Design and Optimization of Cooling Plate for Battery Module of an Electric Vehicle

: With the development of electric vehicles, much attention has been paid to the thermal management of batteries. The liquid cooling has been increasingly used instead of other cooling methods, such as air cooling and phase change material cooling. In this article, a lithium iron phosphate battery was used to design a standard module including two cooling plates. A single battery numerical model was ﬁrst created and veriﬁed as the basis of the module heat transfer model. Orthogonal experimental design method was adopted in the module thermal model to optimize the main parameters in the module: Battery gap, the cross-section size, and the number of coolant channels of the cooling plate. The Surrogate Model was then utilized to further optimize geometry of the cooling plate. Finally, the optimized geometry was rebuilt in the module thermal model for analysis. The comparison showed that the maximum and minimum temperature difference in the cooling plate was reduced by 9.5% and the pressure drop was reduced by 16.88%. It was found that the battery temperature difference and the pressure drop decreased with the increase of the cross-section and number of the coolant channel when the coolant ﬂow rate was constant at the inlet.


Introduction
As an important type of energy storage units, lithium batteries have been developed for many years and their performance has been greatly improved. They have been gradually applied to artificial satellites, robots, and electric vehicles (EV) [1][2][3][4]. Nowadays, more and more electric vehicles are being produced, and lithium batteries are being widely used, but a lot of the heat in the process of using has appeared [5]. The service life, capacity, and internal resistance of the batteries are sensitive to temperature changes. In order to prolong the service life of the battery, it is particularly important to design a battery module with good heat dissipation performance.
Air cooling can meet the requirements of the vehicles in common conditions, but the battery temperature will be higher. When the EV changes the speed frequently or it is at high velocity, the battery is discharging at a high rate, air cooling is unable to meet the requirements of cooling alone [6,7]. Although the cooling effect can be optimized by changing the position, number, and angle of the entrance, adding a guide plate and changing the battery arrangement, it is still difficult to meet the needs of different electric vehicles [8][9][10]. Phase change material (PCM) cooling system controls the temperature of the battery module by the heat absorption and heat release when its material phase changes. Power battery cooling experiments using PCM are easier to meet the needs of the lithium battery cooling system, but the cost is high, and it is used less in electric vehicles [11][12][13].
Since the introduction of a liquid cooling system with high cooling efficiency and reliability [14][15][16], it has gradually occupied the electric vehicle market. The liquid cooling system in the BMW I3 and the Tesla model S, have good sealing and reliability, and can take away the heat of each battery evenly and exhibit good performance in electric vehicles. Patil et al. [17] studied the cooling performance of 20 Ah lithium-ion pouch cell with cold plates along both surfaces by changing the inlet coolant mass flow rates and the inlet coolant temperatures. The enhanced cooling energy efficiency was achieved with a low inlet coolant temperature, low inlet coolant mass flow rate, and a high number of the cooling channels. Panchal et al. [18] experimentally investigated the temperature and velocity distributions within the mini-channel cold plates placed on a prismatic lithium-ion battery cell using water cooling methods. Wang et al. [19] carried out experimental and simulations to study the effect of cooling channels, flow rates, and flow directions at different discharge C-rates. It was found that the maximum temperature reached within the battery decreased as the amount of thermal silica plates and liquid channels increased. Wang et al. [20] designed a new liquid cooling strategy based on thermal silica plates combined with the cooling effect of water. The experimental results demonstrated that the addition of thermal silica plates can greatly improve the cooling capacity.
In this paper, a lithium iron phosphate battery was used to design a standard module which can be quickly interchanged by EV, and then the liquid cooling plate for the module was analyzed by numerical heat transfer analysis. A surrogate model was utilized to further optimize the geometry of the cooling plate.

Thermal Analysis of a Single Battery
The governing equations which were used to solve the time dependent three-dimensional flow problems include the continuity equation, momentum equation, and the energy equation. The equation of state was given in Equations (1)-(5) [21][22][23][24]: Continuity equation Energy equation The main working parameters of the lithium iron phosphate battery [25] are shown in Table 1. The interior part of the battery was simplified as an equivalent solid model and the following assumptions were made for the model: (1) The material properties in lithium batteries were uniformly distributed. Because of the multi-layer structure and manufacturing process of lithium batteries, only the thermal conductivity was anisotropic; (2) Thermal radiation and convection can be neglected inside the lithium battery; (3) The specific heat capacity and thermal conductivity of materials in the lithium batteries were constant and independent of the temperature; (4) When the battery was charged and discharged, the current and heat generation were considered uniformly distributed.
It was difficult to accurately obtain the heat generation rate of batteries due to the complexity of vehicle operating conditions and environment. The internal resistance of the battery was assumed constant under ambient temperature, and the battery resistance was set to 10 mΩ. According to the classic model proposed by Bernardi et al. [26], the heating generation rate of batteries was established below in Equation (6). The polarization heat, chemical reaction heat and the electrode cap heat was not considered in the model.
where, V represents the volume of the battery, in cubic meters, U 0 , the open circuit voltage in volts, U, the working voltage of the battery in volts, T, the temperature in Kelvin, ∂U 0 ∂T is measured experimentally, the value is very small at room temperature with a low discharge rate and can be neglected.
Therefore, Equation (6) can be simplified and expressed as follows: U 298. 15 represents the open circuit voltage of the battery in the temperature of 298.15 K, in volts; R is total internal resistance which is obtained by the internal resistance, R e , and the polarization internal resistance, R p , in ohms.
In addition to the complex heat generation inside the battery, the heat generation outside the battery will also occur, such as the positive and negative electrodes, the confluent and the welding position of the conductor. These heats can be neglected when studying the heat generation of the battery. Equation (7) was used in this paper to estimate the heat generation of the battery. The heat generation rate of the lithium battery at 2C discharge rate was 29, 359.953W/m 3 . C-rate is the measurement of the charge and discharge current with respect to its nominal capacity. Considering the experimental environment and the boundary conditions of simulation, the Boussinesq hypothesis was used for the calculation: (1) The dissipation of fluid viscosity was neglected during the process of fluid flow; (2) except the fluid density, other thermal properties were constant with varying temperature; (3) for density, only the terms related to volume force in momentum equation were included and the temperature of 25 • C was used as the reference temperature for calculation. The thermal properties of the battery are shown in Table 2: The dimension of the battery is 131mm × 65mm × 16mm, the positive and negative electrode columns were not included in the model. The simplified model of the battery was established by CATIA as shown in Figure 1b, the fluid field was created according to the cooling method in Ge's Appl. Sci. 2019, 9,754 4 of 20 experiment [16], as shown in Figure 1c. In the analysis, the natural cooling process of the lithium battery was simulated at 2C discharge rate for a period of 1800 s. The temperature evolution was monitored and outputted at the end of each time step. The results of the cell surface temperature after 1800 s at 25 • C are shown in Figure 2. The maximum temperature was 325.8 K and located in the central area of the battery surface. Surface temperature decreased gradually to the periphery. The lowest temperature of the battery was 322.2 K at the four corners. The temperature difference of the whole battery surface was 3.6 K. The dimension of the battery is 131mm × 65mm × 16mm, the positive and negative electrode columns were not included in the model. The simplified model of the battery was established by CATIA as shown in Figure 1b, the fluid field was created according to the cooling method in Ge's experiment [16], as shown in Figure 1c. In the analysis, the natural cooling process of the lithium battery was simulated at 2C discharge rate for a period of 1800 s. The temperature evolution was monitored and outputted at the end of each time step. The results of the cell surface temperature after 1800 s at 25 °C are shown in Figure 2. The maximum temperature was 325.8 K and located in the central area of the battery surface. Surface temperature decreased gradually to the periphery. The lowest temperature of the battery was 322.2 K at the four corners. The temperature difference of the whole battery surface was 3.6 K. The velocity streamline diagram of air in a natural convection condition surrounding the lithium battery is shown in Figure 3. It can be seen that air flew from boundaries of air domain to the surface of the batteries, and buoyancy increased with the increase of the temperature on the surface of the battery. The air velocity in the central region leaving the battery surface with the highest temperature was 0.1362 m/s.  The velocity streamline diagram of air in a natural convection condition surrounding the lithium battery is shown in Figure 3. It can be seen that air flew from boundaries of air domain to the surface of the batteries, and buoyancy increased with the increase of the temperature on the surface of the battery. The air velocity in the central region leaving the battery surface with the highest temperature was 0.1362 m/s.
To verify the thermal model of the single battery, comparison with the experimental results in paper [25] was plotted in Figure 4. The surface temperature was measured by a K-type thermocouple during the experiment. During the discharging process, the temperature at the monitoring point gradually increased with time. The highest temperature in the experiment and numerical analysis were 53.84 • C and 51.39 • C, respectively, implying a difference within 5%. The reasons for this error may result from the assumptions made in the simulation and the heat generation equation did not take into account the polarization heat, chemical reaction heat, and the electrode cap heat. To verify the thermal model of the single battery, comparison with the experimental results in paper [25] was plotted in Figure 4. The surface temperature was measured by a K-type thermocouple during the experiment. During the discharging process, the temperature at the monitoring point gradually increased with time. The highest temperature in the experiment and numerical analysis were 53.84°C and 51.39°C, respectively, implying a difference within 5%. The reasons for this error may result from the assumptions made in the simulation  The cell discharged at 25 °C without cooling, the maximum temperature can reach 53.84 °C, which was higher than the optimum operating temperature range of the battery. Because of the various usage conditions of the EV battery, high power discharge will occur inevitably. When power batteries are assembled in large quantities, the heat dissipation efficiency becomes low. To solve this problem, it is necessary to design a standard battery module and incorporate a cooling system to ensure the working environment temperature of batteries.

Design of Standard Battery Module
48 volts was chosen as the standard voltage for the battery module. The voltage of the lithium iron phosphate power battery is 3.2 V, and 15 batteries were used in a module. According to dimension of traction battery for electric ve The cell discharged at 25 • C without cooling, the maximum temperature can reach 53.84 • C, which was higher than the optimum operating temperature range of the battery. Because of the various usage conditions of the EV battery, high power discharge will occur inevitably. When power batteries are assembled in large quantities, the heat dissipation efficiency becomes low. To solve this problem, it is necessary to design a standard battery module and incorporate a cooling system to ensure the working environment temperature of batteries. hicles, GB/T 34013-2017 (China standard), the following arrangement scheme was preliminarily designed, as shown in Figure 5.

Design of Standard Battery Module
The liquid cooling plate of the battery module was made of an aluminum plate with a thickness of 2 mm. According to the scheme, the sizes of the aluminum plate and the fluid channel patterns were determined as shown in Figure 6. The geometry of the entrance and exit was 1 mm (height) × 15 mm (width), and the fluid channels were symmetrically arranged in the aluminum plate. For the initial design, all the parallel channels were the same, and the size was 1 mm (height) × 5 mm (width).  The liquid cooling plate of the battery module was made of an aluminum plate with a thickness of 2 mm. According to the scheme, the sizes of the aluminum plate and the fluid channel patterns were determined as shown in Figure 6. The geometry of the entrance and exit was 1 mm (height) × 15 mm (width), and the fluid channels were symmetrically arranged in the aluminum plate. For the initial design, all the parallel channels were the same, and the size was 1 mm (height) × 5 mm (width).
Appl. Sci. 2019, 9, x FOR PEER REVIEW 6 of 26 Figure 6. Initial design of cooling plate. Figure 6. Initial design of cooling plate.
CATIA was employed to build the 3-dimensional battery module. The module had fifteen lithium batteries arranged in the form of a 1 × 15, as shown in Figure 7. The batteries were connected in series, and the total voltage of the module was 48 V. Cooling plates were placed on the top and bottom sides of the battery. At the same time, the silica gel pads were added between the cooling plates and the batteries to improve the heat transfer efficiency, as shown in Figure 8. The dimension of the whole module was 288 mm × 131 mm × 71 mm.  In this study, 50% ethylene glycol and water mixed solution was used as the coolant, whose working temperature range was 5-35 • C. The flow in the channels of the cooling plates was considered as laminar flow. The thermal properties of the coolant at 25 • C were tabulated in Table 3. This work used the ANSYS/FLUENT [27] to model the fluid zone and the solid zone was built, respectively, the model was meshed as shown in Figure 9, and the size of the grids was chosen in such a way that the resultant temperature and pressure drop were independent of the grid size. The inlet flow velocity was 0.5m/s, and the heat generation rate of each battery at 2C discharge rate was 29,359.953W/m 3 .
The inlet coolant temperature was fixed at 25 • C. To model the heat convection at the contact surfaces among cooling plate, silicone pad and battery, the couple walls were established in the interfaces. Radiation heat transfer was not considered in this model. In this study, 50% ethylene glycol and water mixed solution was used as the coolant, whose working temperature range was 5-35°C. The flow in the channels of the cooling plates was considered as laminar flow. The thermal properties of the coolant at 25°C were tabulated in Table 3. This work used the ANSYS/FLUENT [27] to model the fluid zone and the solid zone was built, respectively, the model was meshed as shown in Figure 9, and the size of the grids was chosen in such a way that the resultant temperature and pressure drop were independent of the grid size. The inlet flow velocity was 0.5m/s, and the heat generation rate of each battery at 2C discharge rate was 29,359.953W/m 3 . The inlet coolant temperature was fixed at 25 °C. To model the heat convection at the contact surfaces among cooling plate, silicone pad and battery, the couple walls were established in the interfaces. Radiation heat transfer was not considered in this model.    In order to verify the grid independence, different grid sizes were selected to discretize the model. The result of the grid independence study was plotted in Figure 10. Both the pressure drops and the temperature difference of the cooling plate tended to be stable at the grid of 6.7 × 10 6 . The mesh sizes used for the following In order to verify the grid independence, different grid sizes were selected to discretize the model. The result of the grid independence study was plotted in Figure 10. Both the pressure drops and the temperature difference of the cooling plate tended to be stable at the grid of 6.7 × 10 6 . The mesh sizes used for the following study were 4 mm, 0.5 mm, and 0.3 mm for the battery, silica gel pad, and cooling plate, respectively.
Appl. Sci. 2019, 9, x FOR PEER REVIEW 10 of 26 study were 4 mm, 0.5 mm, and 0.3 mm for the battery, silica gel pad, and cooling plate, respectively. The orthogonal experimental design strategy was chosen in the numerical analysis to screen the optimal configuration and shape parameters of the battery module. Three factors and three levels were carried out to determine the effect of each factor on the pressure difference between the inlet and outlet of the cooling plate (pressure drop), the surface temperature difference of the cooling plate in contact with the silica gel pad (plate temperature difference), and the temperature difference among all the battery surfaces in the module (battery temperature difference). As illustrated in Table  4, the cross section of each channel, battery spacing, and number of channels were taken as design factors with three levels.
Orthogonal test results were presented in Table 5. In Table 6, kij (i = A,B,N,C; j = 1, 2, 3) was the average value of the calculated results shown in Table 5 for each factor at the same level, and the equation of range analysis can be given as follow: In the Equation (8), Ri was the range value of the evaluation index.
The results of the orthogonal test and the range value of three evaluation indexes were tabulated in Tables 5-7. Factor A was the main factor in the three indexes with the largest range, indicating the greatest influence on the indexes, while factor B had the least impact on the three evaluation indexes.   The orthogonal experimental design strategy was chosen in the numerical analysis to screen the optimal configuration and shape parameters of the battery module. Three factors and three levels were carried out to determine the effect of each factor on the pressure difference between the inlet and outlet of the cooling plate (pressure drop), the surface temperature difference of the cooling plate in contact with the silica gel pad (plate temperature difference), and the temperature difference among all the battery surfaces in the module (battery temperature difference). As illustrated in Table 4, the cross section of each channel, battery spacing, and number of channels were taken as design factors with three levels. Orthogonal test results were presented in Table 5. In Table 6, k ij (i = A,B,N,C; j = 1, 2, 3) was the average value of the calculated results shown in Table 5 for each factor at the same level, and the equation of range analysis can be given as follow: In the Equation (8), R i was the range value of the evaluation index.
The results of the orthogonal test and the range value of three evaluation indexes were tabulated in Tables 5-7. Factor A was the main factor in the three indexes with the largest range, indicating the greatest influence on the indexes, while factor B had the least impact on the three evaluation indexes. The effect of factors in different levels on indexes were presented in Figure 11. For the main factor A, the pressure drop index decreased sharply from level 1 to level 3. The battery temperature difference decreased as well, but the slope became smaller. The plate temperature difference decreased from level 1 to level 2 and then increased slightly from level 2 to level 3. Therefore, the level A 3 is best. The trend of factor C was the same as the main factor A, and the level C 3 was chosen. Factor B has the least influence on all indexes. Considering the compactness of the battery module, the level B 1 was preferred. The optimal scheme, A 3 B 1 C 3 was implemented for the following study.
The accuracy of the numerical analysis was verified by comparing the theoretical cooling fluid temperature rise with the simulation value, as shown in Equation (9): ∆t coolant is the temperature difference for coolant; N is the number of batteries; φ 0 is the heat generated per unit time of the cell, φ 0 = I 2 R; m in is the flow rate of the coolant at the entrance.
The numerically predicted outlet temperature rise was 1.1 • C, and very close to the theoretical value. The surface temperature distribution of 15 batteries in the battery module was shown in Figure 12. It can be seen that the maximum temperature of the battery surface was 32.3 • C and the minimum temperature was 26.4 • C. The high temperature zone was close to the outlet in the middle of the module. The minimum temperature was located on the surface of the battery near the inlet of the cooling plate and the battery temperature difference was 5.9 • C. 7 3 1 3 2 4.28 5.9 1.9 8 3 2 1 3 3.97 5.9 1.9 9 3 3 2 1 5.28 6.1 2.1 difference decreased as well, but the slope became smaller. The plate temperature difference decreased from level 1 to level 2 and then increased slightly from level 2 to level 3. Therefore, the level A3 is best. The trend of factor C was the same as the main factor A, and the level C3 was chosen. Factor B has the least influence on all indexes. Considering the compactness of the battery module, the level B1 was preferred. The optimal scheme, A3B1C3 was implemented for the following study. The accuracy of the numerical analysis was verified by comparing the theoretical cooling fluid temperature rise with the simulation value, as shown in equation (9): ∆t is the temperature difference for coolant; N is the number of batteries; ϕ is the heat generated per unit time of the cell, ϕ = I R; m is the flow rate of the coolant at the entrance.
The numerically predicted outlet temperature rise was 1.1°C, and very close to the theoretical value. The surface temperature distribution of 15 batteries in the battery module was shown in Figure  12. It can be seen that the maximum temperature of the battery surface was 32.3 °C and the minimum temperature was 26.4 °C. The high temperature zone was close to the outlet in the middle of the module. The minimum temperature was located on the surface of the battery near the inlet of the cooling plate and the battery temperature difference was 5.9 °C.
The pressure distribution of the cooling plate was shown in Figure 13. The pressure distribution and pressure drop for each channel were similar, revealing good flow consistency. The pressure drop of the cooling plate was 3.85 kPa. The temperature distribution on the cooling surface was illustrated Appl. Sci. 2019, 9, x FOR PEER REVIEW 12 in Figure 14. The lowest temperature on plate surface was 25.2 °C at the inlet end, while the hi temperature was at the plate corners near the outlet end, with a temperature difference of 1.9 ° in large, the plate surface temperature gradually increased from inlet end to out end. The highes lowest temperatures of each battery were plotted in Figure 15, and the maximum temper difference was less than 5 °C. The pressure distribution of the cooling plate was shown in Figure 13. The pressure distribution and pressure drop for each channel were similar, revealing good flow consistency. The pressure drop of the cooling plate was 3.85 kPa. The temperature distribution on the cooling surface was illustrated in Figure 14. The lowest temperature on plate surface was 25.2 • C at the inlet end, while the highest temperature was at the plate corners near the outlet end, with a temperature difference of 1.9 • C. By in large, the plate surface temperature gradually increased from inlet end to out end. The highest and lowest temperatures of each battery were plotted in Figure 15, and the maximum temperature difference was less than 5 • C.

Surrogate Model-based Optimization
Apart from the analysis of the main parameters of the lithium battery modules in the above section, the arrangement and geometric details of channels also had influence on the battery temperature and the cooling plate temperature. In this section, the channels in the cooling plate were further optimized by the surrogate model of the cooling plate in the workbench platform [28,29]. The flow chart of optimization was illustrated in Figure 16.

Surrogate Model-Based Optimization
Apart from the analysis of the main parameters of the lithium battery modules in the above section, the arrangement and geometric details of channels also had influence on the battery temperature and the cooling plate temperature. In this section, the channels in the cooling plate were further optimized by the surrogate model of the cooling plate in the workbench platform [28,29]. The flow chart of optimization was illustrated in Figure 16.
Geometric parameterization was carried out on a quarter of the cooling plate, as shown in Figure 17. L 1 , L 2 , L 3 , H 1 and H 2 were the geometric parameters of the cooling plate and the range of the geometric parameters were tabulated in Table 8.
In the surrogate model, only the cooling plate was considered. To obtain the thermal load on the plate surface, heat flux distribution in the fluent model on the plate surface was first calculated as shown in Figure 18, and then heat flux values were extracted for seven straight lines on the surface of the cooling plate facing the batteries, as illustrated in Figure 19. The extracted values of seven lines were curve fitted by quadratic polynomial and the fitted curves were shown in Figure 20. All the heat flux curves increased towards the center of the plate and reached peak values at Z = 0 mm. The peak value at X = −126 mm was greater than that at X = 126 mm because the temperature difference between the coolant and plate at inlet was greater than that at the outlet. Geometric parameterization was carried out on a quarter of the cooling plate, as shown in Figure  17. L1, L2, L3, H1 and H2 were the geometric parameters of the cooling plate and the range of the geometric parameters were tabulated in Table 8.  To obtain the thermal load on the plate surface, heat flux distribution in the fluent model on the plate surface was first calculated as shown in Figure 19, and then heat flux values were extracted for seven straight lines on the surface of the cooling plate facing the batteries, as illustrated in Figure 18. The extracted values of seven lines were curve fitted by quadratic polynomial and the fitted curves were shown in Figure 20. All the heat flux curves increased towards the center of the plate and reached peak values at Z = 0 mm. The peak value at X = −126 mm was greater than that at X = 126 mm because the temperature difference between the coolant and plate at inlet was greater than that at the outlet.
where, q flux was the heat flux on the cooling plate surface; Z was the coordinate variable along the coordinate Z direction; According to the battery number shown in Figure 7b, the fitting results of X = 0 mm were applied to the corresponding regions of the cooling surface as the thermal boundary conditions of the cell numbers 7, 8, and 9. The fitting results of X = 54 mm were applied to the corresponding regions of the cell numbers 10, 11, and 12. The fitting results of X = −54mm were applied as the thermal boundary conditions of the cell numbers 4, 5, and 6. The fitting results of X = −108mm were applied to the corresponding region of batteries No.2 and No.3. The fitting results of X = 108 mm were applied to the corresponding region of batteries No. 13 and No.14. The fitting results of X = −126 mm and X = 126 mm were applied to the corresponding regions of batteries No.1 and No.15, respectively. The heat flux between two batteries on the cooling plate was set to a constant value of 300 W/m 2 .
The simplified cooling plate was imported into workbench and the parameters were set. The maximum temperature on the surface of the cooling plate and the pressure drop of the cooling plate were taken as the output parameters.
In the experimental design [30][31][32] of surrogate models, a reasonable number of sample points was selected, which can reflect the spatial characteristics of the design in a limited design space by using the mathematical method. The quality of sample points determined the accuracy of the fitted model directly. The central composite experimental design was utilized as the sampling method for all concerned. Surrogate model [33,34] was an approximate mathematical model using an approximate method to fit the discrete data (sample points). The response and change of the target were predicted by design variables in this model. By comparison with the numerical model ( Figure 9) in Section 2, the surrogate model can significantly reduce the computational cost. The sample points obtained by the central composite experimental design was fitted by Kriging model [35]. The determination coefficient was 1 and the root mean square error was 1.7538 × 10 −7 and 3.3085 × 10 −10 in the fitting quality of temperature and pressure response. The fitting accuracy was acceptable and the model was feasible.
The sensitivity of the plate maximum temperature and pressure drop in response to the parameters were shown in Figure 21. The influence of L 1 and H 1 on the pressure drop was more significant than other parameters. The channel distance parameters affected the plate temperature difference in the sequence of L 3 > L 2 > L 1 . Surrogate models with parameter combinations of L 1 , H 1 and pressure drop and combination of L 3 , L 2 , and surface temperature were established, respectively. As shown in Figure 22, the parameters L 2 and L 3 in the surrogate model were positively correlated with temperature, and the influence of L 3 on temperature was greater than that of L 2 . The range of temperature response values was 26.8-27.6 • C. In Figure 23, the parameters L 1 and H 1 were also positively correlated with pressure drop and the range of pressure drop response values was 3.16-3.48 kPa. difference in the sequence of L3 > L2 > L1. Surrogate models with parameter combinations of L1, H1 and pressure drop and combination of L3, L2, and surface temperature were established, respectively. As shown in Figure 22, the parameters L2 and L3 in the surrogate model were positively correlated with temperature, and the influence of L3 on temperature was greater than that of L2. The range of temperature response values was 26.8-27.6°C. In Figure 23, the parameters L1 and H1 were also positively correlated with pressure drop and the range of pressure drop response values was 3.16-3.48 kPa.   The 2 • C temperature difference of the cooling plates was set as the constraint, and the minimum pressure drop was taken as the objective to optimize this model.
Three candidate designs were obtained, and the optimal parameters were selected as shown in Table 9. The optimized size of the cooling plate was presented in Table 10. The pressure drops calculated was 3.2176 kPa and the maximum temperature of cooling plate was 26.99 • C. Comparing with the results, which were not optimized, the plate temperature difference and pressure drop were reduced by 5.24% and 16.88%, respectively.  The 2 °C temperature difference of the cooling plates was set as the constraint, and the minimum pressure drop was taken as the objective to optimize this model.
Three candidate designs were obtained, and the optimal parameters were selected as shown in Table 9. The optimized size of the cooling plate was presented in Table 10. The pressure drops calculated was 3.2176 kPa and the maximum temperature of cooling plate was 26.99°C. Comparing with the results, which were not optimized, the plate temperature difference and pressure drop were reduced by 5.24% and 16.88%, respectively. The numerical model (Figure 9) was then rebuilt with the optimized parameters. Battery surface temperature distribution, the cooling plate temperature distribution and coolant pressure distribution were shown in Figures 24-26, respectively. It can be seen that the maximum temperature of the cooling plate was 26.9°C and the pressure drop was 3.2 kPa. The errors were 0.33% and 0.55% in comparison with the surrogate model for the plate temperature difference and pressure drop, respectively. The numerical model (Figure 9) was then rebuilt with the optimized parameters. Battery surface temperature distribution, the cooling plate temperature distribution and coolant pressure distribution were shown in Figures 24-26, respectively. It can be seen that the maximum temperature of the cooling plate was 26.9 • C and the pressure drop was 3.2 kPa. The errors were 0.33% and 0.55% in comparison with the surrogate model for the plate temperature difference and pressure drop, respectively.

Conclusions
The temperature results predicted by the single battery thermal model showed good agreement with experiments by a difference less than 5%, implying that the heat generation model and the assumptions were reasonable.
A methodology for the design and optimization of the cooling plate for the battery module was proposed. A complex heat transfer model for the whole module was created, including batteries, two cooling plates, silicone gel pads, and coolant. Orthogonal experimental design was implemented by the numerical analysis to optimize the main parameters of the module. The cooling plate geometry was further optimized by the surrogate model method. With the optimized geometry, the cooling plate was rebuilt in the module thermal model for the analysis. The comparison showed that the maximum and minimum temperature difference in the cooling plate was reduced by 5.24% and the pressure drop was reduced by 16.88%.
It was concluded from the orthogonal design analysis that the battery temperature difference and the pressure drop decreased with the increase of the cross-section and number of the coolant channel when the coolant flow rate was constant at the inlet. From the sensitivity analysis of the plate, the maximum temperature and pressure drop in response to the plate geometric parameters in the surrogate models, it was found that the center channel distance, L1, and the size of the inlet plenum exhibited the greatest influence on the pressure drop.

Conclusions
The temperature results predicted by the single battery thermal model showed good agreement with experiments by a difference less than 5%, implying that the heat generation model and the assumptions were reasonable.
A methodology for the design and optimization of the cooling plate for the battery module was proposed. A complex heat transfer model for the whole module was created, including batteries, two cooling plates, silicone gel pads, and coolant. Orthogonal experimental design was implemented by the numerical analysis to optimize the main parameters of the module. The cooling plate geometry was further optimized by the surrogate model method. With the optimized geometry, the cooling plate was rebuilt in the module thermal model for the analysis. The comparison showed that the maximum and minimum temperature difference in the cooling plate was reduced by 5.24% and the pressure drop was reduced by 16.88%.
It was concluded from the orthogonal design analysis that the battery temperature difference and the pressure drop decreased with the increase of the cross-section and number of the coolant channel when the coolant flow rate was constant at the inlet. From the sensitivity analysis of the plate, the maximum temperature and pressure drop in response to the plate geometric parameters in the surrogate models, it was found that the center channel distance, L1, and the size of the inlet plenum exhibited the greatest influence on the pressure drop.