Thermal performance analysis and experimental verification of lithium-ion batteries for electric vehicle applications through optimized inclined mini-channels

Power units (i


Introduction
Vehicular transport supported through sustainably sourced electricity is a prominently explored alternative to address climate change concerns.For example, the 7th of the Sustainable Development Goals by the United Nations (UN report, 2015) focuses on affordable and clean energy.It includes the development of the modern renewable transport sector by 2030 [1].Electric vehicles (EVs) have, therefore, emerged as the next generation option for transport.
The adoption of EVs curbs harmful greenhouse gas emissions of internal combustion engines and reduces noise pollution in metropolitan cities [2].The conventional power unit of an EV is the lithium-ion (Liion) battery pack.These batteries have high energy densities (up to 705 Wh/L),high power densities (10,000 W/L), and low self-discharge rates [3].
Ambient conditions significantly influence the thermal performance of Li-ion batteries.For example, capacity fading is a common phenomenon exhibited at high ambient temperatures [4].The acceptable operational range of these batteries is from 253 K to 333 K, but the optimum range lies within 288 K to 308 K (i.e., 15 • C to 35 • C) [5,6].It has been reported that the thermal performance is critical at temperatures above 313 K and below 293 K [7].This is because capacity degradation occurs above 313 K, and the internal resistance increases when the temperature drops below 293 K. Furthermore, the temperature difference between the cells of the battery pack must not exceed 5 K to guarantee an adequate thermal performance [8].Thus, temperature non-uniformity is a threat to the state of health of the power unit [9].Therefore, Li-ion batteries need management throughout the driving cycle in two ways: performance and heat management [10].
The thermal stress developed in a battery pack must be handled with utmost care to prevent thermal runaway.Thermal runaway is critical as it often results in uncontrolled fire hazards due to the production of flammable gases ensuing from the reaction between the negative electrode and the electrolyte [11].It starts with the decomposition of the solid electrolyte interphase layer when the battery pack is over-charged, over-discharged, or if it is operated at a high ambient temperature.Thus, it is crucial to identify and limit the extent of thermal runaway as a safety measure.A battery thermal management system (BTMS) is required to achieve this.
BTMSs can be classified into four categories.The main two are active cooling systems (ACSs) and passive cooling systems (PCSs).A third category combines ACS with PCS and is known as a hybrid cooling system (HCS).An ACS utilizes air or liquid as the heat transfer medium, whereas a PCS relies on incorporating phase change materials (PCMs) and fins to dissipate heat.In recent years, immersion cooling has emerged as a new BTMS, where a non-conductive dielectric fluid (such as oil) in direct contact with the battery pack is used [12].PCMs, which are the heat transfer media in PCSs, have been investigated as alternatives to ACSs in various references.This is because the high latent heat of a PCM may absorb efficiently the heat emitted by Liion batteries [13,14].The performance can be further improved by enhancing the thermal conductivity of the PCM [15,16].The influence of adding fins and the thermal performance of the PCM in extreme environments has been explained in detail in previous studies [17,18].It was found in [19] that the extensive and intensive properties of the fins and PCM have a significant impact on the thermal performance of the battery and an optimized design can control the battery's temperature within the permissible limits.However, if the PCM runs out of its available latent heat at extreme operating conditions, the thermal management system may fail.Thus, a PCS requires additional provisions to support the cooling system in harsh operating conditions [20].Ref. [21] is relevant, as it presents a study in which the mass and volume of the PCM were minimized using an optimization approach based on the response surface methodology.Such an approach represents a powerful tool to perform multi-objective optimization considering different constraints and system parameters [21].
Air cooling is a popular ACS which enables managing the maximum temperature in a battery pack.However, the thermal performance is not satisfactory at high ambient temperatures as air has a low thermal conductivity and a low specific heat [22].In addition, the high flow rates represent a challenge and the space required for an air-cooled system is larger than for a liquid-cooled system.Conversely, the higher thermal conductivity and specific heat capacity afforded by liquid cooling systems is advantageous [23].The importance of these systems for the efficient operation of a BTMS has been highlighted by some studies [24].Among the available coolants for liquid-cooled battery packs, a commonly employed is the water/glycol solvent, where glycol is used to reduce the freezing point of water [25].The study presented in [26] identified liquid cooling systems as more energy efficient than their aircooled counterparts.For instance, for a 0.5 W power consumption, the temperature of the hottest cell in the battery pack of a liquid-cooled module was lower by 3 K than for an air-cooled module.Due to the high cooling efficiency and compact structure afforded by liquid-cooled battery packs, EV manufacturers such Tesla (Model S), Chevrolet (Bolt), and Audi (e-Tron) favor their use [27].Wavy microchannels and microtubes, which constitute other types of ACS, may be used simultaneously with a biologically synthesized working nanofluid (e.g., silver-water/ethylene glycol, 50:50) to cool Liion batteries, as reported in [28].In this reference, after completely discharging the battery at discharge rates of 1C, 2C, 4C, and 5C (where 1C implies that a fully charged battery rated at 1 Ah should provide 1 A for one hour [29]), the maximum temperature of the battery was maintained respectively at 305.6 K, 310.3 K, 321 K, and 326.7 K [28].A magnetic pulsative nanofluid flow through the microchannels has been also employed for battery cooling [30].The magnitude of the inlet velocity and the Reynolds number were the two parameters identified to impact the battery cooling.The effect of the velocity and temperature of the inlet water on a Li-ion battery pack at a 5C discharge rate was explored in [31].The battery pack temperature was kept below 313 K. Results show that the temperature difference peaked when the inlet water temperature dropped from 293 K to 274 K.
Significant emphasis has been made on the design of mini-channels for battery packs to improve ACSs.For instance, the possibility of installing a cold plate with 5 mini-channels on a Li-ion battery pack was investigated in [32].The study found that an inlet water temperature of 298 K and a mass flow rate of 3 g/s are ideal to maintain the battery pack within the temperature range of 298 K to 313 K for all climatic conditions.The flow pattern of the liquid also impacts the cooling provision.A unique U-turn cold plate with an alternative inlet and outlet crossflow arrangement enables a drop by 32.2% of the maximum temperature in comparison to a parallel-type arrangement, as shown in [33].The shape of the mini-channels also impacts the battery cooling provision.For example, sine and sawtooth wave cross-sections exhibit a better thermal performance than the traditional rectangular mini-channels [34].In another study, divergent-shaped channels with two inlets and one outlet were found to reduce the pressure drop by 7.2% and the maximum temperature by 0.8 K [35].In addition, a counter-flow arrangement of coolant inside the mini-channels reduces the temperature difference within the battery.
The significance of the surface area covered with cold plates/channels was demonstrated in [36].For instance, an enhanced heat transfer was enabled by zig-zag plates as they cover a larger surface area.In turn, this contributed to increasing the thermal performance of the battery module by 28%.The study reported in [37] demonstrated that the  thermal performance of a single cell can be improved by a cold plate retrofit with cooling water flowing through a two-way mini-channel.A parallel mini-channel cold plate was designed for large battery packs in [38].The influence of the outlet design of the mini-channel was found to influence the thermal performance.An optimized design of the cold plate reduced the temperature difference by at least 76% and the pumping power by 81%.In [39], the Latin hypercube sampling (LHS) method was adopted to design serpentine cooling plates for battery cooling.Cooling channel parameters including the fluid inlet velocity, the Reynolds number, the channel dimensions, and the flow pattern were optimized for the best-case scenario.The average temperature decreased by 14% in comparison to the reference temperature.
In [40], the discharge rate, mass flow rate, fluid inlet temperature, and ambient temperature were identified as important input parameters for liquid cooling systems.In this reference three designs with heat pipes were presented, which increased the heat transfer area of the cooling system.The best case achieved a temperature drop of 9.4 K.The performance of parallel-spiral serpentine liquid cooling channels was investigated in [41].It was found that in this channel configuration high flow rates limit the maximum temperature at the expense of pressure drop and temperature difference.A comparative study between serpentine and U-shaped cooling channels in [42] deduced that serpentine channels exhibit a better thermal performance.Similarly, the thermal performance of a square cooling channel is better than that of a circular channel, but it may result in a slight increase in the temperature non-uniformity, as shown in [43].In addition, the aspect ratio of the cooling channel in a liquid cooling system may influence the thermal performance of a battery [44].
An oil-immersed battery cooling system could lower the battery temperature by 33% compared to natural convection [45].This cooling system could also limit the temperature difference in the battery pack by keeping the temperature difference at 2.64 K at the end of a 2C discharge rate.Although a liquid cooling system may decrease the maximum temperature, it may increase the temperature difference in the battery pack.However, a new arrangement of fins on the cooling channels may reduce the maximum temperature by 27.63% and the temperature difference by 35.58% when compared with a pure paraffin cooled battery module [46].An HCS using a composite PCM (CPCM) and liquid cooling was proposed in [47] for cooling a battery pack of 25 cylindrical cells at an ambient temperature of 313 K and a discharge rate of 5C.The CPCM featured 12% expanded graphite.The maximum battery pack temperature and the temperature difference at the end of the discharge rate were 318.24K and 3.49 K, respectively, for a fluid inlet temperature of 313 K.It was observed also that an inlet temperature of less than 298 K perturbs the temperature difference in the battery pack.Direct liquid cooling of a 4S1P cylindrical battery pack (i.e., with 4 cells in series and 1 in parallel) was investigated in [48].It was found that for all dielectric liquids the temperature rise could be limited to less than 5 K for a 2C discharge rate at a fluid mass flow rate of 0.05 kg/s.However, it was concluded in [49] that for fast charging Li-ion batteries, liquid cooling performs better than PCM-based cooling.
The publicly available literature hints toward liquid cooling systems as efficient options to reduce the maximum and average temperatures in a Li-ion battery.Channel parameters like fluid inlet velocity, contactarea between the channels and the battery surface, width and length of the channel, and fluid inlet temperature have been found to   substantially impact the thermal performance of the battery pack.However, to the authors' best knowledge, limited information is available on how the different channel parameters correlate together toward a holistic mini-channel cold plate design that would, in turn, lead to an energy efficient cooling of the battery.To this end, this paper presents an optimized design of a liquid mini-channel cooling system for a prismatic Li-ion battery.A real-time driving cycle at an ambient temperature condition of 313 K has been considered.The influence of design parameters such as aspect ratio, inclination angle of the mini-channel, inlet fluid temperature, and parasitic power consumption have been studied through a broad parametric study.An experimentally validated model of the battery was simulated for 100 different designs of the mini-channel to enable an extensive parametric survey.The influence of each cooling channel parameter on the thermal performance of the battery was investigated individually and then in combination with all other parameters.The goal of the research work was to design an effective and efficient EV battery cooling system where a balance between the cooling achieved in the retrofitted battery and the parasitic power consumption by the cooling system is achieved.While meeting this objective, the paper shows how the structural and flow parameters of a liquid cooling system should be prioritized in terms of their impact on the battery health and energy budget.For example, the rate of convective heat extraction from the heated battery to the coolant can be enhanced by increasing the temperature gradient between the battery and the coolant by having a colder fluid flow through the mini-channel.Alternatively, it can also be enhanced by increasing the convective heat transfer coefficient by, in turn, incrementing the mass flow rate of the coolant.To decide between these two possibilities, the cooling effectiveness and the energy economy of each option need to be assessed.Furthermore, a high coolant flow rate can be achieved by increasing the cross-sectional area of the mini-channel or by increasing the fluid velocity.Parasitic power consumption will rise when pumping a larger mass of coolant (resulting from a larger cross-section of the mini-channel) or when pumping a smaller mass of coolant at a higher velocity (to overcome a larger pressure drop in the mini-channel and achieve a high kinetic energy).This paper accounts for such competitive design aspects by holistically considering both heat transfer and energy economy to take adequate retrofitting decisions for a BTMS.
The widescale existence of hot climate in the two large continents Asia and Africa and the onset of frequent heat waves in Europe [50] and North America [51] indicate that if electric mobility options are promoted to substitute combustion-based vehicles, a large percentage of the EVs will have to endure hot ambient conditions.The present study offers an adequate cooling solution to ensure the safe functioning of power units of EVs, which is imperative for a large-scale transition toward electrification of transport.Table 5 Boundary conditions.

Boundary condition Value
Heat transfer coefficient, h

Research methodology
Given that this paper investigates the thermal management of a prismatic Li-ion battery in extreme ambient conditions, summer conditions in India with an ambient temperature of 313 K (40℃) were considered.As shown in Fig. 1, these conditions prevail across a vast extension of the Indian subcontinent.
The thermal performance of the retrofitted battery was analyzed under a realistic driving cycle.A detailed computational fluid dynamics (CFD) study and a subsequent parametric analysis were carried out to investigate the effect of mini-channel cooling on the battery.The evaluation criteria are based on the aspect ratio of the mini-channels, inclination angle of the mini-channels, fluid inlet temperature, fluid inlet velocity, mass flow rate, Reynolds number, pumping power, cooling work input (that is, cooling load), volume average temperature, and temperature difference.The parametric study entails a multi-criteria decision-making process to select a suitable design for the cooling retrofit.

Design of experiments
This section explains the design of experiments (DOE) framed to obtain the input variables for the present study.Four input parameters were considered: fluid inlet velocity, fluid inlet temperature, minichannel inclination angle, and mini-channel aspect ratio.The lower and upper bounds of all 4 parameters are summarized in Table 1.
The LHS method, commonly used in the existing literature [53], was adopted to generate 100 design points within the lower and upper bounds of each input variable.The method randomly distributes the design points across the search space (i.e., the multi-dimensional space bounded by the maximum and minimum values of each parameter) and guarantees a variety of plausible design points while ensuring a stratified sampling.Each input variable can attain any value within its range.Furthermore, the LHS method has a better distribution of data with fewer design points in comparison to standard random sampling, where a higher number of samples is required to obtain accurate output variables [54,55].Another advantage of this method is its less expensive numerical computations [56].
The LHS method generates DOEs of size 'N' from 'y' variables; that is, y 1 , y 2 , y 3 , …, y n .The range of each variable is then partitioned into nonrepeating intervals with an equal probability of 1/N.The values are randomly selected from the intervals as per the probability density.The 'N' values, which are randomly selected for y 1 , are then paired randomly with 'N' values of y 2 , and so on.Thus, the set of N × n tuples constitutes the LHS distribution of randomly sampled independent variables.(N!) n-1 possible interval combinations exist for given values of N and n [57].
In this paper, the ANSYS Design Explorer was used to generate the LHS-based DOE.Fig. 2 shows the sample selection and distribution of the 100 design points, which are randomly distributed within the set range.

Criteria for evaluation of the thermal performance of the BTMS
The following parameters were considered to investigate the thermal ii.Temperature difference: This output parameter is the difference between the minimum and maximum temperatures on the cell surface.
iii.Aspect ratio (x): It is the ratio of the width (l) to the height (or thickness) (w) of the mini-channel (shown in Fig. 3).The height or thickness is fixed at 2 mm and the width is parametrized.iv.Fluid inlet velocity (v): This is the velocity at which the liquid coolant enters the mini-channel.
v. Mass flow rate (m): This is the mass flow rate of liquid coolant through the mini-channels.
vi. Reynolds number (Re): This is a dimensionless number calculated for each case and its effect is observed on the thermal performance of the Li-ion battery.It is calculated with where Re denotes the Reynolds number, ρ is the density of the fluid, v is the velocity of the fluid at the inlet, D h is the hydraulic diameter of the mini-channel, μ is the dynamic viscosity of the fluid, w is the mini-channel's height or thickness, and l is the mini-channel's width.vii.Inclination angle (i): This is the angle between the longitudinal axes of the mini-channels with respect to the horizontal base of the battery.
viii.Fluid inlet temperature (t i ): This is the temperature at which liquid coolant is supplied at the mini-channel inlet.ix.Pumping power (W P ): This is the power required to pump coolant through the mini-channels.It is calculated as [58] where the friction factor (f) is given by: x. Work input or cooling power required (W c ): This is the work required to supply coolant at a desired temperature at the inlet of the mini-channel.It is calculated using: where q is the cooling load, COP is the coefficient of performance (COP), m is the mass flow rate of coolant, C P is the specific heat of coolant, and t a is the ambient temperature.The work input is calculated by assuming that the refrigeration cycle of the air conditioning system has a constant COP of 2 in all operating conditions [59].

Multi-criteria decision-making for optimal design selection
Based on the parameters defined in Section 2.3, the performance of the BTMS was evaluated for all the 100 design cases considered.The suitability of a particular retrofit configuration is judged based on the average temperature of the volume, the power consumption by the BTMS (cooling power) and the temperature difference.A suitable BTMS is expected to minimize all the 3 parameters.Since different design cases achieve this objective in different levels for the judging criteria, the multi-criteria decision-making algorithm called Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) was adopted to select the most suitable case.
An entropy-based TOPSIS method was implemented to prioritize design cases (according to the 3 judging criteria) without involving any human-induced bias in the selection of the best case [60,61].A more detailed description about the TOPSIS method and explanations for its different stages of formulation can be found in [62].The mathematical equations to implement the entropy-based TOPSIS selection are shown next (in the sequence of computation for the sake of brevity).
Scoring matrix: where D is a matrix of scores (x ij ) belonging to "m" design options under "n" different criteria to assess the suitability for each design.Standardized matrix: where r ij represents the standardized scores.Proportional calculation: where p ij represents the proportion for every score in D.
Entropy calculation: where e j represents the entropy for criterion j.Entropy weight calculation: where w j denotes the weight for criterion j computed by the entropy method.
Weighted matrix calculation: where v ij represents the weighted score.
Ideal solution: where A + is the ideal solution that contains the best values for every criterion (v 1 ). Anti-ideal solution: where A -is the anti-ideal solution that contains the worst values for every criterion In ( 14) and ( 15), J 1 represents the most suitable value of the j th criterion when it is profitable.Conversely, J 2 stands for when it is unprofitable.
Euclidian distance from the ideal solution (S i + ): Euclidian distance from the anti-ideal solution (S i -): Closeness degree calculation (C i + ): Larger values of C i + indicate a better suitability of a particular design (and vice versa).Therefore, the best design is chosen as the one that yields the largest value of C i + .

Numerical model of the BTMS
A battery is an electrochemical unit which consists of electrodes, a separator, and an electrolyte.There are two main considerations toward developing a holistic battery model: the simulation should not be timeconsuming and costly, and it should be accurate.For instance, battery models based on electrochemical reactions are accurate but timeconsuming.
The 14.6 Ah prismatic battery investigated in [63], with dimensions 127 mm × 196 mm × 7 mm, was here considered as it is widely used in EVs.The material specifications of the numerical model are provided in Table 2 [64].ANSYS Fluent 2020 R1 was used for the simulations, which were conducted using the high-performance computing (HPC) facility of IIT-Delhi.
The battery tabs are considered as passive zones and the cell as an active zone because all the electrochemical reactions occur inside the cell.Fig. 3 shows the geometry of the Li-ion cell.The battery is retrofitted with 6 mini-channels (3 each on the X-Y plane surfaces of the cell).As mentioned previously in Section 2.3, the height of the mini-channels was fixed at 2 mm and the width was parameterized.The direction of the coolant flow is in a counter-flow pattern for the two battery surfaces.This pattern of the coolant, in this case water, helps in assessing the localized heating at the outlet.This also prevents hotspots in the vicinity.The structural details of the retrofitted battery are given in Table 3.
The driving cycle (current profile) is shown in Fig. 4.This was adopted from the simulation of a hybrid-electric bus, where the total distance covered and the time taken for the analysis period were 16.55 km and 3000 s respectively [59].The bus is powered by an electric machine with a power rating of 220 kW and a 100 kW fuel cell system based on an unpressurized proton-exchange-membrane.Key parameters of the bus are given in Table 4 [65].The average heat generation in the cyclic load corresponds to that of a 4.25C constant-current (C-C) rate.
The discharge current is positive in the cyclic loading.The assumptions considered in the CFD modelling in this study are summarized below: i. Free convective heat transfer was considered from the surfaces of the retrofitted battery pack.ii.Constant specific heat and density values were considered for the coolant.iii.A laminar viscous model was considered in the simulation.
The taken boundary conditions are listed in Table 5.The complex physics of the Li-ion battery were captured by using the dual potential multi-scale multi-dimensional model (MSMD) approach available in ANSYS Fluent.The anode-separator-cathode sandwich layers hold the overall physics occurring inside the battery.The electrical and thermal fields are solved in the CFD domain using the MSMD approach with the following equations: where σ + is the effective electrical conductivity of the positive electrode, σ − is the effective electrical conductivity of the negative electrode, φ + is the phase potential for the positive electrode, φ − is the phase potential for the negative electrode, J is the volumetric transfer for current density, and q is the heat generation rate during battery operation.The Newman, Tiedemann, Gu, and Kim (NTGK) semi-empirical electrochemical model was selected to conduct the battery simulations.The rationale behind this model choice is that it successfully predicts the coupled thermochemical characteristics of a battery cell, with an average deviation between experimental and numerical results reported to be less than 1 K [66].In an NTGK model, the volumetric transfer for current density (J) in terms of phase potential (φ) is given as: where a is the specific area of the electrode sandwich sheet.Y and U are model parameters, obtained through a curve fitting process of voltagecurrent response curves of a reference battery (with a capacity of 32.77 Ah), and are functions of the depth of discharge (DOD), with where V denotes the volume of the battery and Q Ah stands for its capacity in Ampere-hours.Constant temperature corrections are given as C 1 = 1800 and C 2 = − 0.00095.The details of the NTGK model parameters are provided in Table 6.
Heat is generated because of the reversible and irreversible heat sources in the operation of the battery.Joule heating, electrochemical reaction heating, and entropic heating are the main causes of heat generation inside the battery.The heat source term is given as: The study includes liquid cooling.The governing equations of the process are defined by the fundamental equations of continuity, momentum, and energy, namely The need for a large computational time for the CFD simulations with the NTGK model and the complexity of the solution were relieved by adopting a reduced order method (ROM).The ROM reduces the partial differential equations describing the system to ordinary differential equations and linearizes the non-linear equations.The ROM runs orders of magnitude faster than the original CFD model [67].For example, in [68], a CFD model for an automotive battery module with 28 cells was simulated with and without ROM and the results were compared.The percentage error between the results for 10, 20, 30, and 40 s of simulation time were 1.4%, 0.7%, 0.49%, and 0.59%, respectively.It was also observed that the ROM reduced the simulation time drastically.The CFD run took approximately 20 hours of simulation time on six CPUs, whereas with the ROM the simulation time was in the order of seconds using a single CPU.

Model stability and validity assessment
The numerical model presented in Section 2 is examined in this section through standard tests to ascertain its validity.

Mesh and timestep size independence check
To verify the stability of the model, this section explains the mesh details and the solution independence check performed on mesh and timestep size.Table 7 lists the properties of the mesh.A structured hexahedral mesh was used to ensure high quality.This is shown in Fig. 5, and it has 1,760,662 elements.
Four different grid sizes were tested to assess mesh independence, namely 1,074,132, 1,314,216, 1,760,662 (i.e., the mesh with properties provided in Table 7), and 2,080,785 elements.In these tests, the fluid inlet velocity, inlet temperature, aspect ratio, and inclination angle were set as 0.33 m/s, 299.9 K, 6.3, and 11.3 • respectively.As shown in Fig. 6 (a), the small change in minimum and maximum temperatures confirms the model stability and the grid independence of the numerical solution.The transient response of the model was recorded by taking four different timestep sizes of 2 s, 5 s, 10 s, and 15 s, with results shown in Fig. 6(b).The minor changes in the temperature values demonstrate the timestep size independence of the solution for the present battery model.

Model validation
The approach on laminar flow in rectangular ducts followed in [69] was used to validate the mini-channel cooling system design for this study.The Nusselt number (Nu) for laminar flow is defined as The variation of Nu with the aspect ratio was recorded for different values of aspect ratio and compared with the results available in [69].Fig. 7(a) shows the results of this comparison.It is observed that there is good agreement between the sets of results.The experimental study reported in [70] was used to validate the NTGK battery model used in this paper.In the study, the prismatic Li-ion battery was discharged at a 2C rate at an ambient condition of 299.1 K. Fig. 7(b) shows the results from the validation.The small deviation between the simulation results and the experimental data reported in [70] demonstrates the validity of the battery model.

Experimental validation of the NTGK model
To justify the suitability of the NTGK battery model, in addition to the comparison with the numerical results in [69] and the experimental results in [70], an experimental validation of the model was also carried out.However, for such a verification exercise it was not possible to use the commercial battery described in Section 2.5.Instead, a 50 Ah prismatic Li-ion battery was employed for the experiment as this was available to undertake research activities.This battery has a larger capacity than the 14.6 Ah unit described in Section 2.5, but it enabled it to maintain a safe operation during the experiments upon the occurrence of over-charging or over-discharging incidents.
The implementation of the NTGK model was done in a similar manner for this 50 Ah battery as was done for the 14.6 Ah battery.Fig. 8 shows the experimental setup consisting of the battery (50 Ah), a chargingdischarging station, an infrared (IR) imaging camera, and a PT-100 temperature sensor.The battery was placed horizontally on a glass wool sheet.An FLIR A325sc IR camera was used to obtain thermal images of the battery at discharge rates of 0.8C (40 A) and 0.5C (25 A).The camera has an uncooled Vanadium oxide microbolometer detector that produces thermal images of 320 × 240 pixels with a reading accuracy of ±2 K or ±2%.The standard temperature range of the camera is 253 K to 393 K.
The thermal images retrieved with the experiment were compared with the contours obtained through the numerical study (implementing the NTGK model on the 50 Ah prismatic battery), with results of this comparison shown in Fig. 9.The close agreement between experimental and numerical results ratifies the validity of the NTGK battery model used.

Battery without BTMS under a real driving cycle
As the baseline case, the realistic driving cycle presented in Fig. 4 was first imposed on the Li-ion battery without any BTMS supporting its operation.The battery's volume average temperature variation over the driving cycle is shown in Fig. 10(a).The maximum temperature at the end of the driving cycle was 336.95 K.The variation of heat generated in the battery is shown in Fig. 10(b), with a maximum heat generated of 35 W. Fig. 11 shows the temperature contour of the battery.The DOD at the end of the driving cycle was 0.4.This case was then analyzed against the retrofitted battery with coolant mini-channels, with results discussed in the subsequent sections.

Effect of fluid inlet temperature on a retrofitted battery
The effect of the fluid inlet temperature on the volume average temperature and the temperature difference in the battery is shown in Fig. 12(a).The temperature difference increases with a decrease in fluid inlet temperature, whereas the volume average temperature follows the opposite trend.The minimum and maximum temperature difference values (0.31 K and 13.02 K) occurred at fluid inlet temperatures of 310.2 K and 298.2 K, respectively.
The minimum volume average temperature value was 301.1 K for a fluid inlet temperature of 298.1 K. Also, the maximum volume average temperature value of 315.9 K occurred for a fluid inlet temperature of 310.5 K.It is to be noted that these average temperature extremities A. Verma et al. have different DOEs (input parameters).Except for a few exceptional cases, a decrease in fluid inlet temperature increased the temperature difference in the battery.This is because although intense local cooling induced by mini-channels can substantially cool down certain regions of the battery, the regions distant from the mini-channels create a high temperature gradient across the battery.Therefore, a high degree of cooling provided through very cold fluid may be less desirable due to the high temperature differences.The temperature difference within the cells of the battery pack must be less than 5 K to avoid the uneven temperature distribution that helps preventing the adverse effects of thermal perturbances [8]   Fig. 12(b).The temperature in the battery is 301.4K with a temperature difference of 4.4 K at a fluid inlet temperature of 299.4 K. Thus, the fluid inlet temperature on its own is not sufficient to determine the thermal performance of the mini-channel cooling system.Fig. 12(c) compares the temperature contours for DOEs with fluid inlet temperatures of 312.9 K and 298.1 K.The minimum and maximum temperature difference values are 0.52 K and 6.45 K, respectively, for fluid inlet temperatures of 312.9 K (i = 5 • ) and 298.1 K (i = 68.9• ).Fig. 13 shows the effect of mass flow rate and fluid inlet temperature on the volume average temperature.The increase in mass flow rate enhances the thermal performance for low fluid inlet temperature values.

Effects of mass flow rate, Re, and aspect ratio
The previous section highlighted that fluid inlet temperature can be a determinant input factor in decreasing the volume average temperature of the battery.However, there are other parameters which affect the overall thermal performance of the battery; namely, the temperature difference and the parasitic power consumption (which is directly linked with the pressure drop in the mini-channel).The flow pattern also plays a key role.Fig. 14 shows the counter-flow pattern adopted for this study.The fluid enters and exits at different sides in the mini-channels placed on both surfaces of the battery.This helps in avoiding unnecessary hotspots which would happen if fluid were made to flow in a parallel direction at both planes.
The effects of mass flow rate on the pressure drop across the cell's length and on the volume average temperature in the cell are shown in Fig. 15(a).The values of the volume average temperature for the extremity points are 311.41K and 307.84K for mass flow rates of 0.7 g/s and 23.6 g/s, respectively.Although the few data points for higher mass flow rate conditions exhibit, in general, lower volume average temperatures than those for lower mass flow rates, some low mass flow rates result in reduced values of volume average temperature.These instances indicate that other variables involved in the design (such as fluid inlet temperature, inclination angle, and aspect ratio) have similar dominating effects on volume average temperature.It can be thus concluded that mass flow rate on its own is not sufficient to define the thermal performance of the mini-channel cooling system.It is also noted that no typical trend is followed by the pressure drop against mass flow rate.The pressure drop directly affects the parasitic power consumption required for the mini-channel cooling system.Fig. 15(b) shows the effects that the Reynolds number and the aspect ratio have on the volume average temperature in the cell.These two variables, in combination, can help to intuitively explain several regions of the plot.In this case, increments in their values imply a larger quantity of coolant flows over a wider contact area with the battery surface-in turn, leading to lower volume average temperatures.These are the regions where Re and the aspect ratio determine the thermal performance of the BTMS.However, there are other regions in the plot where these two variables cannot override the effects of other design variables.An example of this is the rise in volume average temperature when Re increases in the ranges 200-600 and 1000-1200 for aspect ratios less than 6.These observations support the idea that other design variables should be considered in conjunction with Re and aspect ratio, through a multi-criteria decision-making process, to select a suitable retrofitting configuration.
Fig. 15(c) compares the temperature contours of the DOEs with similar fluid inlet temperature (309 K) but different aspect ratios (8.2 and 1.1).The DOE with an aspect ratio of 8.2 exhibits fewer hot spots.Additionally, a greater area of the battery is at a lower temperature than for the case of a DOE with an aspect ratio of 1.1.

Effect of inclination angle
Another important dimensional parameter is the angle at which the mini-channels are inclined on the two planes of the battery.Fig. 16(a) shows the variation of the pressure drop with the inclination angle.The pressure drop was calculated for the cell length.There is no definite trend for the variation and the data points are scattered in the search space unevenly.Fig. 16(b) shows the effect of the inclination angle on the volume average temperature in the battery.It is observed that some values of inclination angle yield a better thermal performance than other design points (e.g.exhibiting a lower temperature difference).The reason behind this behavior for some inclination angles is the better outspread of the mini-channels on the two planes.Fig. 16(c) explains this phenomenon.The contours of volume average temperature are compared with two inclination angles (1.4 • and 68.9 • ) having a similar fluid inlet temperature (298 K).The cooling load is almost the same in the two cases, but the difference in volume average temperature can be observed just due to the difference in the angle at which the minichannels are inclined.A. Verma et al.

Parasitic power consumption
The pumping power varies with the position at which the minichannels are placed in the battery.Fig. 17(a) shows this variation.It can be noticed that at some values of inclination angle the pumping power required is reduced.These design points can be marked as favorable for the overall performance of the mini-channel cooling system.The least and most amounts of pumping power are required for mini-channels inclined at angles of 41.9 • and 83.3 • , respectively.
Pumping power is also affected by the fluid inlet velocity and the aspect ratio of the mini-channels.Fig. 17(b) shows the variation of pumping power against fluid inlet velocity and aspect ratio.The pumping power decreases for lower values of aspect ratio and fluid inlet velocity.The least amount of pumping power is required for the design case with a fluid inlet velocity of 0.066 m/s and an aspect ratio of 2.7.
The work input required by the refrigeration cycle is affected by the mass flow rate, the fluid inlet temperature, and the ambient condition.The ambient temperature in this paper is constant at 313 K.The mass flow rate and the fluid inlet temperature were parameterized as design points for the LHS method.Fig. 18 shows the variation of work input required against mass flow rate and fluid inlet temperature.The work input required is less for lower values of both mass flow rate and fluid inlet temperature.
The magnitude of the pumping power is negligible compared to the refrigeration work input required to achieve a low temperature coolant to flow through the mini-channels.The latter, therefore, requires a higher emphasis in the design considerations for an active liquid cooling-based BTMS.To achieve a faster rate of heat extraction from a battery, it is thus more efficient to increase the rate of flow of coolant with a relatively high inlet temperature rather than reducing the inlet temperature to have a low coolant flow rate.
To have an enhanced coolant flow rate, it is further desirable to increase the aspect ratio of the mini-channels rather than increasing the coolant velocity through narrow channels.Larger aspect ratios result in a larger surface area of heat extraction by the coolant from the battery and a broader distribution of the cooling effect over the battery surfaces.This helps in minimizing temperature differences within the battery and leads to a better sustained battery health.

Optimal design selection
The 100 design cases vary widely in terms of the key performance markers considered in the study (i.e.volume average temperature, power consumption by the BTMS, and temperature difference).It should be noted that only the refrigeration power required to supply cold liquid coolant at the inlet of the mini-channels (W c ) was considered as the total power consumption, as W P is substantially lower compared to W c .An entropy-based TOPSIS was implemented on the dataset consolidating the output parameter values for all the cases.These values and subsequent ranks of the cases obtained from TOPSIS are summarized in Table A in the Appendix.The results suggest that Case 15 is the most suitable considering the 3 judging criteria (with a volume average temperature of 313.31 K, a power consumption by the BTMS of 0.85 W, and a temperature difference of 0.42 K).Conversely, Case 84 is the least suitable design (with a volume average temperature of 304.65 K, a power consumption by the BTMS of 2419.87W, and a temperature difference of 12.79 K).
Although Case 84 achieves an overall lower battery temperature, there are zones with hotspots that result in a significant difference between the maximum and the minimum temperature.The substantially large cooling power consumption and the large temperature difference indicate a high degree of local cooling near the coolant flow, while leaving distant regions relatively hot.On the other hand, the minimal power consumption and temperature difference exhibited in Case 15 outweigh the relatively hotter volume average temperature being presented.
It should be highlighted that the rankings of different cases may change if one intends to prioritize a single output parameter over the others.For example, if the goal is to minimize only the volume average temperature with little focus on the cooling power requirement and temperature difference, one might opt to choose Case 8, which results in a minimum volume average temperature (301.14K) -albeit a significant cooling power consumption (965.47W) and temperature difference (6.46 K).

Conclusions
This paper presented a comprehensive analysis of the effects of geometric and thermofluidic parameters on the performance of a liquid coolant-based BTMS for an EV.The battery of the vehicle was simulated with an experimentally validated NTGK model using a realistic driving cycle under hot ambient temperature conditions.The maximum temperature at the end of the driving cycle was 336.95 K.
It was shown that the temperature distribution across the battery significantly depends on the mini-channel inclination angle.Diagonal and vertical mini-channels lead to a more uniform temperature distribution compared to horizontal mini-channels.Heat removal through a very cold fluid flow can lead to a lower volume average temperature of the battery, but it can also trigger undesirable high temperature difference because of intense localized cooling.
Considering the parasitic power consumption of the BTMS, a high coolant flow rate with a relatively high inlet temperature was found to be more efficient than a low coolant flow rate with a relatively cold inlet temperature.The coolant flow rate should preferably be enhanced by increasing the mini-channel aspect ratio than by increasing the fluid velocity.This is because an increased aspect ratio leads to a larger surface area of heat extraction from the battery by the coolant which, in turn, reduces the temperature difference in the battery.
The detrimental effects of high temperature gradients in the battery and high cooling power consumption may not justify a lower volume average temperature obtained in such cases.It would rather be more desirable to achieve a more uniform and less intense cooling with reduced power consumption in the BTMS to strike a balance between battery health and energy economy of the cooling technology.The most suitable case, as suggested by the adopted TOPSIS analysis, resulted in a volume average temperature of 313.31 K, a power consumption by the BTMS of 0.85 W, and a temperature difference of 0.42 K.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Table A1
Summary of the input/output parameters for the BTMS design cases and results of TOPSIS.

Fig. 2 .
Fig. 2. Sample distribution of design variables through the LHS method.

Fig. 3 .
Fig. 3. (a) Depiction of mini-channels arranged at different inclination angles on the cell surface.(b) Single mini-channel.

Fig. 10 .
Fig. 10.Plots for: (a) volume average temperature with time; (b) total heat generation with time.

A
.Verma et al.

Fig. 16 .
Fig. 16.(a) Plot showing the effect of inclination angle on the pressure drop.(b) Plot showing the effects of inclination angle on volume average temperature and temperature difference.(c) Comparative temperature contours for inclination angles of 1.4 • and 68.9 • for a fluid inlet temperature of 298 K.

Fig. 17 .
Fig. 17.Variation of pumping power for input parameters: (a) inclination angle; (b) aspect ratio and fluid inlet velocity.

Fig. 18 .
Fig. 18.Variation of work input against mass flow rate and fluid inlet temperature.
et al.

Table 1
Input parameters.

Table 2
Material specifications.

Table 3
Retrofitted battery structural details.

Table 4
Key parameters of the hybrid bus.

Table 7
Mesh quality.
A.Verma et al.