CFD Modeling and Thermal Analysis of a Cold Plate Design with a Zig-Zag Serpentine Flow Pattern for Li-Ion Batteries

: Heavy-duty vehicles, such as trucks or buses, typically have larger battery packs compared to passenger electric vehicles (EVs). These batteries generate more heat due to the increased power demands of the vehicle. Effective thermal management is therefore crucial to prevent excessive heat buildup and maintain optimal battery performance. This paper aimed to develop a dynamic and efﬁcient cooling system for larger Li-ion batteries used in electric vehicles. In this study, we propose a novel cold plate design featuring a zig-zag serpentine ﬂow pattern within a rectangular proﬁle channel. The chosen design maximizes the coolant coverage over the cold plate’s surface area. To investigate the performance of the cold plate design, we designed and modeled a total of six different cold plates with varying numbers of channels (3, 5, 7, 9, 11, and 13). Preliminary simulations were conducted using Star CCM+ software. The cold plate material selected for its high thermal conductivity was aluminum, while water served as the coolant. Several parameters were optimized, including adjustments to channel width, mass ﬂow rate, heat ﬂux, and inlet coolant temperature. The optimization was conducted to determine the optimal design for the cold plate. We found that the best design conﬁgurations were ﬁve-channel with an 18 mm channel width and a seven-channel with a 16 mm channel width. It was found that the temperature rapidly increased and reached its maximum in the outlet region. In the design with three channels, the maximum temperature attained at the exit region was 330.84 K. The temperature gradually decreased at the exit region when the number of the channels increased from 3 channels to 13 channels and achieved a minimum temperature of 316 K for the design with 13 channels. For these conﬁgurations, heat ﬂuxes of 2 ◦ C and 3 ◦ C were found to be optimal, while a discharge rate of 4 ◦ C was deemed acceptable. The zig-zag design and the obtained results are instrumental in designing and evaluating the performance of cold plates by exploring various parameters. This research contributes to the development of an effective cooling system for large Li-ion batteries in EVs, potentially enhancing their efﬁciency and reliability.


Introduction
From the early 90s, environmentalists began to be concerned about climate change from the various human outcomes.The global energy crisis tremendously affected the lives of people, and generated interest in the field of transport to focus on electric powertrains [1,2].Vehicles which run on fossil fuels became the top contributors to greenhouse gases (GHG).Gases such as carbon dioxide (CO 2 ), hydrocarbons (HC), nitrogen oxides (NO), carbon monoxide (CO), water, etc. are emitted from fossil-fueled vehicles.The transportation sector consumes almost 27% of the world's total energy and contributes nearly 33% of GHG emissions.The concept of an Electric Vehicle (EV) provides a way to reduce the world's GHG.Additionally, it significantly reduces the cost of operation and manufacturing compared to fossil-fueled vehicles as mentioned by Tie and Tan, 2013 [3].From an engineering perspective, temperature management is the most challenging task in designing EVs.Temperature optimization that involves a battery, electric motor, HVAC, and inverter can be facilitated by what is called a battery thermal management system (BTMS), as shown in Figure 1.
tion and dust.For efficient heat transfer, the cold plate is directly in contact with a battery pack.
This paper aimed to develop a cold plate where the coolant flows in a zig-zag manner to envelop the maximum area of contact with the cold plate.The cold was developed in several channel patterns, allowing the water to extract all the heat produced from a battery pack.This paper is organized as follows: 1.The presentation of analytical methods which involve the parameters required to simulate the design; 2. the discussion of the CFD modeling approach; 3. explanation of the algorithm and optimization of the method to analyze the cold plate; and 4. presentation of the effect of the parameters in a different channel of the cold plate.

Literature Review
As the demand for the EV expands, many engineers and researchers are working continuously to improve and enhance the efficiency and performance of these EVs, which involves cold plate technology.Design optimization of 18 cooling plates to investigate the thermal performance conducted by Jarrett and Kim, 2011 [9] showed that they performed a serpentine steady flow, considering the objective function of pressure drop, temperature uniformity, and the average temperature of plates.They found that larger width channels provide the low pressure drops and narrow the channel width toward the outlet, providing the required coolant velocity and increasing the heat transfer.A study conducted by Xun et al., 2013 [10] to investigate thermal management by considering the analytical and numerical method in a multi-dimensional model showed that varying the size and number of cooling channels resulted in a lower average temperature of the battery stack, but the cooling efficiency increased with an increase in the number of channels, which results in irregular temperature distribution.To enhance the heat transfer coefficient, fins are usually installed.A simulation was conducted by Jin et al., 2014 [11] using a designed liquid cold plate (LCP) to optimize the maximum temperature and temperature gradient.LCP contains the inclined fin with better width and angle.The results showed significant improvement in maintaining the surface temperature below 50 °C under a low flow rate.Their study proved that the oblique fin structure advances the conventional cold plate, and a simple oblique fin configuration maximizes the BTMS performance.Research conducted by Huo et al., 2015 [8] on mini channel cold plates with rectangular ducts using two different flow directions established the effect of the direction of flow, the number of channels, inlet mass flow rate of coolant, and ambient temperature.Their simulated results showed that the maximum temperature of the pack decreases with an increase in mass flow rate and the number of channels and suggested that the cooling performance Thermal analysis of cold plate design for battery cooling is crucial for several reasons.Li-ion batteries used in EVs generate heat during operation, and excessive heat can degrade their performance, reduce their lifespan, and even pose safety risks.A well-designed cooling system ensures that the batteries operate within the optimal temperature range, enhancing their efficiency and longevity.Such an analysis enables us to optimize the design parameters to achieve efficient heat dissipation and maintain uniform temperature distribution across the battery cells.Effective cooling systems help prevent thermal runaway events and mitigate the risk of battery overheating.Accurate thermal analysis ensures that the cold plate design can handle the expected heat load and provides a safe operating environment for the batteries.
However, conducting thermal analysis for cold plate designs can present various challenges.Battery packs consist of numerous individual cells that generate heat unevenly.The presence of cell-to-cell variations, geometric complexities, and packaging constraints make thermal analysis challenging.Accurately modeling the thermal behavior of such systems requires sophisticated computational techniques and careful consideration of various factors, such as thermal interfaces and localized heat generation.Analyzing the transient behavior of the cold plate design under different operating conditions is crucial to ensure effective cooling throughout the battery's entire life cycle.
Since the advent of EVs, different types of batteries have been used, such as lead-acid, nickel-cadmium, nickel-metal hydride, lithium-ion, and solid-state batteries.Among them, the lithium-ion battery has a higher energy density, which can save space and allow a compact battery design.However, it is highly sensitive to high temperatures (Yacoub Al Shdaifat et al., 2022) [4].During charging and discharging, the electrochemical process produces electricity, and heat increases the temperature.Hence, BTMS is required to maintain a uniform temperature.The main function of the BTMS is safety, constant performance, and lifespan of the battery.The normal operating condition of BTMS is between 20 • C and 40 • C. If the temperature falls below 10 • C, the battery will slow down the vehicle's performance and if exceeds 80 • C, it leads to thermal runaway (Amalesh and Narasimhan, 2020) [5].Heat generation occurs in two ways: during electrochemical operation and Joule heating.The heat transfer inside the battery can be divided into three parts (Fathabadi, 2014) [6].
(i) The generation of heat from the cell's internal resistance; (ii) Occurrence of change in entropy during cell discharge in the cell components; (iii) Heat transfer takes place by convection to the ambient condition.
Several cooling methods have been implemented in battery packs, including air cooling, liquid cooling, direct refrigerant coolant, phase change method (PCM), thermo-electric modules, and heat pipe modules (Chen et al., 2022) [7].Generally, the air cooling method is associated with natural and forced air convection.Due to the low thermal conductivity of the air, this method requires a large amount of quantity to maintain the uniform temperature of the battery pack.However, this drawback can be mitigated by employing water, which has higher thermal conductivity (Huo et al., 2015) [8].Sometimes liquids involve water, refrigerant, or ethylene glycol.Considering the economy and feasibility, cold plates are more efficient and maintain a safer temperature within the limit.Cold plates generally comprise a thermally conductive material to dissipate the heat produced by the battery pack.The design of the cold plate is typically compact and can fit in the EVs.The overall size and weight reduce the operating and manufacturing cost.The advantage over other methods is that it is less prone to failure, which is affected by vibration and dust.For efficient heat transfer, the cold plate is directly in contact with a battery pack.
This paper aimed to develop a cold plate where the coolant flows in a zig-zag manner to envelop the maximum area of contact with the cold plate.The cold was developed in several channel patterns, allowing the water to extract all the heat produced from a battery pack.This paper is organized as follows: 1.The presentation of analytical methods which involve the parameters required to simulate the design; 2. the discussion of the CFD modeling approach; 3. explanation of the algorithm and optimization of the method to analyze the cold plate; and 4. presentation of the effect of the parameters in a different channel of the cold plate.

Literature Review
As the demand for the EV expands, many engineers and researchers are working continuously to improve and enhance the efficiency and performance of these EVs, which involves cold plate technology.Design optimization of 18 cooling plates to investigate the thermal performance conducted by Jarrett and Kim, 2011 [9] showed that they performed a serpentine steady flow, considering the objective function of pressure drop, temperature uniformity, and the average temperature of plates.They found that larger width channels provide the low pressure drops and narrow the channel width toward the outlet, providing the required coolant velocity and increasing the heat transfer.A study conducted by Xun et al., 2013 [10] to investigate thermal management by considering the analytical and numerical method in a multi-dimensional model showed that varying the size and number of cooling channels resulted in a lower average temperature of the battery stack, but the cooling efficiency increased with an increase in the number of channels, which results in irregular temperature distribution.To enhance the heat transfer coefficient, fins are usually installed.A simulation was conducted by Jin et al., 2014 [11] using a designed liquid cold plate (LCP) to optimize the maximum temperature and temperature gradient.LCP contains the inclined fin with better width and angle.The results showed significant improvement in maintaining the surface temperature below 50 • C under a low flow rate.Their study proved that the oblique fin structure advances the conventional cold plate, and a simple oblique fin configuration maximizes the BTMS performance.Research conducted by Huo et al., 2015 [8] on mini channel cold plates with rectangular ducts using two different flow directions established the effect of the direction of flow, the number of channels, inlet mass flow rate of coolant, and ambient temperature.Their simulated results showed that the maximum temperature of the pack decreases with an increase in mass flow rate and the number of channels and suggested that the cooling performance in different flow directions was lesser despite the increase in mass flow rate.A similar simulation was conducted by Qian et al., 2016 [12] with different numbers of channels in a mini-cold plate and found that a five-channel straight flow design was optimal.They proved that the temperature of the pack was dramatically reduced by increasing the inlet mass flow rate.A comparative study was performed by Panchal et al., 2017 [13] on mini-channel cold plates to determine the temperature and velocity distribution, which were analyzed at different discharge levels, and they found that the temperature in the battery pack increased with the increase in discharge levels.Their research paved the way for the design optimization of cold plates.Analogous to Qian's paper, a serpentine model with a U-shaped flow pattern with a different number of channels was studied and simulated by Deng et al., 2018 [14].A fivechannel design was proven to reduce the temperature to 26 • C compared to the two-channel design.Additionally, coolant temperature increased with an increase in the inlet mass flow rate.In the cold plate channel, a pump is required to pump the coolant at a certain pressure to the cold plate.Using several channels increases the pressure drop, which is one of the main concerns in designing the flow pattern in the cold plate.A pressure drop investigation was conducted by Jiaqiang et al., 2018 [15] in a mini channel cold plate in a serpentine model.By varying the structural parameters in the different series of U-tubes, the pressure drop was determined, paving the way for the design of the U-tube in the serpentine model by considering the parameters which can reduce the pressure drop.The coolant temperature and the rate of flow have a large impact on the cooling performance in cold plates.In a study by Li et al., 2019 [16] via 3D thermal modeling, the effects of the inlet velocity of the coolant were studied.Aging of the pack is caused by high-temperature operation and can be prevented by choosing an adequate coolant velocity.Their results are significant in the design of the flow path of coolants based on the inlet velocity.A significant cold plate design was developed by Amalesh and Narasimhan, 2020 [5], where they proposed eight different flow patterns, including the straight channel, which were rectangular slot, below channel, square-wave channel, arc channel, sine-wave channel, circular slot, and zig-zag channel.Their study found that the proposed design showed compelling cooling performance to the straight channel.One of their results revealed that the zig-zag channel design was the best option for the pressure drop because it covers a larger area surface than a straight channel design.

CFD Modelling
The battery pack used in EV was configured by a series of rectangular stack cells placed on the cold plate.A group of 8-10 battery cells were arranged in a single cold plate.Depending on the load or types of EVs, the number of cold plates used varies in number.Battery Electric Vehicles (BEV) contain 10-12 cold plates whereas BEV trucks contain 14-16 cold plates.This paper aimed to develop and focus on a single cold plate used in larger Li-ion battery vehicles.Cold plates' zig-zag patterns and designs are shown in Figures 2 and 3.    A cold plate is generally a heat exchanger where heat dissipated from the battery pack is absorbed by the flowing coolant in the cold plate.The cold plates are broadly designed in a channel flow path to enclose the maximum area of heat surface which can be absorbed by the coolant.A set of two cold plates (top and bottom plate) was designed, as shown in Figure 4.The outer dimension of the cold plate is 310 mm × 340 mm × 5 mm (Li et al., 2020) [17].The channels for the coolant were modeled in a zig-zag pattern observed A cold plate is generally a heat exchanger where heat dissipated from the battery pack is absorbed by the flowing coolant in the cold plate.The cold plates are broadly designed in a channel flow path to enclose the maximum area of heat surface which can be absorbed by the coolant.A set of two cold plates (top and bottom plate) was designed, as shown in Figure 4.The outer dimension of the cold plate is 310 mm × 340 mm × 5 mm (Li et al., 2020) [17].The channels for the coolant were modeled in a zig-zag pattern observed by Amalesh and Narasimhan, 2020 [5], where they proved zig-zag pattern performs better in cooling performance.
Energies 2023, 16, x FOR PEER REVIEW 6 of 24 by Amalesh and Narasimhan, 2020 [5], where they proved zig-zag pattern performs better in cooling performance.Hence, a zig-zag pattern with a continuous U-tube flow pattern as shown in Figure 3 was developed with a different number of channels.The concern with the zig-zag design is that it can increase the pressure drop.Therefore, the modeling method was carried out using a 6 mm radius along the length, as shown in Figure 2, which carries throughout the plate.This paper initially proposes 6 cold plates with 3, 5, 7, 9, 11 and 13 channel flow Hence, a zig-zag pattern with a continuous U-tube flow pattern as shown in Figure 3 was developed with a different number of channels.The concern with the zig-zag design is that it can increase the pressure drop.Therefore, the modeling method was carried out using a 6 mm radius along the length, as shown in Figure 2, which carries throughout the plate.This paper initially proposes 6 cold plates with 3, 5, 7, 9, 11 and 13 channel flow patterns for the preliminary design.The width and thickness of the channels for the coolant to flow were 12 mm and 2 mm (1 mm on each plate), respectively, as shown in Figure 5.A high thermal conductivity material of aluminum was chosen as a cold plate and assumed to be isotropic and homogenous in this study and water was used as a coolant (Deng et al., 2018) [14].In this study, a Li-ion battery of 100 Ah capacity with a discharge rate of 2 • C was used for the initial analysis.The analysis and simulation were conducted using Star CCM+ software.Hence, a zig-zag pattern with a continuous U-tube flow pattern as shown in Figure 3 was developed with a different number of channels.The concern with the zig-zag design is that it can increase the pressure drop.Therefore, the modeling method was carried out using a 6 mm radius along the length, as shown in Figure 2, which carries throughout the plate.This paper initially proposes 6 cold plates with 3, 5, 7, 9, 11 and 13 channel flow patterns for the preliminary design.The width and thickness of the channels for the coolant to flow were 12 mm and 2 mm (1 mm on each plate), respectively, as shown in Figure 5.A high thermal conductivity material of aluminum was chosen as a cold plate and assumed to be isotropic and homogenous in this study and water was used as a coolant (Deng et al., 2018) [14].In this study, a Li-ion battery of 100 Ah capacity with a discharge rate of 2 °C was used for the initial analysis.The analysis and simulation were conducted using Star CCM+ software.

Analytical Equations
The heat generated from the cell is convected by the fluid: where A is the area of the cell, the h is the heat transfer coefficient, Tcell is the temperature of the battery cell, and Tfluid is the temperature of the coolant and the total temperature rise of the fluid is determined by where ṁ is the mass flow rate, and Cp is the specific heat capacity.The Reynolds number which defines the type of flow is as follows:

Analytical Equations
The heat generated from the cell is convected by the fluid: where A is the area of the cell, the h is the heat transfer coefficient, T cell is the temperature of the battery cell, and T fluid is the temperature of the coolant and the total temperature rise of the fluid is determined by where m˙is the mass flow rate, and Cp is the specific heat capacity.The Reynolds number which defines the type of flow is as follows: where ρ is the density of the water, v is the velocity and D is the hydraulic diameter of the rectangular duct (D = 3.43 mm).For the preliminary analysis test run, the mass flow was set to 10 g/s.The corresponding Reynolds number was 1607, which is laminar flow (Re < 2000).
The laminar model must be selected in the analysis model.Nusselt Number (Nu) defines the heat transfer from fluid (convection) to solid (conduction) across the boundary.
where h is the heat transfer coefficient, D is the hydraulic diameter of the rectangular duct and k is the thermal conductivity of the coolant.The Nu number does not depend on the Reynolds number for laminar flow inside a rectangular duct.But it follows the pattern concerning the aspect ratio (0.167).The Nu theoretical value was found to be approximately 6.25.Hence, the theoretical heat transfer coefficient was 1175 W/m 2 -K (on duct), which lies in the simulation result between 189.26 and 12,000 W/m 2 -K (average HTC).Hence, we can assure the reliability of the simulation model.The pressure drop in the interior channel of the cold plate is where v is the velocity of the fluid, f is the friction factor, l is the channel flow length and D is the hydraulic diameter.The formula for the friction factor is where F is the shape factor and is found to be 0.89 for the non-circular channels (Liu et al., 2014) [18].The pump pressure required to pump coolant to the cold plate is where qm is the mass flow rate of incompressible fluid.This paper solves the steady state condition and Star CCM+ solver is used to solve the governing equations for the conservation of mass, momentum, and energy for a Newtonian incompressible fluid.For the coupling of the continuity and momentum equations, the SIMPLE algorithm was used with second-and third-order equations.This study only considers the steady state condition, and the relevant equations are shown below (Jarrett and Kim, 2011) [9].
where x and u are direction vectors and velocity in cartesian space, respectively.µ is the coolant viscosity, c is the specific heat capacity, and ∆ is the Laplacian operator.Additionally, the heat dissipated from the cold plate to the atmosphere is demonstrated by Newton's law of cooling.q c = h a Ap(Tc − Ta) where q c is the conventional heat dissipation, h a is the heat transfer coefficient of air, Ap is the area of the cold plate, T c is the temperature of the coolant and T a is the temperature of the air.

Algorithm and Optimization Technique
This paper aimed to determine the optimum cold plate among the proposed designs.The main findings were the temperature gradient, pressure drop (∆p), heat transfer (h), and standard deviation of temperature (T σ ).This paper's objective was to minimize the pressure drop between the outlet and inlet and maximize the uniform temperature distribution on the cold plate.The lower the standard deviation temperature on the surface of the cold plate, the larger the uniformity of temperature.The T σ was defined by Huo et al., 2015 [8].
where T avg is the average temperature.From Equation (10), the smaller the standard deviation of temperature, the more uniformity of the temperature on the cold plate surface, and also, we tend to reduce the T avg from the temperature gradient.Both parameters were

CFD Analysis and Physics Model
The analysis and simulation were conducted using the Star CCM+ solver package.The design was imported as a parasolid (.xt) file.Two physics domains were created for coolant (fluid) and plates (solid) with boundary conditions listed in Table 2 and shown in Figure 6.This paper aimed to simulate a model in three-dimensional steady-state state conditions.The laminar flow was employed for initial preliminary test cases.The imprint operation was carried out to create an interface between two plates and coolant plates.and standard deviation of temperature (Tσ).This paper's objective was to minimize the pressure drop between the outlet and inlet and maximize the uniform temperature distribution on the cold plate.The lower the standard deviation temperature on the surface of the cold plate, the larger the uniformity of temperature.The Tσ was defined by Huo et al., 2015 [8].
where Tavg is the average temperature.From Equation 10, the smaller the standard deviation of temperature, the more uniformity of the temperature on the cold plate surface, and also, we tend to reduce the Tavg from the temperature gradient.Both parameters were provided in the Star CCM+ solver.The material properties of the plate and coolant are shown in Table 1.The optimization objectives are as follows: To minimize: Δp, Tσ, Tavg, Tmax; To maximize: h; constraint: the wall of the cold plate ; variable: the mass flow of coolant, the width of the channel;

CFD Analysis and Physics Model
The analysis and simulation were conducted using the Star CCM+ solver package.The design was imported as a parasolid (.xt) file.Two physics domains were created for coolant (fluid) and plates (solid) with boundary conditions listed in Table 2 and shown in Figure 6.This paper aimed to simulate a model in three-dimensional steady-state state conditions.The laminar flow was employed for initial preliminary test cases.The imprint operation was carried out to create an interface between two plates and coolant plates.The meshing of the model is important because the parameters including surface, volume mesh cells, cell nodes, and model element shape have an impact on the accuracy of the results and the numerical behavior of the model.To represent accurate geometry and for better convergence, the polyhedral mesh was chosen for this model.The grid-independent study was conducted to assess the sensitivity of numerical simulations to the grid resolution employed.It aimed to determine the minimum mesh element required to obtain accurate and reliable results without excessive computational resources.Hence, a grid independent study was conducted on a three-channel number cold plate to determine the change in T max with respect to the mesh element.From Table 3, it can be seen that the results diverged when mesh elements increased from 1.36 million.A base size of 3 mm and minimum size of 0.75 mm were applied for the cold plate and a target size of 0.5 mm and minimum size of 0.25 mm were applied for the coolant.A prism layer was introduced between the fluid and solid contact surface to capture the miniature details in the boundary wall.Hence, two prism layers and a prism layer thickness of 0.25 mm were introduced in this model, as shown in Figure 7.In addition, an extrusion of 120 mm (4 times the hydraulic diameter) was applied to both the inlet and outlet region to ensure a fully developed flow as shown in Figure 8, and it did not affect the inlet and outlet flow condition.The inlet mass flow rate of 10 g/s was applied in the preliminary analysis and a heat flux of 7000 W/m 2 was applied on the top surface of the upper plate.Physical models for the coolant and cold plane are shown in Table 4. of the results and the numerical behavior of the model.To represent accurate geometry and for better convergence, the polyhedral mesh was chosen for this model.The gridindependent study was conducted to assess the sensitivity of numerical simulations to the grid resolution employed.It aimed to determine the minimum mesh element required to obtain accurate and reliable results without excessive computational resources.Hence, a grid independent study was conducted on a three-channel number cold plate to determine the change in Tmax with respect to the mesh element.
From Table 3, it can be seen that the results diverged when mesh elements increased from 1.36 million.A base size of 3 mm and minimum size of 0.75 mm were applied for the cold plate and a target size of 0.5 mm and minimum size of 0.25 mm were applied for the coolant.A prism layer was introduced between the fluid and solid contact surface to capture the miniature details in the boundary wall.Hence, two prism layers and a prism layer thickness of 0.25 mm were introduced in this model, as shown in Figure 7.In addition, an extrusion of 120 mm (4 times the hydraulic diameter) was applied to both the inlet and outlet region to ensure a fully developed flow as shown in Figure 8, and it did not affect the inlet and outlet flow condition.The inlet mass flow rate of 10 g/s was applied in the preliminary analysis and a heat flux of 7000 W/m 2 was applied on the top surface of the upper plate.Physical models for the coolant and cold plane are shown in Table 4.The convective heat transfer coefficient for air was applied as 10.0 W/m 2 -K.The relevant reports and plots were created for the simulation result.The iteration was terminated when the difference of value in the was is less than 0.2%, which was considered a better convergence (approx.1000 iterations).The number of cells for the 3-channel design was 1.3 million, whereas for the 13-channel design was 3.6 million.

Coolant
Cold Plate The convective heat transfer coefficient for air was applied as 10.0 W/m 2 -K.The relevant reports and plots were created for the simulation result.The iteration was terminated when the difference of value in the was is less than 0.2%, which was considered a better convergence (approx.1000 iterations).The number of cells for the 3-channel design was 1.3 million, whereas for the 13-channel design was 3.6 million.

Results and Discussion
The cooling performance of the cold plate was investigated in this study.The width of the channel was set to 12 mm in the preliminary analysis.Air was set as a region around the cold plate and other boundary conditions were applied as stated in Table 2.We monitor parameters such as the max temperature of the cold plate (T max ), the pressure drop between inlet and outlet (∆p), heat transfer between plate-coolant (solid-liquid) interface (h), average temperature (T avg ), and standard deviation of temperature (T σ ).The results obtained after 1000 iterations (difference in value < 0.2%) were compared with those of Deng et al., 2018 [14] and Jarrett and Kim, 2011 [9] to ensure and compare the reliability of the results.The temperature uniformity of the cold plate was significant for the battery pack to control the temperature.
(a) Effect of the number of the cooling channel To study the effect of several channels in the cold plate, six designs were developed as shown in Figure 3.The mass flow rate of the coolant was set to 10 g/s.The temperature of the coolant and ambient condition was set to 300 K.The temperature gradient of the six designs was shown in Figure 9.In the below temperature distribution, the coolant flows from the top right and flows out in the bottom left direction.From the temperature gradient it can be seen that the temperature is lower in the inlet region, rapidly increases, and is maximum in the outlet region.This aspect tells the coolant absorbs heat dissipation continuously when it flows through the channel.In design 1 (3-channel), the maximum temperature attain in the exit region was 330.84 K; the temperature gradually decreased in the exit region when the number of the channel increased from design 1 to design 6 and achieved a minimum temperature of 316 K in design 6 (13-channel).From Figure 9, the maximum temperature was potent at the edges of the channel.This indicates the poor heat transfer by convection between air and the plate along the thickness.
Figure 10 shows the growth of the temperature of each design with several channels.The Li-ion battery operates better between 298 K and 318 K.The maximum temperature reached for 11-and 13-channel numbers were 316 K, which is acceptable.Additionally, the maximum temperatures were 318 K and 320 K for 9-and 7-channel numbers respectively, which is moderately acceptable in the preliminary analysis.Nearly 14.84 K reduces when the number of channels increases from 3 to 13.The reason is due to the increased heat transfer that occurs between the plate and coolant when the surface area of the coolant flowing area increases.Hence, Figure 10a demonstrates that the temperature decreases proportionally as the number of channels increases.Further, the number of channels cannot be increased due to the dimension constraint of the plate.Channel numbers 5, 7, 11, and 13 showed similar maximum temperature, and did not vary much.To assess the reliability of the cooling performance, we validated the temperature gradient obtained in our study by comparing it with the findings from Deng et al.'s study (2018) [14].In our comparison, we discovered that Deng et al. reported temperatures of 325 K and 316 K for systems with 3 and 5 channel numbers, respectively.In our study, we observed temperatures of 330 K and 320 K for the corresponding channel numbers.Through this comparison, it became evident that there are slight differences in the temperature values between our study and Deng et al.'s study.While our temperatures were slightly higher, it is important to note that the overall trend of decreasing temperature with increasing channel numbers remained consistent.
Energies 2023, 16, x FOR PEER REVIEW 11 of 24 continuously when it flows through the channel.In design 1 (3-channel), the maximum temperature attain in the exit region was 330.84 K; the temperature gradually decreased in the exit region when the number of the channel increased from design 1 to design 6 and achieved a minimum temperature of 316 K in design 6 (13-channel).From Figure 9, the maximum temperature was potent at the edges of the channel.This indicates the poor heat transfer by convection between air and the plate along the thickness.Figure 10 shows the growth of the temperature of each design with several channels.The Li-ion battery operates better between 298 K and 318 K.The maximum temperature reached for 11-and 13-channel numbers were 316 K, which is acceptable.Additionally, the maximum temperatures were 318 K and 320 K for 9-and 7-channel numbers respectively, which is moderately acceptable in the preliminary analysis.Nearly 14.84 K reduces when the number of channels increases from 3 to 13.The reason is due to the increased heat transfer that occurs between the plate and coolant when the surface area of the coolant flowing area increases.Hence, Figure 10i demonstrates that the temperature decreases proportionally as the number of channels increases.Further, the number of channels cannot be increased due to the dimension constraint of the plate.Channel numbers 5, 7, 11, and 13 showed similar maximum temperature, and did not vary much.To assess the reliability of the cooling performance, we validated the temperature gradient obtained in our study by comparing it with the findings from Deng et al.'s study (2018) [14].In our comparison, we discovered that Deng et al. reported temperatures of 325 K and 316 K for systems with 3 and 5 channel numbers, respectively.In our study, we observed temperatures of 330 K and 320 K for the corresponding channel numbers.Through this comparison, it became evident that there are slight differences in the temperature values between our study and Deng et al.'s study.While our temperatures were slightly higher, it is important to note that the overall trend of decreasing temperature with increasing channel numbers remained consistent.A similar trend can be seen in Figure 10b; the average temperature (T avg ) decreased with the increase in the number of channels, and hence the temperature difference must be lower as possible.The surface standard deviation of temperature tells the uniformity distribution in the cold plate.The lower value of T σ gives better uniformity.From Figure 10c, channel number 13 shows the better uniformity of temperature distribution of 3.02 K whereas the 3-channel number shows 6.01 K, almost the doubled value.This explains that the coolant can absorb more heat from the plate and maintain temperature uniformity with an increase in the number of channels.However, the five-channel design showed a lower T σ than that of the three-channel design.This phenomenon showed better uniformity in design 2 than in design 3.These aspects induce the way for further optimization.The research conducted by Jarrett and Kim (2011) [9] focused on the design optimization of a cold plate, evaluating eight different designs.According to their study, the temperature standard deviation (T σ ) ranged from 1.5 K to 4.0 K across the different designs.In our preliminary analysis, we investigated 6 designs and found that the T σ varied between 3 K and 6 K.While there is a difference in the specific temperature ranges between our study and Jarrett and Kim's research, both studies highlight the variability of T σ as an important factor in cold plate design optimization.Despite the disparities in the absolute values of T σ , the overall emphasis on optimizing the design to reduce temperature variations remains consistent in both studies.The findings from our preliminary analysis align with the notion that T σ can be controlled and minimized through design modifications and improvements.But this trend follows the opposite for pressure drop (∆p).The pressure in the inlet region is comparatively high.When the coolant starts entering the inlet region, the interface area between the plate channel and coolant gradually increases, and the resistance for the coolant flow increases.This eventually decreases the pressure of the coolant flow and results in an increase in pressure drop (∆p).Moreover, the zig-zag pattern and U-bend in the design further resist the flow and increase pressure drop.Therefore, the pressure drop increases proportionally to the number of channels, as shown in Figure 11.Hence more power from the pump is required to pump the coolant to circulate till it reaches the outlet region in design 6 than in design 1.The boundary conditions at the outlet region are applied as the zero pressure outlet and resistance no longer increases; hence, regardless of the number of channel increases, the coolant pressure drop reaches a balance value, as shown in Figure 11.The pressure drop (∆p) obtained in our study was compared to the findings of a relevant existing study conducted by Deng et al. (2018) [14].Specifically, we compared the pressure drop for systems with 3 and 5 channel numbers.In Deng et al.'s study, the pressure drop was reported to be approximately 20,000 Pa and 40,000 Pa, respectively.In contrast, our study demonstrated pressure drops of around 3000 Pa and 6500 Pa for the corresponding channel numbers.The observed discrepancy in the pressure drop comparison can be attributed to differences in the design flow pattern and the mass flow rate of the coolant used between the two studies.Despite these variations, it is important to note that both studies exhibit a similar trend in terms of pressure drop patterns.While our study yielded lower pressure drop values compared to Deng et al.'s study, this can be explained by the differences in design and coolant characteristics.The variations in flow pattern and mass flow rate inevitably influence the pressure drop outcomes.However, the fact that the overall trend remains consistent suggests that the fundamental behavior of the system is maintained, albeit with varying magnitudes.Therefore, while there may be differences in the absolute values of the pressure drop between our study and the existing literature, the overall trend observed in both studies is in agreement.This reinforces the reliability of our findings and highlights the importance of considering the impact of design factors and coolant characteristics when interpreting and comparing pressure drop results in similar systems.
Additionally, the velocity of the coolant decreases due to the zig-zag pattern and U-bend in the flowing channel.Consideration of the pressure drop parameter allows for the selection of the optimization phase.Another parameter that shows the cooling performance of the cold plate is the Heat transfer rate (W).The heat is transferred from the contact area or the interface between the cold plate and coolant.The heat transfer decreases with the increase in the number of channels, as shown in Figure 12.This explains the heat transfer equation which is Q = m.c.∆T,where m is the mass, c is the specific heat and ∆T is the temperature difference.
When the number of channels increases from design 1 to design 6, the removal of material increases, and hence the conduction of heat transfer in the cold plate (solid) reduces; therefore, it reduces the heat transfer to the coolant.However, design 2 showed a higher heat transfer value of 722 W than that of design 1, which was 713 W.There was almost a 39% increase in heat transfer rate between design 2 and design 6, which shows the enhancement of the cooling performance of the cold plate.The average heat transfer coefficient between the plate and coolant was found to be 1.245 W/m 2 -K for all designs.From the above-described parameters result, the T σ , T max , and T avg were better in design 5 and 6 but showed better performance gradually in designs 2, 3, and 4, in terms of ∆p and h.In further analysis, due to the dimension constraint and high-pressure drop, designs 5 and 6 were kept unchanged for comparative study for further analysis and channel width changes in designs 2, 3, and 4. The summary of preliminary results is shown in Table 4.By comparing our simulation results with the existing numerical study, we established a level of confidence in the accuracy and validity of our findings.The validation process helped verify that our simulation methodology and assumptions are consistent with established literature, further reinforcing the reliability of our result.Thus, proceeding with the optimization technique.selection of the optimization phase.Another parameter that shows the cooling perfor mance of the cold plate is the Heat transfer rate (W).The heat is transferred from the con tact area or the interface between the cold plate and coolant.The heat transfer decrease with the increase in the number of channels, as shown in Figure 12.This explains the hea transfer equation which is Q = m.c.ΔT, where m is the mass, c is the specific heat and ΔT i the temperature difference.When the number of channels increases from design 1 to design 6, the removal o material increases, and hence the conduction of heat transfer in the cold plate (solid) re duces; therefore, it reduces the heat transfer to the coolant.However, design 2 showed higher heat transfer value of 722 W than that of design 1, which was 713 W.There wa almost a 39% increase in heat transfer rate between design 2 and design 6, which show the enhancement of the cooling performance of the cold plate.The average heat transfe coefficient between the plate and coolant was found to be 1.245 W/m 2 -K for all designs From the above-described parameters result, the Tσ, Tmax, and Tavg were better in design and 6 but showed better performance gradually in designs 2, 3, and 4, in terms of Δp and h.In further analysis, due to the dimension constraint and high-pressure drop, designs and 6 were kept unchanged for comparative study for further analysis and channel width changes in designs 2, 3, and 4. The summary of preliminary results is shown in Table 4 By comparing our simulation results with the existing numerical study, we established a level of confidence in the accuracy and validity of our findings.The validation proces helped verify that our simulation methodology and assumptions are consistent with es tablished literature, further reinforcing the reliability of our result.Thus, proceeding with the optimization technique.

(b) Effect of change in channel width
Designs 2, 3, and 4 were considered to change the width (wp) of the channel.Th channel width was changed from 12 mm to 14 mm and 16 mm and 18 mm for design and the thickness remains constant.Due to design constraints in designs 3 and 4, the chan nel width changed to 14 mm and 16 mm (not 18 mm).The simulation was run with th same boundary conditions and inlet mass flow rate of 10 g/s and the results were analyzed and compared with those of designs 5 and 6.
Figure 13 shows the temperature gradient after channel width changes to 14 mm (a) 16 mm (b), and 18 mm (c).It is observed that there were no changes in temperature gra dient and almost similar trends were obtained from the preliminary analysis.There wa a correlation between the aspect ratio of the rectangular duct and the velocity.The velocity (b) Effect of change in channel width Designs 2, 3, and 4 were considered to change the width (wp) of the channel.The channel width was changed from 12 mm to 14 mm and 16 mm and 18 mm for design 2 and the thickness remains constant.Due to design constraints in designs 3 and 4, the channel width changed to 14 mm and 16 mm (not 18 mm).The simulation was run with the same boundary conditions and inlet mass flow rate of 10 g/s and the results were analyzed and compared with those of designs 5 and 6.
Figure 13 shows the temperature gradient after channel width changes to 14 mm (a), 16 mm (b), and 18 mm (c).It is observed that there were no changes in temperature gradient and almost similar trends were obtained from the preliminary analysis.There was a correlation between the aspect ratio of the rectangular duct and the velocity.The velocity of the coolant decreases from 0.42 m/s to 0.36 m/s, to 0.31 m/s, and to 0.278 m/s for channel widths of 14 mm,16 mm, and 18 mm respectively.This decrease in velocity directly affects the average HTC, which observed negligible changes of nearly 0.06% and 0.09% in designs (a) and (b), respectively.Figure 14 shows the Max temperature vs. temperature gradient and pressure drop.This decrease in velocity also affects the T σ shown in Figure 15, where there is a negligible increase in the T σ with an increase in channel width.
But when compared to the preliminary analysis with design 5 and 6 give better temperature uniformity.The significant result that occurred by changing the width channel is the pressure drop (∆p); the pressure drop was drastically reduced when the channel width increased from 12 mm.This aspect is due to the lower resistance for the coolant and provides a large surface area for the coolant to flow.Hence, the design with a 16 mm channel width seems to achieve low-pressure drop.Among them, designs 2b, 2c, and 3b achieved a better pressure drop, and there were no significant changes in the heat transfer (W) compared to the preliminary design.
Hence, in this section, we conclude that changes in channel width show compelling decreases in the pressure drop from the preliminary analysis.T max , T σ , and h show only negligible changes.From this analysis, designs 5 and 6 show better performance in terms of T max and T σ at the expense of pressure drop.To reduce the T σ and maximum temperature and also to overcome the pressure drop between the inlet and outlet, further investigation is required.Employing this analysis results shown in Table 5, designs 2b, 2c, and 3b show improvement compared to those in the preliminary analysis.Hence, we considered designs 2b, 2c, and 3b for the next optimization phase.
of the coolant decreases from 0.42 m/s to 0.36 m/s, to 0.31 m/s, and to 0.278 m/s for channel widths of 14 mm,16 mm, and 18 mm respectively.This decrease in velocity directly affects the average HTC, which observed negligible changes of nearly 0.06% and 0.09% in designs (a) and (b), respectively.Figure 14 shows the Max temperature vs. temperature gradient and pressure drop.This decrease in velocity also affects the Tσ shown in Figure 15, where there is a negligible increase in the Tσ with an increase in channel width.But when compared to the preliminary analysis with design 5 and 6 give better temperature uniformity.The significant result that occurred by changing the width channel is the pressure drop (Δp); the pressure drop was drastically reduced when the channel width increased from 12 mm.This aspect is due to the lower resistance for the coolant and provides a large surface area for the coolant to flow.Hence, the design with a 16 mm channel width seems to achieve low-pressure drop.Among them, designs 2b, 2c, and 3b achieved a better pressure drop, and there were no significant changes in the heat transfer (W) compared to the preliminary design.But when compared to the preliminary analysis with design 5 and 6 give better temperature uniformity.The significant result that occurred by changing the width channel is the pressure drop (Δp); the pressure drop was drastically reduced when the channel width increased from 12 mm.This aspect is due to the lower resistance for the coolant and provides a large surface area for the coolant to flow.Hence, the design with a 16 mm channel width seems to achieve low-pressure drop.Among them, designs 2b, 2c, and 3b achieved a better pressure drop, and there were no significant changes in the heat transfer (W) compared to the preliminary design.Hence, in this section, we conclude that changes in channel width show compelling decreases in the pressure drop from the preliminary analysis.Tmax, Tσ, and h show only negligible changes.From this analysis, designs 5 and 6 show better performance in terms

(c) Effect of inlet mass flow rate
In this section, we checked whether the inlet flow rate affects the variations in parameters.From the study of Deng et al., 2018 [14], the inlet flow rate affects the variation in T max , T σ , ∆p, and h.Hence, the inlet mass flow rate was increased to 15 g/s (laminar flow) for designs 2b, 2c, and 3b.The obtained results were compared with the previous results.Figures 16 and 17 show that the maximum temperature was reduced to 314 K from 320 K and also T σ was reduced, as shown in Table 6, which was a compelling improvement in cooling performance, but the pressure drop increased by 49% in each case.This phenomenon explains that the increase in mass flow rate has an impact on T max , T σ , and ∆p.Additionally, mass flow rate did not affect much in heat transfer, which had a slight increase in all designs.Therefore, a further increase in mass flow would increase the performance of the cold  Therefore, a further increase in mass flow would increase the performance of the cold plate but further increase the pressure drop by nearly 50%.Hence designs 2b, 2c, and 3b did not differ much in the cooling performance of the cold plate.Therefore, a further increase in mass flow would increase the performance of the cold plate but further increase the pressure drop by nearly 50%.Hence designs 2b, 2c, and 3b did not differ much in the cooling performance of the cold plate.
(d) Effect of change in heat flux Until Section 4 (c), the 2C discharge rate (7000 W/m 2 ) was used for the analysis.Further investigation was performed on designs 2c and 3b with a higher discharge rate of 3C, 4C, and 5C.The heat flux applied on the top surface of the upper plate was changed to 11,000 W/m 2 , 15,000 W/m 2, and 19,000 W/m 2 from the respective discharge rate.The aim of this section (d) is to find optimal condition of the cold plate under different discharge rates.We found that an increase in the heat flux increases the T max , T σ , and h.T max increased to nearly 9K in each case, as shown in Figure 18.The pressure drop remained constant for all cases concerning each design. of this section (d) is to find the optimal condition of the cold plate under different discharge rates.We found that an increase in the heat flux increases the Tmax, Tσ, and h.Tmax increased to nearly 9K in each case, as shown in Figure 18.The pressure drop remained constant for all cases concerning each design.In Table 7, it is shown that both designs showed similar Tmax and negligible changes in both designs concerning different heat flux.Hence design 2c and 3b with a discharge rate of 2C and 3C were found to be the optimal designs for under operating condition of the battery pack and also in uniform distribution of temperature.However, designs with  The simulation results show a small decrease in temperature by 1 K and a change of pressure drop from 6.355 × 10 3 Pa to 6.116 × 10 3 Pa.There were no changes in Tσ and h.Hence the change of channel width by 2 mm at the outlet side reduced the temperature by 1 K. Therefore, it showed no compelling changes to the result when the width of the channel at the outlet increased.
In this paper, modeling, and simulation were conducted in a zig-zag channel cold plate in a steady state condition.The objective was to enhance the cooling performance of the cold plate for bigger Li-ion batteries without extracting more power from the pump In this paper, modeling, and simulation were conducted in a zig-zag channel cold plate in a steady state condition.The objective was to enhance the cooling performance of the cold plate for bigger Li-ion batteries without extracting more power from the pump through optimization.Initially, six sets of the cold plate were designed based on a number of channels.Aluminium was used for cold plates and water as a coolant.A preliminary analysis was conducted by providing a heat flux of 7000 W/m 2 (2C discharge rate) to obtain the baseline values.The simulation results were gathered based on temperature evolution, pressure drop, heat transfer between solid-fluid interface, and surface standard deviation of temperature.Preliminary results showed that a cold plate with a larger number of channels has good temperature uniformity (T σ ), i.e., the 13-channel cold plate had T σ = 3.2 K and the 3-channel cold plate had T σ = 6.01K and maximum temperature T max for the 3-channel cold planet was 330.84 K whereas for the 13-channel cold plate was 316 K.This trend was opposite in case of pressure drop.When the number of channels increased from 3 to 13, resistance increased.Hence, the 13-channel cold plate showed a larger pressure drop (13.34 × 10 3 Pa) compared to the 3-channel cold plate (3.84 × 10 3 Pa).Heat transfer rate follows the same trend of T max and T σ , and this is due to the removal of material leading to the decrease in the conduction of the cold plate.From this result, further optimization was carried out to maximize the heat transfer rate and minimize the T max , T σ and ∆p.Further optimization was carried out on 5-, 7-and 9-channel cold plates by increasing the channel width with a mass flow rate of 10 g/s.The results showed that an increase in channel width decreased the velocity of the coolant and also showed a significant improvement in pressure drop and negligible changes in T max , T σ , and no changes in heat transfer rate.The third step of optimization was conducted by increasing the mass flow rate from 10 g/s to 15 g/s (laminar flow) for 5-and 7-channel cold plates.It was observed that there was a significant reduction in the temperature evolution (T max = 314 K) in all cases, surface standard deviation (T σ = 2.7 K to 3.08 K), and heat transfer rate (h = 726 W to 729 W).With this optimization method, we observed that the 5-and 7-channel numbers were optimal when the battery discharge rate of 2C was applied.Further investigation was carried out to analyze those channel numbers with higher discharge rates.The result showed that all the parameters increased with an increase in heat flux.The discharge rate of 2C and 3C are provided under the operating temperature.Hence, to obtain 4C and 5C under optimal conditions, the inlet temperature of the coolant was reduced from 300 K to 293 K in the 5-channel design.The temperature gradient was reduced to nearly 6 K in all discharge rates.One observation from all simulation analyses was that the maximum temperature occurs on the outlet side of the cold plate.Therefore, an increase in channel width of 2 mm on the outlet side showed only a negligible 1 K.This did not show any compelling outcome.Overall, our findings have significant implications when bigger Li-ion batteries are used.

Conclusions
Efficient cooling of the battery pack directly impacts the overall efficiency of heavyduty vehicles.High battery temperatures can reduce the energy efficiency of the battery system, resulting in decreased range and increased energy consumption.Effective thermal management optimizes the cooling process, allowing the batteries to operate at their ideal temperature range, enhancing overall vehicle efficiency.In this paper, a zig-zag coolant flow cold plate was designed and simulated.The influence of the number of channels, channel width, mass flow rate, and operating under different discharges was investigated to enhance the cooling performance of the cold plate.
The simulation results were gathered based on temperature evolution, pressure drop, heat transfer between solid-fluid interface, and surface standard deviation of temperature.The increase in the number of channels increased the pressure drop but showed good uniform temperature and reduction in maximum temperature.Preliminary results showed that a cold plate with a larger number of channels had good temperature uniformity (T σ ), i.e., the 13-channel cold plate had T σ = 3.2 K and the 3-channel cold plate had T σ = 6.01K and the maximum temperature T max for the 3-channel cold plate was 330.84 K whereas for the 13-channel cold plate was 316 K.This trend was opposite in case of pressure drop.When the number of channels increased from 3 to 13, resistance increased.Hence, the 13-channel cold plate showed a larger pressure drop (13.34 × 10 3 Pa) compared to the 3-channel cold plate (3.84 × 10 3 Pa).Heat transfer rate followed the same trend of T max and T σ , this is due to the removal of material leading to the decrease in the conduction of the cold plate.
The heat transfer rate decreased with the number of channels increasing.The pressure drop was excessive in the 11 and 13 channels and there was a poor uniform temperature in the 3-channel cold plate.The increase in the channel width decreased the pressure drop significantly and showed no compelling changes to other parameters.The 5-channel of 16 mm and 18 mm width and the 7-channel of 16 mm width showed improvements in pressure drop.The increases in mass flow rate reduced the maximum temperature, and improved surface standard temperature and heat transfer rate but increases the pressure drop by nearly 49%.The reduction of inlet coolant temperature showed improvement in the reduction of maximum temperature at discharge rates of 2C, 3C, and 4C in the 5-and 7-channel designs.

Recommendations for Future Work
While this paper provided important parameter values to be considered by implication of related EV architecture, there are several areas wherein additional study is required to improve the cooling performance of the cold plate.One important area for future investigation is to provide an optimum condition for 5C or a higher discharge rate.In that case, one way might be to design a different channel width in a cold plate, i.e., a small width on the inlet side and an enlargement toward the outlet side.
In this study, water was used as a coolant.Further investigation can be carried out using different fluids such as water-glycol or refrigerant to achieve a comparable cooling performance to water.The angle of the zig-zag can be varied without an expensive increase of the pressure drop and can be investigated to maximize the area where coolant can be covered.The ambient condition may be another factor that could affect the performance of the cold plate.The ambient temperature and HTC can be varied at different levels to help in understanding the variation in the parameters.

Figure 1 .
Figure 1.The architecture of EV vehicles using a cold plate.

Figure 1 .
Figure 1.The architecture of EV vehicles using a cold plate.

Figure 5 .
Figure 5. Dimension of the channel.

Figure 5 .
Figure 5. Dimension of the channel.

Figure 7 .
Figure 7.The meshed model with two prism layers.Figure 7. The meshed model with two prism layers.

Figure 7 . 24 Figure 8 .
Figure 7.The meshed model with two prism layers.Figure 7. The meshed model with two prism layers.

Figure 8 .
Figure 8. Extrusion for the fully developed flow.

Figure 9 .
Figure 9. Temperature gradient for the preliminary analysis.

Figure 9 .
Figure 9. Temperature gradient for the preliminary analysis.

Energies 2023 ,
16, x FOR PEER REVIEW 13 of 24 (a) Temperature gradient for different numbers of channels (b) Average Temperature for different numbers of channels (c) Standard Deviation of temperature for different numbers of channels

Figure 13 .Figure 13 .
Figure 13.Evolution of temperature for the channel change in width.

Figure 13 .
Figure 13.Evolution of temperature for the channel change in width.

Figure 14 .
Figure 14.Parameter analysis by changes in channel width.

Figure 14 .
Figure 14.Parameter analysis by changes in channel width.

Figure 14 .
Figure 14.Parameter analysis by changes in channel width.

Figure 15 .
Figure 15.Heat transfer and T σ results.

Energies 2023 , 24 Figure 16 .
Figure 16.Temperature gradient with a mass flow rate of 15 g/s.

Figure 16 . 24 Figure 16 .
Figure 16.Temperature gradient with a mass flow rate of 15 g/s.
(d) Effect of change in heat flux

Figure 18 .
Figure 18.Temperature evolution of designs 2c and 3b with different heat fluxes.

Figure 18 .
Figure 18.Temperature evolution of designs 2c and 3b with different heat fluxes.

Figure 20 .
Figure 20.Change of channel width at the outlet side.

Figure 20 .
Figure 20.Change of channel width at the outlet side.The simulation results show a small decrease in temperature by 1 K and a change of pressure drop from 6.355 × 10 3 Pa to 6.116 × 10 3 Pa.There were no changes in T σ and h.Hence the change of channel width by 2 mm at the outlet side reduced the temperature

Table 1 .
Star CCM+ solver.The material properties of the plate and coolant are shown in Table1.The optimization objectives are as follows:To minimize: ∆p, T σ , T avg , T max ; To maximize: h; constraint: the wall of the cold plate ; variable: the mass flow of coolant, the width of the channel; Material properties.

Table 4 .
Physics model for preliminary analysis.

Table 4 .
Physics model for preliminary analysis.