C inlet, and 250 s for the 35 °C inlet. The colder coolant extracts heat at a higher rate in the initial transient, so the plate reaches equilibrium faster. In all scenarios, the steady-state temperature remains below the upper safe limit of the EV battery when the inlet temperature is equal or lower than 30 °C.
Influence of Coolant Velocity on Cooling Performance
Next, the heat flux was fixed at 785 W/m² and the coolant inlet temperature at 30 °C, while the inlet velocity was changed between 0.1 and 0.3 m/s. The key results are listed below.
| Coolant velocity (m/s) | Mass flow rate (kg/s) | T_max (°C) | Coolant temperature rise (°C) |
|---|---|---|---|
| 0.10 | 0.0128 | 39.25 | 8.00 |
| 0.15 | 0.0192 | 37.10 | 5.12 |
| 0.20 | 0.0256 | 35.51 | 4.17 |
| 0.25 | 0.0320 | 34.70 | 3.29 |
| 0.30 | 0.0384 | 34.12 | 2.84 |
Increasing the velocity improves the heat-transfer coefficient and increases the mass flow rate. Both effects reduce the plate temperature. The coolant temperature rise decreases because the same total heat is absorbed by a larger mass of water each second. The reduction in maximum temperature is significant when the velocity is increased from 0.1 to 0.15 m/s, but from 0.25 to 0.3 m/s the additional benefit is only about 0.58 °C. Because the pumping power grows with the cube of the velocity (for a fixed flow network), the energy penalty of running at 0.3 m/s is much larger than at 0.2 m/s. Therefore, the selected operating velocity of 0.2 m/s satisfies the thermal requirement of the EV battery module while keeping the energy consumption of the recirculation pump at an acceptable level.
The transient simulations demonstrate that the stabilization time is shortened from about 250 s at 0.1 m/s to only 100 s at 0.3 m/s. In practical EV battery operations, a fast system response is desirable when the EV battery suddenly enters a high-discharge condition. A moderate increase in coolant velocity can reduce the required response time and avoid temperature spikes.
Effect of Heat-Generation Rate on the Bionic Liquid-Cooled Plate
Marine EV battery systems may operate under different discharge rates depending on the load demand. I therefore studied the cooling performance of the optimized bionic plate at five different heat fluxes: 400, 600, 785, 1000, and 1200 W/m². The inlet coolant temperature and the inlet velocity were maintained at 30 °C and 0.2 m/s, respectively. The resulting maximum temperatures are presented below.
| Heat flux (W/m²) | T_max (°C) | Coolant temperature rise (°C) |
|---|---|---|
| 400 | 32.77 | 2.12 |
| 600 | 34.00 | 3.18 |
| 785 | 35.51 | 4.17 |
| 1000 | 37.10 | 5.30 |
| 1200 | 38.30 | 6.37 |
As the heat flux increases from 400 W/m² to 1200 W/m², the maximum temperature of the bionic plate increases from 32.77 °C to 38.30 °C. The coolant temperature rise also increases linearly from 2.12 °C to 6.37 °C, which is consistent with the energy balance equation. At heat fluxes below 1000 W/m², the battery stays well inside its ideal operating window of 25–40 °C. At 1200 W/m², the plate temperature reaches 38.3 °C, which is close to the upper limit of the recommended range. If the EV battery is expected to work regularly under such high heat-generation rates, a higher coolant velocity or a lower inlet temperature would be necessary to maintain a safe thermal condition.
The transient temperature contours for the five heat fluxes show that when the heat flux lies in the range from 400 to 785 W/m², the plate reaches a steady state at roughly 150 s. At 1000 and 1200 W/m², the steady-state time increases to about 200 s. Thus, thermal equilibrium is reached slightly later under higher heat generation because the energy accumulated in the solid structure is larger and requires additional time to be transported to the coolant. In all simulated cases, the plate cools relatively uniformly and no runaway phenomenon is observed because the continuous liquid flow provides a stable boundary condition.
Energy Consumption and System-Level Benefits
In a marine EV battery thermal-management system, the cooling loop is driven by a pump that circulates coolant through the liquid-cooled plate. The hydraulic power required by the pump is proportional to the product of the volume flow rate and the pressure rise. Because the flow rate is constant in my comparison, the ratio of pump power between the bionic and conventional plates is equal to the ratio of their pressure drops. Thus, the bionic plate consumes about 14.2% less pumping power than the conventional plate while simultaneously providing a lower maximum temperature. This is an uncommon achievement in the field of liquid cooling, where typical modifications that improve heat transfer tend to increase pressure loss. We have shown that by choosing a naturally inspired branched structure, the boundary-layer interruption can be achieved without excessive form drag, which leads to a mutually beneficial result of enhanced cooling and reduced energy consumption.
Moreover, the better temperature uniformity of the bionic plate can extend the cycle life of the EV battery module because it reduces the non-uniform degradation of the individual cells. In a severely temperature-inhomogeneous battery pack, some cells may age faster than others, leading to capacity mismatch and reducing the usable energy of the entire pack. The improved temperature distribution provided by the optimized bionic plate is therefore beneficial not only for thermal safety but also for the long-term economics of the marine EV battery.
Potential Manufacturing and Integration Considerations
Although the bionic liquid-cooled plate contains a more complex internal channel than a conventional straight-fin plate, modern manufacturing methods such as additive manufacturing and metal stamping make its fabrication feasible. The plate is comprised of a bottom tray, an upper lid, and possibly an internal insert that defines the hexagonal array. The bionic structure’s regular repeats simplify the manufacturing tooling compared with other free-form fractal channels. From a mechanical perspective, the hexagonal cells can also serve as structural stiffeners, reducing the deformation of the plate under the pressure of the coolant and the compression load from the EV battery stack. Because the optimal plate is lightweight and uses a modest number of hexagon units, it is suitable for marine applications where both space and weight are constrained.
Main Findings from the Orthogonal Experiments
The orthogonal experiment data provided several important insights into how the internal geometry of the bionic plate affects the thermal performance of an EV battery:
- The transverse gap between hexagons, parameter \(b\), is the dominant factor for both maximum temperature and pressure drop. A smaller \(b\) creates more wall surface area but also leads to higher friction and pressure loss.
- The hexagon size \(a\) is the second most significant parameter for the maximum temperature, but it is less important than \(b\) for pressure drop.
- The longitudinal gap \(c\) has a moderate effect on pressure drop, while the distance from the array to the outlet \(d\) has the least influence on both responses.
- In almost all configurations, the hottest zone appears near the outlet corners. Adding more hexagons near the outlet can effectively mitigate that hot spot.
- There is a trade-off between temperature and pressure drop; the Pareto optimization found the best geometry with \(a=30\) mm, \(b=8\) mm, \(c=50\) mm, and \(d=90\) mm.
Transient Response and Temperature Uniformity Index
The transient maximum temperature is an important metric for evaluating an EV battery cooling system under a realistic discharge cycle. In my transient simulations, the heat flux is applied instantaneously at time zero, which corresponds to a step change in the battery power. The temporary overshoot of temperature can be observed if the coolant flow rate is insufficient. For the optimized bionic plate, the maximum temperature increases monotonically and reaches its asymptotic value without any oscillatory overshoot, because the thermal mass of the aluminum plate and the water act as a damping medium. The plate’s temperature uniformity at steady state can be assessed using the standard deviation of surface temperatures. The bionic plate’s standard deviation is lower than that of the conventional plate by roughly 15%, further demonstrating improved thermal homogeneity. This improvement is partly due to the lateral spreading of the coolant stream that is caused by the root-like hexagon arrangement.
The field synergy angle analysis offers an additional explanation for the enhanced heat transfer. In the conventional plate, the velocity is almost parallel to the wall and the temperature gradient is normal to the wall. Therefore, the synergy angle is often close to 90°, which means that the convective term of the energy equation is less effective. In the bionic plate, the velocity vector is continually turned when it flows around the six faces of each hexagon. Some streamlines become locally aligned with the temperature gradient, thereby improving the effective heat convection. The repeated splitting and rejoining of the streamlines in the staggered arrangement creates multiple small vortices that exchange heat directly from the heated surface to the coolant. The observed synergy-angle distribution is consistent with these interpretations and confirms that the proposed bionic design brings a truly field-synergic improvement compared with the conventional design.
Robustness and Adaptability of the Bionic Liquid-Cooled Plate
Another important feature of the optimized bionic liquid-cooled plate is its adaptability to off-design operation. Marine EV battery systems often face varying cooling loads due to changing propulsion power, charging currents, and ambient temperatures. The simulations of coolant velocity from 0.1 to 0.3 m/s show that the bionic plate retains a smooth monotonic response without developing severe hot spots even at low flow rates. At 0.1 m/s and a heat flux of 785 W/m², the maximum temperature is 39.25 °C, which is just within the safe threshold. In real applications, a flow rate lower than 0.1 m/s might be used during standby or low-power cruising to save pump energy. The structure’s large effective heat-transfer area allows it to remain sufficiently effective even when the mass flow is reduced.
At elevated inlet temperatures (35 °C), the maximum plate temperature reaches 40.41 °C, which approaches the upper limit of the recommended range for the EV battery. In tropical marine environments where the seawater or freshwater available for coolant heat exchange is warmer, a refrigeration chiller or an additional phase-change material thermal buffer may be required. The bionic plate geometry is compatible with such hybrid cooling strategies because its external dimensions are identical to those of the standard liquid-cooled plate used in the existing battery pack. Hence, it can be integrated without modifying the battery module’s overall architecture.
Limitations and Future Work
This study has a few limitations. First, the numerical model assumes uniform heat flux over the top surface of the liquid-cooled plate, which represents an idealized simplification of the heat generation inside a real EV battery. In practice, the heat generation is non-uniform and coupled with electrochemical kinetics. Future work should couple a spatially distributed battery heat source with a three-dimensional thermal-fluid model to more accurately predict the hot spots and pack-level temperature gradients.
Second, the Reynolds number is low (around 680) in the base case, and I treated the flow as laminar. However, at higher velocities, transitional or turbulent flow may occur in some regions, particularly behind the hexagonal obstacles. Including a transition turbulence model would improve the model fidelity for a wider range of flow conditions.
Third, the optimization was performed using a linear response-surface fit of sixteen CFD runs. Although the \(r^2\) values are acceptable, nonlinear interactions between geometric parameters may exist. Future work could employ a higher-order response surface, Kriging models, or advanced evolutionary algorithms together with a larger number of CFD evaluations to refine the optimal solution.
Fourth, only the steady-state and simple step-transient behavior were analyzed. In practice, a marine EV battery may be subjected to a dynamic discharge profile with varying current. A system-level simulation that couples the thermal model with a battery equivalent-circuit model could be used to evaluate the real operational effectiveness of the bionic liquid-cooled plate.
Finally, I did not perform an experimental study in this work because the primary goal was to optimize the internal channel design by numerical simulation. Nonetheless, the validation based on published experimental data supports the current numerical approach. Future experiments should be carried out on a prototype of the bionic liquid-cooled plate to measure the pressure drop and temperature distribution using thermocouples and infrared thermography. Those data will further strengthen the conclusions and facilitate the industrial application of this EV battery cooling technology.
Summary and Conclusions
In this thesis, I have systematically investigated a bionic liquid-cooled plate for marine EV battery thermal management using CFD simulations, orthogonal experimental design, multi-objective optimization, and comparative analyses. The main conclusions can be summarized as follows:
- The proposed bionic liquid-cooled plate, which combines leaf-vein hexagonal cells with tree-root-like staggered branching, provides better thermal performance than a conventional straight-channel plate without consuming more energy. At a fixed inlet velocity of 0.2 m/s and inlet temperature of 30 °C, the maximum temperature of the bionic plate is 35.51 °C, which is 0.7 °C lower than that of a conventional plate under identical operating conditions.
- The pressure drop of the bionic plate is 163.79 Pa, which is 14.2% lower than that of the conventional plate. Thus, the bionic plate not only cools the EV battery better but also reduces the pumping power needed for coolant circulation.
- The orthogonal experiment analysis showed that the transverse gap between hexagonal elements is the dominant geometric parameter affecting both the maximum temperature and pressure drop. The effect significance ranking for maximum temperature is b > a > c > d, while for pressure drop the ranking is b > c > a > d.
- The multi-objective optimization with NSGA-II produced a Pareto frontier. Selecting the trade-off design with \(a=30\) mm, \(b=8\) mm, \(c=50\) mm, and \(d=90\) mm yields a maximum temperature of 35.51 °C and a pressure drop of 163.79 Pa, both in good agreement with the algorithm’s predictions.
- The velocity field analysis demonstrates that the hexagonal elements repeatedly interrupt the boundary layers and cause local flow mixing, which is more effective in heat transfer than the straight parallel flow in a conventional plate. The synergy-angle contour confirms the favorable alignment of velocity and temperature gradients in the enhanced heat-transfer region.
- For the bionic plate, lowering the coolant inlet temperature from 35 °C to 25 °C reduces the maximum battery temperature by 10 °C while the coolant temperature rise remains constant at about 4.17 °C. Increasing the inlet velocity from 0.1 to 0.3 m/s decreases the highest temperature from 39.25 °C to 34.12 °C, but the additional benefit beyond 0.2 m/s is relatively small.
- Variation of the heat-generation rate from 400 W/m² to 1200 W/m² increases the maximum temperature from 32.77 °C to 38.30 °C. For heat fluxes below 1000 W/m², the optimized plate keeps the EV battery within the ideal operating range using a coolant inlet temperature of 30 °C and a velocity of 0.2 m/s.
In summary, the bionic liquid-cooled plate offers a robust, energy-efficient solution for the thermal management of marine EV battery systems. Its unique leaf-vein/tree-root-inspired internal structure represents a promising alternative to conventional liquid-cooling designs.