With the intensification of global energy crises and environmental pollution, the development of clean and efficient transportation has become an urgent priority. Within this context, battery electric vehicles have emerged as a pivotal direction in the automotive industry’s transition towards sustainability. My research focuses on the thermal management of EV battery pack, which presents one of the most critical engineering challenges for ensuring the performance, safety, and longevity of electric vehicles. It is widely recognized that lithium-ion batteries exhibit optimal performance and service life only within a specific operating temperature range, typically between 20°C and 45°C. Moreover, a maximum temperature difference of less than 5°C across the battery module is necessary to maintain capacity consistency and prevent localized degradation. Thus, the battery thermal management system (BTMS) serves both to suppress peak temperatures during high-rate discharge and to maintain a uniform temperature distribution across the EV battery pack. The data confirm that liquid-cooling thermal technology has become a mainstream choice for the thermal management of the EV battery pack, owing to its technological maturity, stable performance, and high cooling capacity. A liquid-cooled plate is a critical component in a liquid-cooled thermal management system, as it is through this structure that heat is transferred from the module to the cooling fluid. Consequently, I designed a novel liquid-cooled plate that incorporates discrete, inclined, and staggered rib-grooved units inside its rectangular channels. The staggered ribs encourage flow mixing between adjacent channels to equalize the flow rate, while the grooves generate longitudinal swirls to enhance convection. This study seeks to overcome the drawbacks of conventional straight-channel liquid-cooled plates, including their low heat transfer efficiency and uneven inlet flow distribution.
1. Theoretical and Numerical Methodology
To analyze the thermal performance of the EV battery pack under realistic operating conditions, I adopted a one-dimensional/three-dimensional electrochemical-thermal coupled model. The electrochemical model, based on Newman’s theory, captures the ionic transport and charge transfer within the cell, while the three-dimensional thermal model examines the spatial temperature distribution across the battery module. The formation of a mathematical model is significant because it enables a detailed coupling mechanism between the chemical reaction and heat transfer. The total heat generation rate during discharge originates from the sum of reversible heat and irreversible heat. The irreversible potential, in turn, is from activation overpotential and ohmic losses within the cell. I calculate this heat source with the following equation:
$$Q_{tot} = Q_{rev} + Q_{irr}$$
which can be further expressed in terms of cell potential and temperature by:
$$Q_{tot} = a j F T \frac{\partial U}{\partial T} + a j F \eta + j^{2} \sigma_{eff}^{-1}$$
Where:
$a$ is the specific surface area of the solid particles, $j$ is the current density, $F$ is the Faraday constant, $T$ is the local battery temperature, $U$ is the open-circuit voltage, $\eta$ is the overpotential, and $\sigma_{eff}$ is the effective electrical conductivity. I considered the temperature dependence of material properties using the Arrhenius equation that is given as:
$$\phi = \phi_{ref} \exp\left[\frac{E_{act}}{R_u} \left( \frac{1}{T_{ref}} – \frac{1}{T} \right)\right]$$
Through this equation, the state of charge, internal resistance, and heat generation rates are inherently linked to the temperature field. The geometry model of the EV battery pack includes, as shown in Table 1, a liquid-cooled plate, a thermal pad, and a battery module having a dimension of 182 mm × 66 mm × 59 mm.
2. Design of the Rib-grooved Plate Structure
I included two basic liquid-cooled plates in the study. The first one is a traditional straight-channel liquid-cooled plate, which serves as the reference case. The second one is the newly designed liquid-cooled plate integrated with a series of rib and groove units, which are characterized by their discrete, inclined, staggered arrangement and the slant angle. Both plates were designed to share the same overall size. However, my design is distinct in that the traditional straight channels are transformed into a rectangular cavity where ribs and grooves are periodically patterned. The cooling water enters from the inlet located on the left side and flows towards the outlet on the right side. Table 1 presents the main geometric parameters of the liquid-cooled plates.
Table 1: Specifications of the liquid-cooled plates used in simulations
| Parameter | Straight channel plate | Rib-grooved plate |
|---|---|---|
| Overall length L1 | 262 mm | 262 mm |
| Internal channel length L2 | 182 mm | 182 mm |
| Plate height H | 12 mm | 12 mm |
| Upper/lower thickness e1/e2 | 4 mm | 4 mm |
| Channel height s1 | 4 mm | 4 mm |
| Channel width n1 | 3.5 mm | － |
| Fin/channel distance n2 | 6.5 mm | － |
| Groove depth s3 | － | 2 mm |
| Rib height s2 | － | 4 mm |
| Rib/ Groove width Wr/Wg | － | 2.6 mm |
| Rib/ Groove length Lr/Lg | － | 7.8 mm |
| Inclination angle α | － | 45° |
| Opposite angle β | － | 135° |
Simultaneously, I built the numerical model regarding the following assumptions: (i) the coolant is an incompressible Newtonian fluid, (ii) the flow is considered steady and laminar, (iii) the material properties of the solid parts are homogeneous and isotropic, (iv) the outer surfaces of the system are perfectly insulated, and (v) gravity is negligible. Since the flow of water within the channels is laminar, I applied the continuity equation, the momentum equation, and the energy equation for the fluid domain, which are expressed respectively in three-dimensional Cartesian coordinates:
$$\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial z} = 0$$
$$\rho_w \left( u\frac{\partial u}{\partial x} + v\frac{\partial u}{\partial y} + w\frac{\partial u}{\partial z} \right) = – \frac{\partial p}{\partial x} + \mu \left( \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} + \frac{\partial^2 u}{\partial z^2} \right)$$
$$ \rho_w C_w \left( u \frac{\partial T}{\partial x} + v \frac{\partial T}{\partial y} + w \frac{\partial T}{\partial z} \right) = \lambda_w \left( \frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} + \frac{\partial^2 T}{\partial z^2} \right)$$
Here, u, v, and w are the components of the velocity vector, $p$ is the pressure, and $T$ is the local temperature. The properties of the cooling water, identified by subscript $w$, include density, specific heat capacity, thermal conductivity, and dynamic viscosity. I selected these equations because they indicate the relationship between the velocity field and heat transfer rate. The numerical simulation applies the boundary conditions listed in Table 2 for all cases studied:
Table 2: Boundary condition configurations
| Type of condition | Traditional plate | Rib-grooved plate |
|---|---|---|
| Initial battery temperature | 25 °C | 25 °C |
| Coolant inlet velocity u | 0.17 m/s | 0.17 m/s |
| Outlet pressure p_out | 0 Pa | 0 Pa |
| Cooling medium | Water | Water |
| Flow state | Laminar | Laminar |
| Discharge rate C-rate | 7C | 7C |
For the studied EV battery pack, I used the following evaluation indicators to quantify the performance of the liquid-cooled plates:
(i) The maximum temperature of the battery module $T_{max}$ to assess cooling capability;
(ii) The standard deviation of temperature $T_{\sigma}$ across the contact surface to assess temperature uniformity;
(iii) The pressure drop $\Delta P$ to assess the flow energy consumption. These measures are calculated using the formulas set out below:
$$T_{max} = \max\{T_i\}$$
$$T_{\sigma} = \sqrt{\frac{\sum_{j=1}^{n} \left( T_j – T_{av}\right)^2}{n}}$$
$$\Delta P = P_{in} – P_{out}$$
I verify mesh independence to ensure the numerical results do not depend on the grid count. I created a total of five types of grids for each plate. The maximum temperature and the pressure drop changes between the grids are found to be lower than 0.5%, confirming that the grid independence is reached near the 3.6 million cells. Finally, I validate the simulation model developed against experimental discharge voltage profiles at 1C, which are available from literature reports. The resultant data curve from my simulation closely aligns with experimental findings, the maximum deviation between the two fitting being limited to 3.4%. This close match therefore verifies the accuracy of my modeling procedure and the assumptions I used.
3. Comparative Assessment of Thermal Performance
3.1 Conventional vs Rib-Grooved Pattern
To systematically compare the thermal performance of the two plates, I simulated the entire EV battery pack with a cooling flow velocity of 0.17 m/s under a 7C discharge rate. The performance metrics of the EV battery pack for the different plate types are summarized in Table 3:
Table 3: Overall performance indicators
| Indicator | Straight channel plate | Rib-grooved plate | Difference |
|---|---|---|---|
| T_max (°C) | 51.55 | 48.99 | -2.56 |
| T_σ (°C) | 1.45 | 0.87 | -0.58 |
| ΔP (Pa) | 134.60 | 206.52 | +71.92 |
| Nu | 31.08 | 55.96 | +80.1% |
| f | 0.262 | 1.135 | +333.2% |
| PEC | － | 1.28 | － |
Compared with the conventional straight-channel liquid-cooled plate, the newly designed rib-grooved liquid-cooled plate reduces $T_{max}$ by 2.56°C and improves the uniformity of the contact surface by 0.58°C. The data in Table 3 confirm that the pressure drop, however, increases by 71.92 Pa due to the increased flow resistance. The flow field at the middle cross-section in my simulation is dominated by longitudinal swirls, which are generated by the presence of grooves. In detail, the grooves act as turbulence promoters, generating secondary flow vortices. These longitudinal vortices enhance convective heat transfer because they bring fresh coolant from the core region into contact with the hot channel wall and facilitate the mixing between fluid layers. As a result, the thermal boundary layer becomes thinner, and heat exchange between the fluid and wall surface increases significantly. Moreover, the ribs redirect the fluid and enable communication between adjacent channels, preventing localized hotspots caused by uneven channel-wise flow. My results confirmed through the field synergy theory that a smaller synergy angle (β) between the velocity and temperature gradients points toward enhanced convection. Calculation of the synergy angle distribution at a cut plane for both the original and optimized plates shows that the optimized distribution has considerably lower β values at pre-defined points in the downstream region.
3.2 Impact of Flow Rate and C-rate
In practical operations, the EV battery pack may be subject to different cooling flow rates and discharge requirements. I therefore investigated the effect of these two parameters on the cooling performance of the rib-grooved liquid-cooled plate. A parametric analysis was conducted with the flow rate ranging from 0.09 m/s to 0.17 m/s in steps and with the discharge rate ranging from 3C to 7C. Table 4 summarizes the key findings:
Table 4: Observed effects of flow rate and discharge rate
| Parameter studied | Observation range | Trend with inlet velocity | Trend with C-rate |
|---|---|---|---|
| Pressure drop ΔP | 60.24–184.17 Pa | Increases with velocity | Change <2% when varying C-rate |
| Maximum temperature | 3.3°C reduction window | Decreases with velocity | Increases with C-rate |
| Temperature standard deviation | ΔTσ=0.6492 °C at 7C | Decreases with velocity | Increases with C-rate |
It is noteworthy that the discharge rate itself influences the heat generation rate, thereby affecting the cooling load of the EV battery pack. At high C-rates, i.e., high heat generation rate, increasing the inlet velocity yields more pronounced benefits in reducing the maximum battery temperature. In contrast, the pressure drop is nearly insensitive to changes in discharge rate under the same inlet velocity. This indicates that pressure dissipation is purely a hydrodynamic effect related to the flow rate and geometry, confirming that the C-rate mainly influences the thermal performance of the EV battery pack.
4. Structural Optimization Based on Array Configuration
4.1 Orientation and Arrangement
To determine the effect of the orientation of the rib-grooved unit, I considered four configurations. In the first configuration, the upper rows were arranged with an inclination angle of 135°, and the lower rows with 135°. In the second configuration, the angles were the opposite, while the third and fourth configurations followed different mirroring rules. The data obtained from the simulations were organized in a table. Among the four design types, the so-called wave orientation design, which has adjacent rows of grooves with opposite inclination and a wave-like flow path, proved to be the preferred arrangement. The key benefit of this wave-like arrangement is that coolant is subjected to periodic directional changes, promoting continuous destabilization of the flow and enhancing the intensity of fluid perturbation and mixing. Although the pressure drop of this arrangement is somewhat higher compared to a single-side incline design, the difference is small. For example, the maximal increase compared to the lowest pressured design is only 11.82 Pa.
4.2 Optimal Number of Rows and Columns
I varied the number of rows and columns while the remaining parameters were unchanged to understand the influence of the rib-and-groove quantity and array distribution on performance. Table 5 shows the results for different rows:
Table 5: Comparison of models with different numbers of rib-grooved rows
| Number of rows | T_max (°C) | T_av (°C) | T_σ (°C) | ΔP (Pa) | Nu | f |
|---|---|---|---|---|---|---|
| 3 | 50.78 | 35.51 | 1.26 | 71.02 | 36.89 | 0.42 |
| 4 | 49.88 | 35.01 | 1.12 | 109.06 | 48.55 | 0.63 |
| 5 | 49.41 | 34.58 | 0.94 | 136.10 | 57.12 | 0.75 |
| 6 | 49.20 | 34.22 | 0.83 | 205.93 | 69.36 | 1.14 |
Increasing the number of rows leads to a larger number of longitudinal swirls in the flow field, which strengthens the disturbance and mixing of the fluid. Thus, heat transfer and temperature uniformity are improved. However, the flow resistance also increases significantly. Considering the trade-off between performance and flow consumption, I selected the model with 5 rows as optimal. By repeating the analysis for the number of columns (from 6 to 9), I observed that the number of columns also increases $Nu$ and $f$ values. However, excessive rib columns can block flow redistribution between channels, hindering the temperature uniformity. A column number of 7 is thus deemed the optimal structure, as it gives a low $T_{\sigma}$ and yet moderate $f$ value, leading to high performance evaluation criteria.
5. Orthogonal Experimental Design and Range Analysis
Following the determination of optimum orientation and best number of rows/columns, I focused on the detailed dimensional characteristics of the rib-grooved structure. I chose four geometric factors, each adjusted over four levels, concerning the tilting angle, column spacing, row spacing, and rib-grooved length. I selected the $L_{16}(4^5)$ orthogonal array which enables the design to cover the variable space with a modest number of test cases. Table 6 lists the factors and levels.
Table 6: Variables and related stages in the orthogonal experimental planning
| Levels | Angle α (°) | Column space d2 (mm) | Row spacing d1 (mm) | Length L (mm) |
|---|---|---|---|---|
| 1 | 75 | 12.0 | 10.0 | 7.2 |
| 2 | 60 | 12.5 | 10.5 | 7.8 |
| 3 | 45 | 13.0 | 11.0 | 8.4 |
| 4 | 30 | 13.5 | 11.5 | 9.0 |
The output data from the simulations applied to each of the 16 rows in the orthogonal table were collected in Table 7, from which I gathered the effect of each factor on the mean values of the three performance indicators, as well as their extreme differences.
Table 7: Result matrix for the L16(4^5) orthogonal experiments
| Case | α | d2 | d1 | L | Tmax(°C) | Tσ(°C) | ΔP(Pa) |
|---|---|---|---|---|---|---|---|
| 1 | 75 | 12 | 10 | 7.2 | 49.30 | 0.964 | 210.65 |
| 2 | 75 | 12.5 | 10.5 | 7.8 | 49.89 | 1.051 | 219.80 |
| 3 | 75 | 13 | 11 | 8.4 | 49.43 | 0.981 | 267.64 |
| 4 | 75 | 13.5 | 11.5 | 9.0 | 48.89 | 0.897 | 348.32 |
| 5 | 60 | 12 | 10.5 | 8.4 | 49.51 | 0.968 | 209.90 |
| 6 | 60 | 12.5 | 10 | 9.0 | 49.79 | 1.089 | 219.33 |
| 7 | 60 | 13 | 11.5 | 7.2 | 49.81 | 0.927 | 183.69 |
| 8 | 60 | 13.5 | 11 | 7.8 | 49.55 | 0.918 | 198.76 |
| 9 | 45 | 12 | 11 | 9.0 | 49.27 | 0.872 | 186.06 |
| 10 | 45 | 12.5 | 11.5 | 8.4 | 49.44 | 0.891 | 178.26 |
| 11 | 45 | 13 | 10 | 7.8 | 49.82 | 0.960 | 163.59 |
| 12 | 45 | 13.5 | 10.5 | 7.2 | 49.98 | 0.966 | 159.30 |
| 13 | 30 | 12 | 11.5 | 7.8 | 50.12 | 0.999 | 146.25 |
| 14 | 30 | 12.5 | 11 | 7.2 | 50.38 | 1.026 | 141.63 |
| 15 | 30 | 13 | 10.5 | 9.0 | 49.57 | 0.922 | 153.55 |
| 16 | 30 | 13.5 | 10 | 8.4 | 49.90 | 0.963 | 148.62 |
In the range analysis, the R-value for each factor is computed as the difference between the maximal and minimal mean values of the corresponding responses. Using this, I ranked the factors in order of sensitivity. For the maximum battery temperature, the order of influence is: L > α > d2 > d1. Thus, the length and the angle affect the cooling performance of the EV battery pack to the greatest extent. In contrast, the order of the effect on the temperature standard deviation is: d2 > d1 > α > L, which indicates that the temperature uniformity is predominantly governed by the periodic spacing of the rib-grooved arrays. The pressure drop is most sensitive to the inclination angle α and the length L. By combining the optimum levels from the three single-objective range analysis results, I determine the final optimal geometric solution. The ideal structure consists of an inclination angle of 45°, a column spacing of 13.5 mm, a row spacing of 11.5 mm, and a rib-grooved length of 7.5 mm. This combination simultaneously realizes modest pressure loss, a minimal standard deviation of temperature, and a low maximum cell temperature within the bounds of the present design.
6. Full CFD-based Single-objective Genetic Algorithm Optimization
Orthogonal tests can help to optimize dimensions; however, the arrangement and positions of rib-groove units within the liquid-cooled plate also play an important role in minimizing the temperature gradient and reducing the flow resistance. To further improve the structural design, I switched to a full CFD-based optimization procedure. According to this continuous approach, the space inside the liquid-cooled plate is discretized into a grid of candidate positions for the ribs and grooves. I divided the available planar space into 14 columns and 5 rows, creating a potential placement map of 70 locations. This mapping gave a binary encoding for each point, so that this chromosome vector represents the arrangement pattern of ribs. The position of a particular rib-groove unit is defined by the coordinates:
$$P_{i,j} = \left( a_1 + (i-1)p_1, \; b_1 + (j-1)p_2 \right), \quad i = 1,\ldots,14, \; j=1,\ldots,5$$
where $a_1 = 56$ mm, $b_1 = 4.65$ mm and $p_1 = 13.5$ mm, $p_2 = 11.5$ mm are the distances between the locations. The binary variable for whether the current location holds a rib-groove is written as:
$$C_{i,j} = \begin{cases} 0 & \text{No rib-groove placed at } P_{i,j} \\ 1 & \text{Rib-groove is kept at } P_{i,j} \end{cases}$$
If the objective function was based on maximum temperature, the optimizer would simply maintain all rib-groove units, as strengthening the heat transfer would necessarily lower the peak temperature, though energy consumption and pressure drop would be high. Conversely, if pressure drop was the only criterion, the optimizer would remove all ribs, but this would worsen the thermal control. To strike a balance between the two targets, I formulate a single objective function as:
$$J = T_{\sigma}$$
Where $T_{\sigma}$ measures the temperature dispersion along the contact surface of the liquid-cooled plate. This single-objective optimization is thus intended to minimize $T_{\sigma}$ in the EV battery pack. I embedded this objective function in a MATLAB/COMSOL co-simulation framework where the genetic algorithm was coupled with Computational Fluid Dynamics. The GA handles the chromosome encoding of the rib-groove existence, and for each chromosome, which is transmitted to COMSOL automatically. In this full CFD setup, the CFD model was run with no surrogate approximations, and the computed temperature standard deviation is returned to the GA. I selected a maximum number of generations of 100 and population size of 50. The iteration process converged before the 26th generation, when the values of the objective function approached an asymptotic value of $T_{\sigma} = 0.68°C$. The optimal pattern resembles a spatially non-uniform layout: the zones in the front part of the flow field close to the inlet show a low density of ribs, whereas the rear part of the plate preserves as many units as possible. There is an important thermo-hydraulic explanation behind this outcome: the inlet coolant is at its lowest temperature, and its cooling capacity is already high. Therefore, removing ribs at this location does not harm the thermal performance. On the other hand, reducing the ribs in that zone reduces flow resistance, which is associated with decreased pumping losses. However, by the time the coolant travels to the rear portion, it has absorbed heat and its temperature is higher, necessitating sustained heat exchange enhancement by maintaining the rib-grooved units. Moreover, the retention of ribs in the downstream half promotes flow mixing between the channels. As a direct consequence, the optimized distribution provides a more uniform temperature distribution along the longitudinal direction of the EV battery pack. The improvement in the flow field in the optimized arrangement is also apparent through the lower synergy angle β values, which indicate an improved alignment between the velocity field and the temperature gradient field. The results of the optimization are summarized in Table 8.
Table 8: Performance comparison of initial and optimized rib-groove layouts
| Layout | T_max (°C) | T_σ (°C) | ΔP (Pa) |
|---|---|---|---|
| Initial layout (uniform grid) | 50.51 | 1.02 | 142.43 |
| Optimal layout (GA / CFD) | 50.70 | 0.68 | 131.09 |
| Relative difference | +0.38% | −33% | −9% |
Upon comparing the data, the optimized liquid-cooled plate maintained the maximum temperature of the EV battery pack almost unchanged, with only a marginal increase of 0.4% compared to the initial structure. Meanwhile, the temperature standard deviation was decreased by 33%, indicating that the temperature of the battery module is spatially more uniform. Finally, the pressure drop decreases by 9%, which reduces parasitic energy consumption of the cooling system. Therefore, the optimized liquid-cooled plate yields a more balanced performance: it effectively regulates the temperature of the EV battery pack while also reducing the energy burden of the BTMS. This demonstrates the soundness of using the full CFD model with a single-objective genetic algorithm, as the search process can uncover non-intuitive design configurations of rib-groove distributions.
7. Conclusions
In this research, a novel rib-grooved liquid-cooled plate with a discrete and inclined layout of ribs and grooves was proposed, studied, and optimized to ensure the correct thermal management of an EV battery pack. The most important conclusions drawn from this work can be summarized as follows:
(1) Numerical simulation has confirmed that the novel plate improves the cooling capability and the temperature uniformity of the EV battery pack. Specifically, relative to the standard straight-channel cooling plate, the maximum temperature decreased by 2.56°C and the temperature standard deviation was lowered by 0.58°C under identical conditions, with only a small additional pressure drop of 71.92 Pa. This outcome is achieved due to the longitudinal swirl flow generated by grooves and to the flow-distribution equalization among channels induced by the ribs.
(2) The general characterization of the operating parameters of the battery cooling system showed that increasing the inlet velocity generally lowers both the maximum temperature and the temperature standard deviation of the EV battery pack, while it linearly increases the pressure drop. The discharge current had a negligible effect on the coolant pressure drop but greatly affected the temperature field, because of changes in heat generation.
(3) Using four possible orientations to classify the rib sequence position, the wave-like arrangement displayed better thermal performance. The optimal row and column number counts are found to be 5 and 7, respectively, for the present dimensions. Additional analysis through orthogonal tests indicates that the best overall geometry is achieved at 45° tilt angle, 13.5 mm column spacing, 11.5 mm row spacing, and 7.5 mm rib-groove length.
(4) In a further step of the optimization procedure, the rib-groove layout is customized by the integration of a full CFD model with a single-objective GA. The algorithm optimally reduces the number of ribs and grooves in the upstream direction while retaining them in the downstream region. As a consequence, the optimized plate decreases the temperature standard deviation by 33% and reduces pressure drop by 9% relative to an initial uniformly patterned layout. This means the BTMS as a whole can run more efficiently without substantially compromising the thermal regulation of the EV battery pack.