I approached this study as a thermal-management designer who needs to keep a marine power battery within a narrow temperature band while also reducing the energy spent on pumping coolant. The electric vehicle battery pack literature gave me a strong starting point because an electric vehicle battery pack and a marine power battery share the same fundamental challenge: heat is generated unevenly, the available space is limited, and the cooling system must remain lightweight, reliable, and energy-efficient. In my work, I used a 16.18 kWh marine power battery as the reference heat source. The corresponding battery heat generation was about 250 W, which I converted into a top-surface heat flux of approximately 785 W/m2 for the liquid-cooled plate. I set the target operating window between 25 °C and 40 °C and aimed to keep the internal temperature difference below 5 °C, following the usual requirements for an electric vehicle battery pack and a marine power battery.
My central idea was to improve the internal channel architecture rather than simply increasing flow rate. Increasing flow rate can always reduce temperature, but it also increases pressure drop and pump power. In an electric vehicle battery pack, that penalty directly reduces driving range. In a marine power battery, the same penalty reduces operational efficiency and may require a larger pump. Therefore, I designed a bionic liquid-cooled plate inspired by leaf veins and tree roots. The hexagonal units resemble the vein network of a leaf, while their arrangement follows a tree-root-like branching pattern. I then optimized four geometric parameters: the hexagon size a, the transverse distance b between two hexagons, the longitudinal distance c between two hexagons, and the distance d from the hexagon array to the outlet. The overall plate dimensions were 773 mm × 634 mm × 6 mm, with a 2 mm fluid-domain thickness, a 2 mm inlet height, and a 32 mm inlet width. I treated the region containing the bionic units as the enhanced heat-transfer zone and the surrounding region as the ordinary heat-transfer zone. The exact geometry is shown in the inserted image, which represents the general electric vehicle battery pack context that motivated my marine power battery design.
Governing Equations and Numerical Framework
I solved the conjugate heat transfer problem using a finite-volume method. The flow was assumed to be steady, incompressible, and laminar. I neglected gravity, viscous dissipation, and radiation, and I treated the thermophysical properties as constant. The governing equations were the continuity equation, the momentum equation, and the energy equation. For an incompressible coolant, the mass conservation equation reduces to
$$ \nabla \cdot \mathbf{u} = 0 $$
where u is the velocity vector. The momentum conservation equation is
$$ \frac{\partial (\rho \mathbf{u})}{\partial t} + \nabla \cdot (\rho \mathbf{u}\mathbf{u}) = -\nabla p + \nabla \cdot (\mu \nabla \mathbf{u}) + \mathbf{S} $$
where ρ is density, p is pressure, μ is dynamic viscosity, and S represents source terms. The energy conservation equation is
$$ \frac{\partial (\rho T)}{\partial t} + \nabla \cdot (\rho \mathbf{u} T) = \nabla \cdot \left( \frac{\lambda}{C_p} \nabla T \right) + S_t $$
where T is temperature, λ is thermal conductivity, Cp is specific heat capacity, and St is the volumetric heat source. For the coolant flow, I estimated the Reynolds number as
$$ Re = \frac{\rho V d_h}{\mu} $$
At an inlet velocity of 0.2 m/s, the calculated Reynolds number was about 680. Therefore, I selected the laminar model for the internal flow. I used a pressure-based solver with the coupled algorithm, second-order upwind discretization for momentum and energy, and a transient formulation with a time step of 1 s. The inlet was set as a velocity inlet, the outlet was set as a pressure outlet, and all external walls except the heated top surface were adiabatic. The initial temperature was 303.15 K, and the coolant inlet temperature was 30 °C unless otherwise stated. The working fluid was water and the solid material was aluminum. The thermophysical properties are summarized in Table 1.
| Material | Density (kg/m3) | Dynamic viscosity (kg/m·s) | Thermal conductivity (W/m·K) | Specific heat (J/kg·K) |
|---|---|---|---|---|
| Water | 998.2 | 0.001003 | 0.6 | 4182 |
| Aluminum | 2719 | — | 1555 | 3485 |
For the heat generation side, I used the classical decomposition of battery heat production:
$$ Q = Q_R + Q_P + Q_J + Q_S $$
where QR is reaction heat, QP is polarization heat, QJ is Joule heat, and QS is side-reaction heat. In a practical electric vehicle battery pack, side-reaction heat is often small, so I simplified the total heat generation as
$$ Q = Q_R + Q_P + Q_J $$
with
$$ Q_P = I^2 R_P $$
$$ Q_J = I^2 R_o $$
where I is current, RP is polarization resistance, and Ro is ohmic resistance. For heat transfer within the battery and toward the cold plate, I considered conduction, convection, and radiation. Conduction follows Fourier’s law:
$$ q_n = -\lambda \frac{\partial T}{\partial n} $$
Convection follows Newton’s law of cooling:
$$ Q = h A (T_1 – T_2) $$
Radiation follows the Stefan–Boltzmann law:
$$ P = \varepsilon \sigma (T^4 – T_s^4) $$
In my numerical model, radiation was neglected because its contribution was small compared with conduction and forced convection. This assumption is common for an electric vehicle battery pack and for a marine power battery with a liquid-cooled plate.
Mesh, Independence, and Validation
I generated a structured hexahedral mesh to reduce numerical diffusion and computational cost. The two-dimensional block topology was created first, and then the mesh was extruded in the third direction. More than 88 % of the cells had a quality above 0.9. To ensure that the mesh did not control the results, I tested five mesh sizes from 987,282 cells to 9,548,515 cells. As the cell count increased, the maximum temperature decreased and gradually approached a plateau, while the pressure drop increased and then stabilized. At 4,740,770 cells, further refinement changed the maximum temperature by less than 0.2 °C and changed the pressure drop by a negligible amount. Therefore, I used approximately 4.74 million cells for all subsequent simulations. This mesh resolution gave a good balance between accuracy and computational time for an electric vehicle battery pack scale problem and for the present marine power battery cold plate.
I validated the numerical model against a published experimental data set for a liquid-cooled plate with a 6 mm total thickness and a 2 mm channel thickness. The validation case used a 5 C discharge condition and a heat flux of 3412 W/m2. The inlet coolant temperature was 25 °C, and the inlet mass flow rates were 0.5 g/s, 1 g/s, 1.5 g/s, and 2 g/s. I compared the computed maximum temperature with the experimental values. The maximum relative error remained below 5 % for all four flow rates. This agreement gave me confidence that the model could predict the temperature and pressure behavior of a liquid-cooled plate for an electric vehicle battery pack and for a marine power battery. Table 2 summarizes the validation outcome.
| Mass flow rate (g/s) | Maximum temperature error (%) | Acceptable range |
|---|---|---|
| 0.5 | < 5 | Yes |
| 1.0 | < 5 | Yes |
| 1.5 | < 5 | Yes |
| 2.0 | < 5 | Yes |
External Parameter Screening
Before optimizing the internal bionic geometry, I screened two external parameters: fluid-domain thickness and inlet coolant velocity. These parameters are important because they influence both the maximum temperature and the pressure drop. In an electric vehicle battery pack, the available space is usually tightly constrained by module stacking, so the cold plate cannot simply be made thicker without limit. In a marine power battery, the same space limitation exists, and additional pump energy also reduces system efficiency.
I kept the total plate thickness constant and changed only the internal fluid-domain thickness from 1 mm to 4 mm. The inlet velocity and coolant temperature were fixed. Table 3 shows the observed trend. The maximum temperature first decreased and then increased, while the pressure drop decreased monotonically as thickness increased. The lowest maximum temperature occurred at a 2 mm fluid-domain thickness. When the thickness was 2 mm, the coolant flow rate was larger than at 1 mm, which improved heat removal. When the thickness increased beyond 2 mm, the solid aluminum layers became thinner or the internal flow distribution became less effective, and the thermal conduction path changed unfavorably. The pressure drop continued to fall with thickness because the hydraulic resistance decreased. I selected 2 mm as the working fluid-domain thickness because it gave the best temperature control while keeping the pressure drop within an acceptable range for an electric vehicle battery pack and a marine power battery.
| Fluid-domain thickness (mm) | Maximum temperature trend | Pressure drop trend | Decision |
|---|---|---|---|
| 1 | Higher | Highest | Rejected |
| 2 | Lowest | Moderate | Selected |
| 3 | Slightly higher | Lower | Rejected |
| 4 | Higher | Lowest | Rejected |
I then studied the inlet velocity effect. I compared three plate concepts: a conventional liquid-cooled plate, a honeycomb liquid-cooled plate, and my bionic liquid-cooled plate. The inlet velocity varied from 0.1 m/s to 0.3 m/s. For all three designs, the maximum temperature decreased as velocity increased. However, the reduction became slower above 0.2 m/s. This behavior is typical for an electric vehicle battery pack: increasing flow rate helps until the thermal boundary layer becomes thin enough that further flow only adds pumping loss. At 0.2 m/s, the cooling benefit remained strong and the pump penalty was still reasonable. Therefore, I selected 0.2 m/s as the baseline inlet velocity. Table 4 summarizes the velocity screening logic.
| Inlet velocity (m/s) | Temperature trend | Pressure-drop penalty | Decision |
|---|---|---|---|
| 0.10 | Highest maximum temperature | Lowest | Insufficient cooling |
| 0.15 | Lower | Low | Acceptable |
| 0.20 | Low | Moderate | Selected |
| 0.25 | Slightly lower | Higher | Marginal gain |
| 0.30 | Lowest | Highest | Excess pump energy |
Orthogonal Experiment for the Bionic Geometry
After fixing the fluid-domain thickness at 2 mm and the inlet velocity at 0.2 m/s, I designed a four-factor, four-level orthogonal experiment. The four factors were the hexagon size a, the transverse distance b, the longitudinal distance c, and the distance d from the hexagon array to the outlet. The levels are listed in Table 5. This design allowed me to evaluate the individual influence of each geometric parameter without running a full factorial study. Such an approach is especially useful for an electric vehicle battery pack cold plate, because the design space is large and computational cost is significant. It is also useful for a marine power battery, where the cold plate must be optimized for a specific hull or container layout.
| Factor | Level 1 | Level 2 | Level 3 | Level 4 |
|---|---|---|---|---|
| a: hexagon size (mm) | 20 | 26 | 32 | 38 |
| b: transverse distance (mm) | 8 | 12 | 16 | 20 |
| c: longitudinal distance (mm) | 30 | 40 | 50 | 60 |
| d: distance to outlet (mm) | 80 | 90 | 100 | 110 |
The sixteen orthogonal cases and their simulation results are shown in Table 6. Each case had a different combination of a, b, c, and d. I recorded the maximum temperature and the pressure drop. The results showed that the maximum temperature generally decreased as the pressure drop increased. In other words, stronger cooling usually required more pumping energy. This trade-off is central for an electric vehicle battery pack and for a marine power battery, because the thermal-management system must not consume excessive energy. The best design should therefore sit on a suitable compromise between temperature and pressure drop.
| Case | a (mm) | b (mm) | c (mm) | d (mm) | Tmax (°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 |
I used range analysis to rank the significance of each factor. For temperature, the range values gave the order b > a > c > d. For pressure drop, the order was b > c > a > d. This means that the transverse distance b was the most influential parameter for both objectives. The hexagon size a was the second most important factor for temperature, while the longitudinal distance c was the second most important factor for pressure drop. The outlet distance d had the smallest influence on both objectives, although it still affected flow distribution near the outlet. Table 7 presents the range analysis.
| Response | a range | b range | c range | d range | Ranking |
|---|---|---|---|---|---|
| Maximum temperature | 0.21 | 0.74 | 0.17 | 0.08 | b > a > c > d |
| Pressure drop | 3.81 | 17.46 | 6.83 | 4.84 | b > c > a > d |
The temperature contours from the sixteen cases shared a common feature: the highest temperature appeared at the two corners near the outlet. This happened because the coolant entered at one side, absorbed heat along the flow path, and became warmer before reaching the outlet. The corners near the outlet were also regions of low velocity and weak mixing, so heat accumulated there. This behavior is important for an electric vehicle battery pack because local hot spots can accelerate aging and increase thermal runaway risk. It is equally important for a marine power battery because uneven temperature can reduce usable capacity and cycle life.
Multi-Objective Optimization
Range analysis alone could not determine the best combination because temperature and pressure drop are conflicting objectives. Therefore, I fitted the orthogonal data to continuous functions and then applied a multi-objective optimization algorithm. I treated a, b, c, and d as variables x1, x2, x3, and x4. The fitted pressure drop and temperature models were
$$ y_p = 0.224917 x_1 – 1.292 x_2 – 0.07405 x_3 – 0.03645 x_4 + 181.0079 $$
$$ y_t = -0.01108 x_1 + 0.059625 x_2 – 0.0006 x_3 + 0.00245 x_4 + 35.18467 $$
I assessed the fit quality with the coefficient of determination
$$ r^2 = 1 – \frac{\sum_{i} \left( \frac{Z_i – Z_{i,CFD}}{Z_{i,CFD}} \right)^2}{n} $$
The temperature fit gave r2 = 0.81, and the pressure-drop fit gave r2 = 0.63. These values were sufficient for optimization because the fitted models captured the main trends. The optimization problem was stated as
$$ \min F(x_1,x_2,x_3,x_4) = \left\{ \min F_1(x_1,x_2,x_3,x_4), \min F_2(x_1,x_2,x_3,x_4) \right\} $$
subject to
$$ 20 \le x_1 \le 38 $$
$$ 8 \le x_2 \le 20 $$
$$ 30 \le x_3 \le 60 $$
$$ 80 \le x_4 \le 110 $$
I used the NSGA-II algorithm because it is well suited to multi-objective problems with conflicting objectives. I set the population size to 50, the maximum generation to 150, and the fitness function deviation to 0.0001. The algorithm produced a Pareto front in which lower maximum temperature corresponded to higher pressure drop. This matched the trend from the orthogonal experiment. After examining the trade-off, I selected the solution with a predicted maximum temperature of 35.49 °C and a predicted pressure drop of 170.08 Pa. The corresponding geometry was a = 30 mm, b = 8 mm, c = 50 mm, and d = 90 mm. I then rebuilt the model with these parameters and ran a full CFD simulation. Table 8 compares the predicted and simulated values.
| Quantity | Optimization prediction | CFD result | Relative error |
|---|---|---|---|
| Maximum temperature (°C) | 35.49 | 35.51 | 0.00056 |
| Pressure drop (Pa) | 170.08 | 163.79 | 0.038 |
The errors were small enough to confirm that the optimization workflow was reliable. I therefore adopted a = 30 mm, b = 8 mm, c = 50 mm, and d = 90 mm as the final bionic liquid-cooled plate for the remaining comparisons. This optimized design is intended to be a practical candidate for an electric vehicle battery pack and for a marine power battery because it improves cooling without changing the inlet size, inlet shape, or mass flow rate.
Comparison with Conventional and Honeycomb Liquid-Cooled Plates
I compared three plates under identical boundary conditions: a conventional liquid-cooled plate, a honeycomb liquid-cooled plate, and my optimized bionic liquid-cooled plate. The coolant temperature was 30 °C, the inlet velocity was 0.2 m/s, and the heat flux was 785 W/m2. Because the inlet geometry and velocity were the same, the volumetric flow rate was also the same. Therefore, any difference in pressure drop directly reflected the internal flow resistance, and any difference in temperature directly reflected the internal heat-transfer structure. This comparison is especially meaningful for an electric vehicle battery pack and for a marine power battery, because the pump should not be oversized just to compensate for a poor internal design.
Table 9 summarizes the quantitative comparison. The pressure drop of the conventional plate was 190.91 Pa. The honeycomb plate reduced it to 165.66 Pa. The bionic plate reduced it further to 163.79 Pa. Thus, the bionic plate had a 14.2 % lower pressure drop than the conventional plate and a slightly lower pressure drop than the honeycomb plate. The maximum temperature of the conventional plate was 36.20 °C, while the bionic plate reached 35.51 °C. The bionic plate therefore reduced the maximum temperature by about 0.7 °C relative to the conventional plate and by about 0.5 °C relative to the honeycomb plate. This improvement was achieved purely by internal geometry, not by increasing flow rate.
| Plate type | Maximum temperature (°C) | Pressure drop (Pa) | Relative pressure-drop reduction vs. conventional |
|---|---|---|---|
| Conventional liquid-cooled plate | 36.20 | 190.91 | — |
| Honeycomb liquid-cooled plate | 36.01 | 165.66 | 13.2 % |
| Bionic liquid-cooled plate | 35.51 | 163.79 | 14.2 % |
The temperature field also revealed a difference in uniformity. In the conventional and honeycomb plates, the isotherms in the rear section were convex. In the bionic plate, the isotherms were concave, which indicated better temperature uniformity. I also sampled the average temperature along lines perpendicular to the flow direction. Near the inlet, the conventional plate performed slightly better because its straight channels delivered coolant quickly to the entrance region. However, after the flow entered the enhanced heat-transfer zone, the bionic plate produced lower average temperatures along most of the plate. This showed that the bionic structure was particularly effective in the middle and rear regions, where heat accumulation is usually most severe in an electric vehicle battery pack and in a marine power battery.
I also recorded the transient temperature response. Both plates showed a rapid temperature rise followed by stabilization. The bionic plate reached a lower steady maximum temperature. In the first 50 s, the conventional plate controlled the temperature slightly better because the straight channels had lower initial thermal resistance. After 50 s, the bionic plate controlled the temperature better and approached steady state with a lower slope. This means the bionic design can reduce the long-term hot-spot temperature while maintaining acceptable transient behavior. Such behavior is valuable for an electric vehicle battery pack during repeated acceleration and fast charging and for a marine power battery during load changes.
Velocity Field and Synergy-Angle Analysis
To explain why the bionic plate achieved both lower temperature and lower pressure drop, I examined the velocity field and the field-synergy angle. The velocity contours showed that the highest velocity occurred near the outlet in all plates. The four corners had very low velocity because they were outside the main flow path. In the conventional plate, the rectangular ribs divided the domain into parallel channels. The coolant moved in a relatively uniform direction with a moderate velocity, and the flow remained stable. In the bionic plate, the hexagonal units created a tree-root-like distribution. When the coolant met a hexagon, it split into two streams. The enhanced heat-transfer zone therefore contained many local accelerations, separations, and reattachments. The velocity magnitude in the enhanced zone was lower than in the outer zone, but the flow direction changed frequently. This repeated interruption of the thermal boundary layer promoted mixing and improved heat transfer.
I used the field-synergy principle to quantify the coupling between the velocity field and the temperature gradient. The synergy angle is defined as
$$ \cos\beta = \frac{\mathbf{u} \cdot \nabla T}{|\mathbf{u}| \, |\nabla T|} $$
When the angle between the velocity vector and the temperature gradient is small, the dot product is large and the convective heat transfer is strong. When the angle approaches 90°, the velocity and temperature gradient are poorly aligned, and heat transfer is weaker. In my simulations, regions with synergy angle below 90° appeared at the front of each rib or hexagon and behind each obstacle. The bionic plate contained many more hexagonal units than the conventional plate contained rectangular ribs. As a result, the bionic plate had a larger area with favorable synergy angle. The repeated breaking and reformation of the boundary layer in the tree-root-like arrangement also enhanced local heat transfer. This explains why the bionic plate achieved a lower maximum temperature despite having a lower pressure drop. The lower pressure drop came from the streamlined hexagonal shape and the distributed flow paths, while the better heat transfer came from the repeated boundary-layer disruption and improved field synergy.
Table 10 summarizes the qualitative field comparison. For an electric vehicle battery pack, this combination is advantageous because it reduces both thermal risk and pumping loss. For a marine power battery, the same combination reduces auxiliary power consumption and improves temperature uniformity across the pack.
| Feature | Conventional plate | Bionic plate | Implication |
|---|---|---|---|
| Main flow path | Parallel straight channels | Tree-root-like hexagonal network | Bionic path promotes mixing |
| Boundary layer | Stable along channels | Repeated breaking and reformation | Higher local heat transfer |
| Pressure drop | Higher | Lower | Lower pump energy |
| Temperature uniformity | Less uniform | More uniform | Better pack reliability |
| Synergy angle area | Smaller favorable area | Larger favorable area | Better velocity-gradient coupling |
Effects of Coolant Temperature
I then studied how the coolant inlet temperature affected the bionic plate. I fixed the heat flux at 785 W/m2 and the inlet velocity at 0.2 m/s. The coolant temperature was set to 25 °C, 30 °C, and 35 °C. As expected, the maximum temperature increased with coolant temperature. The maximum temperature was 30.46 °C at 25 °C, 35.51 °C at 30 °C, and 40.41 °C at 35 °C. Interestingly, the temperature difference between the inlet and outlet remained nearly constant at about 4.17 °C. This happened because the flow rate and internal geometry were unchanged, so the amount of heat absorbed by the coolant per unit mass was similar. The coolant temperature therefore shifted the entire temperature profile upward or downward without changing the overall temperature rise along the flow direction.
The time required to reach steady state also depended on coolant temperature. At 25 °C, the plate reached steady state in about 150 s. At 30 °C, it took about 200 s. At 35 °C, it took about 250 s. Lower coolant temperature provided a larger initial temperature difference between the plate and the coolant, which accelerated heat removal and shortened the transient period. For an electric vehicle battery pack, a lower coolant temperature can improve fast-charging performance, but it may require additional refrigeration energy. For a marine power battery, the available seawater or onboard coolant temperature may vary, so the control system should account for this effect.
| Coolant temperature (°C) | Maximum temperature (°C) | Inlet-outlet temperature difference (°C) | Approximate stabilization time (s) |
|---|---|---|---|
| 25 | 30.46 | 4.17 | 150 |
| 30 | 35.51 | 4.17 | 200 |
| 35 | 40.41 | 4.17 | 250 |
Effects of Coolant Velocity
Next, I fixed the coolant temperature at 30 °C and the heat flux at 785 W/m2, and I varied the inlet velocity from 0.1 m/s to 0.3 m/s. The maximum temperature decreased as velocity increased. At 0.1 m/s, the maximum temperature was 39.25 °C. At 0.2 m/s, it was 35.51 °C. At 0.3 m/s, it was 34.12 °C. The inlet-outlet temperature difference also decreased with velocity: about 8 °C at 0.1 m/s, about 4.17 °C at 0.2 m/s, and about 2.84 °C at 0.3 m/s. This occurred because a higher velocity increased the mass flow rate for the same inlet area, so the coolant carried away more heat per unit time and experienced a smaller temperature rise.
The stabilization time decreased as velocity increased. At 0.3 m/s, the plate reached steady state in about 100 s. At 0.2 m/s, it took about 150 s. At 0.1 m/s, it took about 250 s. Higher velocity improved both the heat-transfer coefficient and the heat capacity rate of the coolant. However, the pressure drop increased with velocity, and the pump power required to drive the flow increased. This trade-off is critical for an electric vehicle battery pack because higher pump power reduces vehicle range. It is also critical for a marine power battery because auxiliary power consumption reduces overall system efficiency. My earlier screening showed that 0.2 m/s was a reasonable balance between cooling performance and pump penalty.
| Inlet velocity (m/s) | Maximum temperature (°C) | Inlet-outlet temperature difference (°C) | Approximate stabilization time (s) |
|---|---|---|---|
| 0.10 | 39.25 | 8.00 | 250 |
| 0.20 | 35.51 | 4.17 | 150 |
| 0.30 | 34.12 | 2.84 | 100 |
Effects of Heat Generation
Finally, I studied the effect of battery heat generation. I fixed the coolant temperature at 30 °C and the inlet velocity at 0.2 m/s. I varied the top-surface heat flux from 400 W/m2 to 1200 W/m2. The maximum temperature increased with heat flux. At 400 W/m2, the maximum temperature was 32.77 °C. At 785 W/m2, it was 35.51 °C. At 1200 W/m2, it was 38.3 °C. The inlet-outlet temperature difference also increased: about 2.12 °C at 400 W/m2, 3.18 °C at 600 W/m2, 4.17 °C at 785 W/m2, 5.3 °C at 1000 W/m2, and 6.37 °C at 1200 W/m2. Because the flow rate was constant, a higher heat flux forced the coolant to absorb more heat per unit mass, which produced a larger temperature rise along the flow direction.
The stabilization time remained about 150 s for heat fluxes up to 785 W/m2 and increased to about 200 s at 1000 W/m2 and 1200 W/m2. The bionic plate maintained the maximum temperature below 40 °C even at 1200 W/m2 under the selected flow condition. This is important because an electric vehicle battery pack may experience high heat generation during fast charging or aggressive driving, and a marine power battery may experience high heat generation during rapid acceleration or heavy load operation. The bionic plate therefore offers a useful thermal buffer, although higher heat fluxes would eventually require a higher coolant velocity or a lower coolant temperature.
| Heat flux (W/m2) | Maximum temperature (°C) | Inlet-outlet temperature difference (°C) | Approximate stabilization time (s) |
|---|---|---|---|
| 400 | 32.77 | 2.12 | 150 |
| 600 | — | 3.18 | 150 |
| 785 | 35.51 | 4.17 | 150 |
| 1000 | — | 5.30 | 200 |
| 1200 | 38.30 | 6.37 | 200 |
Engineering Interpretation and Energy Savings
The pressure drop is directly related to the pump power required to circulate the coolant. For a given volumetric flow rate, the pump power can be expressed as
$$ P_{pump} = \frac{\Delta p \, \dot{V}}{\eta} $$
where Δp is the pressure drop, V is the volumetric flow rate, and η is the pump efficiency. Because I kept the inlet velocity and inlet geometry constant, the volumetric flow rate was identical for the conventional plate and the bionic plate. Therefore, the 14.2 % reduction in pressure drop translated directly into a lower required pumping power. In an electric vehicle battery pack, this means less parasitic energy consumption and a longer driving range. In a marine power battery, this means lower auxiliary load and better overall energy efficiency. The bionic plate therefore offers a rare combination: lower maximum temperature and lower pressure drop at the same flow rate.
The tree-root-like hexagonal arrangement is the key to this behavior. The hexagonal shape is streamlined relative to a rectangular rib, so it produces less irreversible pressure loss. The distributed branching pattern guides the coolant into many small streams instead of forcing it through a few long straight channels. This reduces the peak velocity and avoids large recirculation zones. At the same time, the repeated splitting and recombination of the flow continuously disrupts the thermal boundary layer. The result is stronger local heat transfer without a large global pressure penalty. This is why the bionic plate outperformed the conventional plate in both temperature and pressure drop.
For an electric vehicle battery pack, the design is attractive because thermal management must be compact, lightweight, and energy-efficient. For a marine power battery, the design is attractive because the battery room may have limited space and the cooling system must operate reliably under continuous load. The same bionic plate concept could be adapted to different cell formats, module sizes, and pack layouts by scaling the hexagonal units and adjusting the branching distance. The four geometric parameters a, b, c, and d provide a practical design space for such adaptation.
Summary of Main Findings
My study produced several quantitative conclusions. First, the bionic liquid-cooled plate reduced the maximum temperature by about 0.7 °C compared with a conventional liquid-cooled plate and by about 0.5 °C compared with a honeycomb liquid-cooled plate. Second, it reduced the pressure drop by 14.2 % compared with the conventional plate, and all sixteen orthogonal cases had a pressure drop below the conventional value of 190.91 Pa. Third, the bionic plate improved temperature uniformity, especially in the middle and rear regions where hot spots usually form in an electric vehicle battery pack and in a marine power battery. Fourth, the velocity field showed that the enhanced heat-transfer zone had lower local velocity but frequent flow splitting, which promoted mixing and boundary-layer renewal. Fifth, the synergy-angle analysis showed a larger favorable area in the bionic plate, which explained its better convective heat transfer.
The operating-condition study added further insight. Coolant temperature mainly shifted the temperature level but did not change the inlet-outlet temperature difference under fixed flow conditions. Coolant velocity strongly affected both the maximum temperature and the temperature difference, but higher velocity also increased pump power. Heat generation increased the maximum temperature and the temperature difference, but the bionic plate kept the maximum temperature below 40 °C for heat fluxes up to 1200 W/m2 at 0.2 m/s and 30 °C coolant. These results are relevant to an electric vehicle battery pack during fast charging and to a marine power battery during high-load operation.
| Finding | Quantitative result | Design implication |
|---|---|---|
| Maximum temperature reduction vs. conventional plate | About 0.7 °C | Lower hot-spot risk |
| Maximum temperature reduction vs. honeycomb plate | About 0.5 °C | Better than simpler hexagonal design |
| Pressure-drop reduction vs. conventional plate | 14.2 % | Lower pump power |
| Best geometric parameters | a = 30 mm, b = 8 mm, c = 50 mm, d = 90 mm | Optimized bionic layout |
| Best fluid-domain thickness | 2 mm | Balanced conduction and flow |
| Best inlet velocity | 0.2 m/s | Balanced cooling and pump energy |
| Coolant temperature effect | Maximum temperature 30.46–40.41 °C for 25–35 °C coolant | Lower coolant improves cooling but may cost refrigeration energy |
| Coolant velocity effect | Maximum temperature 39.25–34.12 °C for 0.1–0.3 m/s | Higher velocity improves cooling but raises pressure drop |
| Heat-generation effect | Maximum temperature 32.77–38.30 °C for 400–1200 W/m2 | Bionic plate maintains feasible temperatures |
Conclusions
I designed and optimized a bionic liquid-cooled plate for a marine power battery by combining leaf-vein-inspired hexagonal units with a tree-root-like branching layout. I used a 16.18 kWh marine power battery as the reference heat source and a 785 W/m2 heat flux as the baseline thermal load. I validated the numerical model against published experimental data, with maximum temperature errors below 5 %. I then screened the fluid-domain thickness and inlet velocity, and selected 2 mm and 0.2 m/s as the baseline conditions. Using a four-factor, four-level orthogonal experiment, I found that the transverse distance b was the most influential geometric parameter for both temperature and pressure drop. For temperature, the significance order was b > a > c > d. For pressure drop, the significance order was b > c > a > d. I fitted the orthogonal data and used NSGA-II to obtain a Pareto front. The selected optimum was a = 30 mm, b = 8 mm, c = 50 mm, and d = 90 mm. The predicted and simulated results agreed well, with a maximum-temperature error of 0.00056 and a pressure-drop error of 0.038.
Compared with a conventional liquid-cooled plate, the optimized bionic plate reduced the maximum temperature by about 0.7 °C and the pressure drop by 14.2 % under the same inlet velocity and flow rate. It also improved temperature uniformity and maintained a lower maximum temperature in the middle and rear regions. The velocity field showed that the bionic structure created repeated splitting and recombination, which disrupted the thermal boundary layer and enhanced mixing. The synergy-angle field showed a larger favorable area in the bionic plate, confirming better coupling between the velocity field and the temperature gradient. These mechanisms explain why the bionic plate can achieve better cooling with lower pumping loss.
The operating-condition study showed that coolant temperature mainly shifts the overall temperature level, coolant velocity strongly controls both maximum temperature and temperature difference, and heat generation increases both maximum temperature and temperature difference. The bionic plate maintained the maximum temperature below 40 °C for heat fluxes up to 1200 W/m2 at 0.2 m/s and 30 °C coolant. These results are directly relevant to an electric vehicle battery pack and to a marine power battery because they show how the same bionic cold-plate concept can be tuned for different thermal loads and different cooling resources. In future work, I would combine the current thermal model with a pump-power model, test additional bionic topologies, and evaluate the design under transient duty cycles representative of an electric vehicle battery pack and a marine power battery.