Enhancing thermal management in bat- tery electric vehicles using phase change materials Master’s thesis in Sustainable Electric Power Engineering and Electromobility Yang Zhang DEPARTMENT OF MECHANICS AND MARITIME SCIENCES CHALMERS UNIVERSITY OF TECHNOLOGY Gothenburg, Sweden 2025 www.chalmers.se www.chalmers.se Master’s thesis 2025 Enhancing Thermal Management in Battery Electric Vehicles Using Phase Change Materials Yang Zhang Department of Mechanics and Maritime Sciences Division of Vehicle Engineering and Autonomous Systems. Chalmers University of Technology Gothenburg, Sweden 2025 Enhancing Thermal Management in Battery Electric Vehicles Using Phase Change Materials YANG ZHANG © YANG ZHANG, 2025. Supervisor: Hamed Jamshidi, Volvo Cars Examiner: Simone Sebben, Chalmers Department of Mechanics and Maritime Sci- ences Master’s Thesis 2025 Department of Mechanics and Maritime Sciences Division of Vehicle Engineering and Autonomous Systems Chalmers University of Technology SE-412 96 Gothenburg Telephone +46 79 352 8428 Cover: Solid-liquid distribution during the phase change of PCM as shown in Com- sol. Typeset in LATEX, template by Kyriaki Antoniadou-Plytaria Printed by Chalmers Reproservice Gothenburg, Sweden 2025 iv Enhancing Thermal Management in Battery Electric Vehicles Using Phase Change Materials YANG ZHANG Department of Mechanical and Maritime Sciences Chalmers University of Technology Abstract With the development of the e-mobility industry, the thermal management of power electronic devices such as inverters in battery electric vehicles (BEVs) has become increasingly prominent, especially with today’s trend of high power density and sys- tem integration, where traditional cooling methods face many challenges. This thesis focuses on the application of phase change materials (PCMs) in the thermal manage- ment of inverters, aiming to improve the thermal management system temperature control capability. First, an inverter power loss model considering switching loss and conduction loss is constructed in matlab to simulate the inverter power loss under real driving conditions. On this basis, a fluid-thermal coupling simulation model was constructed in COMSOL Multiphysics to analyze the thermal response of PCM materials under different layout configurations. This study systematically evaluates the effects of various PCM layouts on temperature rise control and optimizes their thermal buffer performance while satisfying the volume constraints. The simulation results show that a reasonably designed PCM thermal management scheme can sig- nificantly reduce the peak temperature of key inverter components and lower the rate of temperature change to reduce the thermal shock, thus improving the thermal stability and reliability of the system and extending the service life of the inverter. This study provides a theoretical basis and engineering reference for the design of an efficient and compact thermal management system for electric vehicles. Keywords: Battery Electric Vehicle (BEV); Inverter; Thermal Management; Phase Change Material (PCM); Multiphysics Simulation; Power Loss Modeling; COMSOL; Thermal Reliability. v Acknowledgements This thesis demonstrates my long and in-depth exploration of high-fidelity multi- physics field simulation and optimization. I would like to express my sincere gratitude to Volvo Cars for providing me with this program, which has provided me with invaluable hands-on opportunities. First and foremost, I would like to express my sincere gratitude to my supervisor, Dr. Hamed Jamishidi, whose clear guidance, technical expertise, and continuous encouragement played a crucial role throughout the research process, and who was always available to provide timely and valuable comments to show the way forward. I would also like to thank my examiner, Prof. Simone Sebben, for her invaluable feedback which helped me to refine my research. In addition to this a special thanks to my colleagues and friends in the company who helped make the research process fun. I would also like to give a special thanks to my teammate Henry, whose cooperation, creativity and teamwork helped me understand how I can work better as a team to solve problems. Finally, I would like to thank all the people who supported me. This project has not only enriched my knowledge, but also given me a meaningful personal experience! Yang Zhang, Gothenburg, 2025 vii List of Acronyms Below is the list of acronyms that have been used throughout this thesis: EVs Electrical Vehicles BEVs Battery Electrical Vehicles AC Alternating Current DC Direct Current PCM Phase Change Materials NePCM PCM with nanocomposite added TCE Thermal Conductivity Enhancer PCM-HEX PCM Heat Exchanger HTF Heat transfer fluid MF Metal Foam PPI Pores Per Inch MOSFET Metal–Oxide–Semiconductor Field-Effect Transistor FOC Field-oriented control BOBYQA Bound Optimization BY Quadratic Approximation ix x Symbols ρ Air Density[kg/m3] Cd Air resistance coefficient A Windward area[m2] v Velocity[m/s] Fdrag Air resistance[N] a Acceleration[m/s2] Frolling Rolling resistance[N] µ Rolling resistance coefficient m Mass of the car[Kg] ωmotor Motor speed rw Wheel radius[m] G Gear ratio Twheel Wheel output torque[N/m] Tmotor Motor output torque[N/m] Id d-axis curren[A] ωbase Base speed λm Permanent magnetic flux[Wb] Ld d-axis inductance[H] Iq q-axis curren[A] Lq q-axis inductance[H] Istator Stator current [A] ϕ Porosity Vvoid Volume of pores in metal foam Vsolid Solid volume in metal foam Vtotal Total volume of metal foam t Time instant [s] xi ia(t), ib(t), ic(t) Phase currents of PMSM in phases a, b, c [A] ux+(t), ux−(t) Switching states of the upper (+) and lower (-) switches in phase x (x = a, b, c), dimensionless (1 = ON, 0 = OFF) iSx+(t), iSx−(t) Instantaneous current through the upper (+) and lower (-) switch- ing device of phase x [A] ω = 2πfm Angular frequency of the fundamental modulation component fsw Switching frequency of the PWM carrier vmx(t) Modulation voltage signals for phases x S1 to S6 Six inverter MOSFET switches 2 µs Dead-time inserted between upper and lower switches Isw(t) Instantaneous current through each switching device |Isw(t)| Absolute value of instantaneous current (used for energy lookup) Von(Isw, Tj) On-state voltage drop as a function of current and junction tem- perature Eon(Isw, Tj) Turn-on switching energy loss from datasheet lookup Eoff(Isw, Tj) Turn-off switching energy loss from datasheet lookup Pcond(t) Instantaneous conduction loss power Psw(t) Instantaneous switching loss power Ptotal(t) Total instantaneous inverter power loss Vdc(t) Instantaneous DC bus voltage Vref Reference DC voltage for datasheet losses Tj Junction temperature (assumed constant at 25◦C) xii Contents List of Acronyms ix Nomenclature x List of Figures xv List of Tables 1 1 Introduction 2 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Theory 5 2.1 Inverter loss model construction . . . . . . . . . . . . . . . . . . . . . 5 2.1.1 Vehicle dynamics calculations . . . . . . . . . . . . . . . . . . 6 2.1.2 Motor speed and output torque calculations . . . . . . . . . . 7 2.1.3 Motor current calculation . . . . . . . . . . . . . . . . . . . . 7 2.1.3.1 Field weakening control strategy . . . . . . . . . . . 7 2.1.3.2 q-axis current . . . . . . . . . . . . . . . . . . . . . . 7 2.1.3.3 Stator current . . . . . . . . . . . . . . . . . . . . . . 7 2.1.4 Inverter input current calculation . . . . . . . . . . . . . . . . 8 2.1.4.1 Inverter Topology and Switching Signals . . . . . . . 8 2.1.4.2 Deriving Device Currents from Phase Currents and Switching States . . . . . . . . . . . . . . . . . . . . 8 2.1.5 Inverter Loss Modeling Methodology . . . . . . . . . . . . . . 9 2.1.5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.5.2 Modulation and Switching State Reconstruction . . . 9 2.1.5.3 Loss Model Formulation . . . . . . . . . . . . . . . . 10 2.1.5.4 Numerical Implementation . . . . . . . . . . . . . . . 10 2.1.6 Result validation . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 Working concept of PCM . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 PCM materials and properties . . . . . . . . . . . . . . . . . . . . . . 12 2.3.1 Organic PCMs . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3.2 Inorganic PCMs . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3.3 Eutectics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3.4 PCM selection and use . . . . . . . . . . . . . . . . . . . . . . 14 2.4 Thermal Conductivity Enhancer(TCE) . . . . . . . . . . . . . . . . . 14 xiii Contents 2.4.1 Fin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.4.2 Nanocomposite . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.4.3 Metal Foam . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3 Methods 18 3.1 Geometry design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.2 Numerical procedure and model validation . . . . . . . . . . . . . . . 19 3.2.1 PCM and MF . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2.2 Coolant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.2.3 Numerical simulation methods . . . . . . . . . . . . . . . . . . 20 3.2.4 Mesh and time step independent test . . . . . . . . . . . . . 20 3.3 Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.4 Validation of the numerical model . . . . . . . . . . . . . . . . . . . 22 3.4.1 Heat Transfer Validation . . . . . . . . . . . . . . . . . . . . . 22 3.4.2 PCM model simulation validation . . . . . . . . . . . . . . . . 23 4 Results and discussion 25 4.1 The effect of PCM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.1.1 The effect of PCM in simple model . . . . . . . . . . . . . . . 25 4.1.2 The effet of PCM configuration in the real geometry . . . . . . 27 4.2 The effect of metal foam . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.3 A new design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.3.1 The effect of the cylindrical structure . . . . . . . . . . . . . . 35 4.3.2 Integrating cylindrical structures into realistic models . . . . . 37 4.3.3 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 4.3.3.1 Parameters . . . . . . . . . . . . . . . . . . . . . . . 45 4.3.3.2 Optimization methods and goal setting . . . . . . . . 46 4.3.3.3 Optimization results . . . . . . . . . . . . . . . . . . 47 5 Conclusion 51 Bibliography 53 A Appendix 1 I xiv List of Figures 2.1 Electric vehicle powertrain configuration . . . . . . . . . . . . . . . . 5 2.2 Drive Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Comparison of power loss results: proposed method vs. reference data. 11 2.4 Typical PCM Temperature Characteristics . . . . . . . . . . . . . . . 12 2.5 Schematic diagram of the fin . . . . . . . . . . . . . . . . . . . . . . . 15 2.6 Schematic diagram of metal foam structure . . . . . . . . . . . . . . . 16 3.1 Cooling system and radiator schematic . . . . . . . . . . . . . . . . . 18 3.2 The three views of the model . . . . . . . . . . . . . . . . . . . . . . 19 3.3 Heat transfer results validation . . . . . . . . . . . . . . . . . . . . . 23 3.4 Comparison chart with the results of Rehman and Park . . . . . . . . 24 4.1 Model diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.2 Temperature response curve over time . . . . . . . . . . . . . . . . . 26 4.3 Heat sink with integrated PCM . . . . . . . . . . . . . . . . . . . . . 27 4.4 Comparison of MOSFET temperature with and without PCM-enhanced radiator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.5 Phase change rate at different times . . . . . . . . . . . . . . . . . . . 29 4.6 MOSFET temperature variation under different metal foam porosities 30 4.7 Temperature at porosity 0.5 . . . . . . . . . . . . . . . . . . . . . . . 31 4.8 Longitudinal section of the MOSFET region . . . . . . . . . . . . . . 32 4.9 Temperature distribution at t = 100 s along the longitudinal section of the MOSFET region for PCM/metal foam composites with different porosities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 4.10 The distribution of phase change rate in the PCM region under dif- ferent porosities (0.1, 0.3, 0.5, 0.7 and 0.9) at t = 100 s . . . . . . . . 34 4.11 Cylindrical structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.12 Comparison of temperature response with and without copper cylin- drical structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.13 Integrated cylindrical heat sink . . . . . . . . . . . . . . . . . . . . . 38 4.14 Comparison of temperature response of MOSFET devices with and without copper cylindrical structures at different porosity conditions . 39 4.15 Temperature variation on MOSFET with and without cylindrical structure at porosity 0.3 . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.16 Temperature distribution of PCM area at each time in the fifth cycle when there is a cylindrical structure . . . . . . . . . . . . . . . . . . . 40 xv List of Figures 4.17 Temperature distribution of PCM area at each moment in the fifth cycle without cylindrical structure . . . . . . . . . . . . . . . . . . . . 41 4.18 Phase change rate diagram of PCM region of integrated copper pillar structure at different time points (85s, 90s, 95s, 100s, 105s) . . . . . . 42 4.19 Phase change rate diagram of PCM region without copper pillar struc- ture at different time points (85s, 90s, 95s, 100s, 105s) . . . . . . . . . 43 4.20 Schematic diagram of spatial distribution of regions with different porosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.21 Comparison of MOSFET Temperature Variation in the First Driving Cycle Before and After Optimization . . . . . . . . . . . . . . . . . . 47 4.22 Comparison of MOSFET temperature changes from the second to the fifth cycle before and after optimization . . . . . . . . . . . . . . . . . 48 xvi List of Tables 2.1 Thermal and physical properties of various organic PCMs. Data com- piled from multiple sources (Abhat, 1983; Hasnain, 1998; Babich, Hwang and Mounts, 1992; Khudhair and Farid, 2004; İbrahim Dinçer and Rosen, 2010; Abbas et al., 2019; Koschenz and Lehmann, 2004; Pielichowska and Pielichowski, 2014; Abdul Hussain Ayash, 2019; Sarı and Kaygusuz, 2003; Sari and Kaygusuz, 2002). Specific refer- ences are provided in the table. . . . . . . . . . . . . . . . . . . . . . 13 3.1 Parameters of the PCM used . . . . . . . . . . . . . . . . . . . . . . . 19 3.2 Coolant parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.3 Results dependence on grid size variations . . . . . . . . . . . . . . . 21 3.4 Results dependence on time step variations . . . . . . . . . . . . . . . 21 4.1 Optimization parameters and their value ranges . . . . . . . . . . . . 45 4.2 Optimal parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 1 1 Introduction 1.1 Background With the continuous growth of the global motor vehicle population, greenhouse gas emissions have shown a significant upward trend, which is particularly prominent in developing countries. Driven by the dual drive of economic development stage and urbanization process, this emission trend will continue to grow inertia in the fore- seeable medium and long term (Jaramillo et al., 2022). To meet this environmental challenge, electric transportation (E-mobility) has emerged as a sustainable solu- tion, the core of which is the adoption of a new generation of clean energy vehicles. Among many technical paths, electric vehicles (EVs) have been widely regarded as the most promising low-carbon transportation option due to their significant po- tential for carbon emission reduction and advantages of technological advancement (Cambridge University Press, n.d.). However, the development of electric vehicles has always faced challenges due to energy conversion issues. One way to solve this problem is to use high-efficiency and high-power density electronic devices (Jaguemont, Boulon and Dubé, 2016; Zhang et al., 2020). The motor inverter is one of the important electronic modules in the power part of electric vehicles and plays a vital role in the overall energy efficiency of the vehicle. It converts the DC power in the battery into the AC power required by the motor. The inverter contains transistor modules, which are subjected to very high heat flux. The heat load generated by the transistor module at full load is 100-150 W/cm2, which is expected to increase to 500 W/cm2 in the future due to the increase in current capacity and switching frequency (Wang et al., 2022). The temperature of the inverter will also affect its output power, which in turn affects the normal operation of electric vehicles, so we need to develop advanced thermal man- agement technologies that can handle high heat flux density (Cai et al., 2016; Erp, Georgios Kampitsis and Elison Matioli, 2019). Using a proper cooling system can ef- fectively improve the performance of the inverter (Lajunen, Yang and Emadi, 2018). To stabilize the inverter temperature, researchers have developed a variety of efficient cooling technologies for tram inverters (Chang et al., 2017; Gautier Rouaze et al., 2021; Lei, Xin and Liu, 2022; Wang et al., 2022b). Han et al. conducted an exper- imental study on the heat dissipation performance of various heat sinks and found the heat sink with the best overall performance - serpentine heat sink, which has good heat transfer ability. In addition, they also optimized the overall structure of 2 1. Introduction the heat sink (Han, Guo and Ding, 2021). Bostanci et al. conducted an experimen- tal study on the performance of spray cooling in motor inverter cooling. When using spray cooling, the maximum heat flux that the inverter can withstand is 400/cm2 and the temperature can be kept below 150◦C(Huseyin Bostanci et al., 2012). Wang et al. (2023) systematically studied the thermodynamic performance of the Toyota Prius inverter under single-phase and two-phase cooling conditions by combining theoretical analysis and numerical simulation methods. The research team used R134a refrigerant as the two-phase cooling medium and water as a single-phase cooling control. The experimental data showed that compared with the traditional single-phase cooling system, the two-phase cooling technology showed significant ad- vantages in key performance indicators (Wang, McCluskey and Bar-Cohen, 2013). In addition to the significant thermal load of the inverter under steady-state oper- ating conditions, the transient characteristics of the electric vehicle power system also pose a key challenge. Specifically, when the vehicle is accelerating suddenly, the inverter output power increases in a step-like manner, and its response time constant is very low. This dynamic response mismatch causes the thermal sensor and the cooling system to be unable to track temperature changes in a timely man- ner, which in turn leads to a serious consequence: Thermal cycle stress increases, reducing the life of the inverter. Using PCM technology is one way to solve this problem. Phase Change Materials (PCMs) are a type of thermal management medium that undergoes a phase change within a characteristic phase change temperature zone. Their thermodynamic properties are manifested in temperature control through the isothermal absorption/release of latent heat during the phase change process. Based on their high heat capacity characteristics and dynamic thermal response capabil- ities, this type of material can effectively buffer transient thermal shocks, and is therefore particularly suitable for inverter thermal management systems with inter- mittent power characteristics, showing significant advantages in improving energy conversion efficiency and equipment operation sustainability. The key parameter for material selection is the characteristic phase change temperature. To achieve opti- mal thermal management performance, it is necessary to ensure that the melting point of the PCM is close to the actual operating temperature of the inverter(İsmail Gürkan Demirkıran, Oliveira and Erdal Cetkin, 2022; Mehwish Mahek Khan et al., 2023). Although it is undeniable that although PCM has excellent thermal man- agement performance, it also faces some problems, such as low thermal conductivity and stability in multiple cycles (Gil et al., 2010).To address these issues, many researchers have tried different approaches such as using thermal conductivity en- hancers (fins, metal foams, nanoparticles), using different geometries of heat transfer surfaces, packaging techniques, and hybrid PCM material development (Al-Salami et al., 2024; Low, Qin and Duan, 2024).Among these methods, the use of metal foam can significantly improve the performance of PCM, and metal foams with different porosity and PPI have different abilities to improve PCM performance. PPI (Pores Per Inch) refers to the number of pores within one linear inch of the material (Cui et al., 2022; Shi et al., 2023). 3 1. Introduction In this thesis, a new heat sink design for vehicle inverter using PCM and metal foam is proposed with the objective, and its heat dissipation capacity under actual driving cycle is simulated. At the same time, there is no research on the thermal resistance of metal foams with different porosities when used together with PCM in the current literature. 1.2 Objectives The aim of this master’s thesis is to design a new vehicle inverter cooling device that utilizes PCM as a cooling enhancer to improve the thermal management performance of the inverter and enhance its ability to cope with power surges. In the initial phase of the project, MATLAB is utilized to develop a comprehensive power loss model for the inverter. The power loss of the inverter is accurately evaluated using actual driving condition data as inputs and is used as the main heat source for thermal management simulation. After that, COMSOL Multiphysics was utilized for detailed design and analysis to simulate the thermal performance of the heat sink under different design parameters. Through iterative optimization, the configuration with the best thermal management performance is determined. 4 2 Theory This chapter highlights the most important basic points of the paper and introduces the theoretical ideas of electrical engineering, heat transfer and materials science behind the design and numerical simulation. 2.1 Inverter loss model construction Power electronics play a key role in converting the electrical energy in the battery to a traction motor. Figure 2.1 illustrates one possible configuration of an electric vehicle powertrain. An inverter converts the DC current flowing from the battery system into the required AC current, which is then fed into the electric motor to provide kinetic energy for the electric vehicle. Figure 2.1: Electric vehicle powertrain configuration During the operation of an electric vehicle, the power semiconductor devices in the inverter generate conduction and switching losses. The heat generated by these losses leads to an increase in chip temperature, which in turn affects performance and reliability. This study focuses on the thermal behavior of the inverter under frequent and rapid acceleration and deceleration conditions. Based on a specific driving condition, the power loss of the inverter is calculated and thermally analyzed in COMSOL as a heat source to evaluate the temperature distribution and heat dissipation characteristics. The driving conditions used are shown in Figure 2.2. 5 2. Theory Figure 2.2: Drive Cycle The following detailed calculation of the inverter losses of the electric vehicle for this driving condition is carried out. The required traction force is calculated by vehicle dynamics analysis to further derive the motor speed and torque. Subsequently, based on the vector control strategy, the d-axis and q-axis current calculations under weak magnetic control are considered to finally obtain the motor stator current and inverter input current. Then, the losses are calculated by combining the inverter input current and the inverter operating principle. 2.1.1 Vehicle dynamics calculations A vehicle needs to overcome a variety of external resistances during driving, including rolling resistance when the car is driving on a flat road, air resistance, and inertia during acceleration.In this Fdrag = 1 2ρCdAv2 (2.1) where Fdrag is air resistance, which comes from the force of air on the vehicle, and its magnitude is proportional to the square of the vehicle’s speed. ρ is the air density, Cd is air resistance coefficient, A is the vehicle’s frontal area, v is the velocity. The vehicle’s acceleration is calculated from the velocity data using the numerical differentiation method: a = dv dt (2.2) For rolling resistance Frolling Frolling = µmg (2.3) where µ is rolling resistance coefficient, m is the mass of the car, g is the gravity acceleration.When the car is driving on a flat road, the total vehicle traction is Ftraction = m · a + Fdrag + Frolling (2.4) 6 2. Theory 2.1.2 Motor speed and output torque calculations The motor speed depends on the wheel speed and the transmission ratio, and is calculated as follows ωmotor = v rw · G (2.5) where rw is wheel radius, G is gear ratio, the wheel output torque is determined by the traction and wheel radius, as shown in the formula Twheel = Ftraction · rw Furthermore, the motor output torque is determined by the wheel torque and the transmission ratio: Tmotor = Twheel G = Ftraction · rw G (2.6) 2.1.3 Motor current calculation 2.1.3.1 Field weakening control strategy In a Field Oriented Control (FOC) strategy, the d-axis current (Id) is primarily used to regulate the magnetic field. When the motor is running below the base speed, Id is typically set to 0 to maintain the maximum torque-to-current ratio. However, when the motor speed exceeds the base speed (ωbase), magnetic field weakening control is required to maintain constant power operation by applying a negative Id to reduce the magnetic flux: Id = 0 ωmotor ≤ ωbase − (ωmotor−ωbase)·λm Ld ωmotor > ωbase (2.7) where λm is permanent magnetic flux,Ld is d-axis inductance 2.1.3.2 q-axis current The q-axis current (Iq) is mainly used to generate electromagnetic torque, and its calculation formula is as follows: Iq = Tmotor 1.5p(λm + (Lq − Ld)Id) (2.8) where p is motor pole pairs, Lq is q-axis inductance,the formula shows that when weak magnetic control is used, the d-axis current will affect the calculation of the q-axis current. 2.1.3.3 Stator current The three-phase stator current of the motor is calculated from Id and Iq Istator = √ I2 d + I2 q (2.9) this current is used to evaluate the motor operating status and its current demand on the inverter 7 2. Theory 2.1.4 Inverter input current calculation After getting the phase current waveforms of the PMSM in one drive cycle, the next step is to estimate the current waveforms of each switching device in the inverter. This is critical for subsequent loss calculations.Consider a three-phase two-level in- verter with six switching devices (one up and one down switch per phase). This is critical for subsequent loss calculations. 2.1.4.1 Inverter Topology and Switching Signals The inverter we study is controlled using the third harmonic injection space vector PWM (SVPWM) method while having a fixed switching frequency fs according to the relevant tables, and we also need to insert a dead time tdead. The switching signal of each upper switch Sx+ (x = a, b, c) is generated according to the PWM modulation index and switching frequency, and the dead time is added to avoid breakdown. 2.1.4.2 Deriving Device Currents from Phase Currents and Switching States At any given moment t, the instantaneous current flowing through each switching device depends on the corresponding phase current and switching state. For a-phase, ia(t) means instantaneous phase current, and ua+(t) and ua−(t) means the switching state of the upper and lower switches, respectively (+ means on, - means off). Then the currents flowing through the upper and lower switching devices in phase a are given by the following equation: iSa+(t) = ua+(t) · ia(t) (2.10) iSa−(t) = ua−(t) · (−ia(t)) (2.11) Where the negative sign indicates that the direction of the current in the lower switch is opposite to the phase current, which represents the renewal or reverse conduction current. Similarly, for phases b and c: iSb+(t) = ub+(t) · ib(t), iSb−(t) = ub−(t) · (−ib(t)) (2.12) iSc+(t) = uc+(t) · ic(t), iSc−(t) = uc−(t) · (−ic(t)) (2.13) The instantaneous input DC current idc(t) drawn from the DC bus is then calculated as the sum of the currents flowing through the upper switches of each inverter leg: Idc(t) = iSa+(t) + iSb+(t) + iSc+(t) (2.14) This represents the total current drawn from the DC source, as power is transferred between the DC side and the three-phase AC load. 8 2. Theory 2.1.5 Inverter Loss Modeling Methodology Based on the previously computed three-phase inverter output currents, we proceed to estimate the inverter’s internal power losses. These losses are primarily associated with the switching and conduction characteristics of the power semiconductor de- vices. The following section presents a detailed methodology for reconstructing the switching behavior and computing instantaneous power losses using datasheet-based interpolation and modulation signal analysis. 2.1.5.1 Overview Accurate estimation of inverter power losses is critical for evaluating system effi- ciency, thermal management, and reliability. In this work, a physics-informed loss model is developed for a two-level voltage-source inverter employing silicon carbide (SiC) MOSFET devices. The model captures both conduction and switching losses, and is implemented in MATLAB using actual device characteristics obtained from manufacturer datasheets. The model reconstructs the switching behavior of each power device based on the modulation strategy and calculates the instantaneous power losses as a function of time. The aim is to provide a time-resolved, device-level loss profile that can be used for thermal simulations and efficiency assessments. 2.1.5.2 Modulation and Switching State Reconstruction The inverter is controlled using a sinusoidal pulse-width modulation (PWM) strategy with third harmonic injection (THIPWM). This technique modifies the reference voltage signals to increase the output voltage range and reduce harmonic distortion. The three-phase modulation signals are defined as follows: vma(t) = m sin(ωt) + m 6 sin(3ωt), vmb(t) = m sin ( ωt − 2π 3 ) + m 6 sin (3ωt − 2π) , vmc(t) = m sin ( ωt + 2π 3 ) + m 6 sin (3ωt + 2π) , (2.15) where m is the modulation index and ω = 2πfm is the angular frequency of the fundamental component. These continuous-time modulation signals are compared against a high-frequency triangular carrier waveform of frequency fsw to generate initial binary gate signals for the inverter switches. To prevent shoot-through faults due to simultaneous con- duction of upper and lower switches in the same inverter leg, a dead-time of 2 µs is inserted into each leg. Based on this PWM logic with dead-time insertion, the switching status of each of the six MOSFETs (S1 to S6) is reconstructed at every simulation time step. Each switch is either in an ON (conducting) or OFF (non-conducting) state. Transitions 9 2. Theory between these states correspond to switching events that cause additional switching energy losses. 2.1.5.3 Loss Model Formulation The inverter loss model includes two primary components: conduction loss and switching loss. • Conduction loss: When a switch is conducting current, its instantaneous conduction loss is calculated as Pcond(t) = |Isw(t)| · Von(Isw, Tj), where Isw(t) is the instantaneous current through the device, and Von is the on-state voltage drop obtained via interpolation from manufacturer-provided lookup tables as a function of current magnitude and junction temperature Tj. In this work, Tj is assumed to be constant at 25◦C for simplification. • Switching loss: When a switch transitions from OFF to ON or vice versa, it dissipates finite energy per switching event. The switching energy losses are given by Esw = Eon(Isw, Tj) or Eoff(Isw, Tj), also obtained from datasheet-based lookup tables. The instantaneous switch- ing power loss is computed by scaling the energy losses by the switching fre- quency and the instantaneous DC bus voltage: Psw(t) = fsw · (Eon(Isw, Tj) + Eoff(Isw, Tj)) · Vdc(t) Vref , where Vref is the reference voltage used in the datasheet measurements (e.g., 850 V), and Vdc(t) is the instantaneous DC bus voltage. The total instantaneous power loss of the inverter is obtained by summing the con- duction and switching loss contributions over all six switches: Ptotal(t) = ∑ devices ( Pcond(t) + Psw(t) ) . 2.1.5.4 Numerical Implementation The loss model is fully implemented in MATLAB. The modulation waveforms are generated analytically, and PWM gate signals are produced via digital comparison with dead-time insertion. The switching states of the six inverter devices are recon- structed accordingly at a high sampling rate (1 MHz). Three-phase output currents and the DC bus voltage are modeled as time-dependent inputs to the loss calculations. Device characteristics such as on-state voltage drop (Von), turn-on energy (Eon), and turn-off energy (Eoff) are extracted from manufac- turer datasheets and interpolated via 1D linear interpolation functions at the fixed junction temperature of 25◦C. 10 2. Theory The model outputs a high-resolution, time-resolved loss power waveform Ptotal(t) over the simulation duration (e.g., 0.1 s). This detailed loss profile enables further analysis for thermal management, efficiency evaluation, and inverter design opti- mization. 2.1.6 Result validation Figure 2.3 demonstrates the loss results calculated using the methodology of this pa- per compared to the reference data. Although there are some errors, the predictions are still within acceptable limits. Therefore, the loss model has sufficient accuracy to be used as a heat source input in subsequent thermal simulations. Figure 2.3: Comparison of power loss results: proposed method vs. reference data. 2.2 Working concept of PCM Phase Change Materials (PCMs) are special materials, usually with a unique melting point, that are subject to a reversible phase change when the temperature reaches the melting point. PCMs can absorb or release large amounts of latent heat during the phase change process while maintaining a nearly constant temperature. This property allows it to be used in thermal energy storage and temperature regulation applications. Figure 2.4 shows the typical temperature behaviour of a PCM. It shows that the PCM can absorb a large amount of heat during the phase transition, this heat is used to overcome the phase transition, the PCM maintains a constant temperature during the process. 11 2. Theory Figure 2.4: Typical PCM Temperature Characteristics 2.3 PCM materials and properties In recent years, extensive research has been conducted on the thermal and phys- ical properties of various PCMs. PCMs are generally classified into three major categories: inorganic,organic and eutectic materials. The selection of an appropri- ate PCM requires a comprehensive evaluation of several key factors, including its melting point, latent heat of fusion, density, thermal conductivity, and chemical sta- bility. It is essential to ensure that the chosen PCM aligns with the specific thermal management requirements and operational conditions of the intended application to achieve optimal performance and reliability. 2.3.1 Organic PCMs Organic PCMs often have a definite melting point, which can range from low to high temperatures, depending on their molecular structure. They have good nucleation behaviour, resulting in minimal or negligible subcooling effects during the phase change process. These characteristics contribute to their reliability and stability in thermal energy storage applications (Sharma et al., 2009). The following table shows some of the common organic phase change materials and their related parameters. 12 2. Theory PCM Melting temperature[◦C] Latent heat of fusion[kJ/kg] Density [kg/m3] Thermal Conductivity [W/m · K] Refs Caprylic acid 16.5 149 1033 No data (Abhat, 1983) Propylpalmitate(C17H34O2) 19 186 No data No data (Hasnain, 1998) PEG600 22 127.2 1232 No data (İbrahim Dinçer and Rosen, 2010) ParaffinC13–C24 22-24 189 900 0.21 (Khudhair and Farid, 2004) 1-Iodehexadecane 22.2 131 No data No data (Babich, Hwang and Mounts, 1992) n-Octadecane(C18H38) 28 244 814 0.358 (Abbas et al., 2019,Khudhair and Farid, 2004,Koschenz and Lehmann, 2004) ParaffinC22–C45 58-60 189 920 0.21 (Khudhair and Farid, 2004) n-Heptacosane(C27H56) 58.8 235 No data No data (Pielichowska and Pielichowski, 2014,Abdul Hussain Ayash, 2019) Palmiticacid 60-61 197.9 942 No data (Sarı and Kaygusuz, 2003,Sari and Kaygusuz, 2002) Table 2.1: Thermal and physical properties of various organic PCMs. Data compiled from multiple sources (Abhat, 1983; Hasnain, 1998; Babich, Hwang and Mounts, 1992; Khudhair and Farid, 2004; İbrahim Dinçer and Rosen, 2010; Abbas et al., 2019; Koschenz and Lehmann, 2004; Pielichowska and Pielichowski, 2014; Abdul Hussain Ayash, 2019; Sarı and Kaygusuz, 2003; Sari and Kaygusuz, 2002). Specific references are provided in the table. 2.3.2 Inorganic PCMs Inorganic phase change materials consist mainly of salt hydrates and metal alloys. Salt hydrates have a fixed melting point, a high latent heat, and a low cost. However, their practical application often encounters difficulties such as inconsistent melting, which can result in density gradients, settling and phase separation during repeated phase change cycles. These problems can adversely affect the long-term thermal reliability and stability of the material (Cabeza et al., 2003). Metal alloys tend to have high melting points and are therefore commonly used in high temperature thermal storage applications. In addition to their high melting points, these alloys exhibit excellent stability and thermal reliability (Liu, Saman and Bruno, 2012). Among them, binary and ternary alloys consisting of elements such as aluminium, copper, magnesium and zinc have the highest latent heat, both by mass and by volume. However, it is worth noting that not all combinations of these elements are suitable for use as phase change materials, as various combina- tions differ in their phase change behaviour, thermal stability and compatibility with specific applications and require careful analysis (Scopus.com, 2025) 2.3.3 Eutectics Eutectic systems are homogeneous mixtures of two or more components, each with its own melting point, which, when mixed in specific proportions, exhibit a single, sharp melting and solidification point. This property ensures that eutectic mixtures typically undergo phase transitions simultaneously, behaving like a single substance during melting and solidification. Eutectic materials can be classified as organic- organic systems, inorganic-inorganic systems or organic-inorganic systems (Hasnain, 1998). One of the main advantages of eutectic phase change materials is the ability to adjust the melting temperature and latent heat value by selecting the appropriate component materials and adjusting the composition ratio, thus allowing precise control of the thermal properties to meet specific application requirements (Singh et al., 2021). 13 2. Theory 2.3.4 PCM selection and use Several key factors must be systematically evaluated in the use of PCMs to enhance the thermal management performance of automotive inverters. These factors include selecting PCMs with melting points that match the inverter’s operating tempera- ture range to ensure effective heat absorption and release under normal and peak load conditions. In addition, the material must have excellent thermal reliability and cycling stability, maintaining consistent phase change behaviour and thermal properties over multiple heating and cooling cycles. In addition to thermal performance, practical considerations such as ease of ma- terial processing and fabrication, availability of raw materials, and overall cost of production and system integration need to be taken into account to ensure eco- nomic viability. Other key factors include the thermal conductivity of the PCM (which directly affects the rate of heat transfer); chemical stability (to prevent ma- terial degradation over time); compatibility with encapsulation materials; and safety aspects such as flammability and potential toxicity. 2.4 Thermal Conductivity Enhancer(TCE) A major disadvantage of PCM is that PCM itself has a low thermal conductivity, usually only about 0.5. This results in PCM that is close to a heat source being able to absorb heat and melt, while PCM that is far from the heat source is not able to function. Therefore, it is important to find ways to increase the thermal conductivity of PCM. 2.4.1 Fin Of all the methods, the use of highly thermally conductive fins is perhaps the sim- plest and most straightforward (Wang, Zhang and Xia, 2017). The incorporation of thermally conductive fins establishes enhanced heat transfer paths in phase change material (PCM) systems, facilitating the directional diffusion of heat to the distal region through its extended surface structure. The fin-enhanced thermal network compensates for the molecular-level thermal resistance properties of organic phase change materials through macro-geometry optimisation, demonstrating a synergis- tic approach to thermal management system design. When using fins, factors such as their shape, size, quantity, and assembly with the PCM need to be considered. Figure 2.5 shows the structure of a typical fin. 14 2. Theory Figure 2.5: Schematic diagram of the fin Weng et al. (Weng et al., 2019) studied various PCM-fin systems. They found that the temperature of the system was lower when using the branch fin structure as compared to the conventional fin structure, and among all twelve fin structures, the X-shaped fin had the best results.Sharma et al. (Sharma et al., 2019) (Sharma, Agarwal and Prabhakar, 2023) investigated twelve different fin designs and com- pared them with two benchmark cases without fins. They found that two fin designs exhibited different thermal performance than before when the PCM volume fraction was the same. Liu et al. (Liu et al., 2023) designed and optimised an enhanced hybrid cooling system with an integrated PCM and liquid-cooled fin in order to be used under long-term cycling.Kalapala et al. (Influence of operational and de- sign parameters on the performance of a PCM based heat exchanger for thermal energy storage – A review, 2018) focused on various operational and design factors to improve the thermal performance of PCM-HEX. According to their findings, the geometrical orientation of the heat transfer fluid (HTF), the temperature and mass flow rate, the tube structure, and the arrangement and sizing of the fins all have an impact on the results. 2.4.2 Nanocomposite Addition of conductive nanoparticles to PCM enhances its thermal conductivity. Suresh Kumar and Kalaiselvam investigated the effect of addition of copper oxide nanoparticles to palmitic acid on its thermal properties (Suresh Kumar and Kalai- selvam, 2017).P. Manoj Kumar et al., 2023) investigated the effect of MgO nanopar- ticles on the thermal properties of inorganic PCM and the results showed that the thermal conductivity increased to 0.902 W/mK when the concentration of MgO NP was 0.75 per cent.Kalidasan et al. (P. Manoj Kumar et al., 2023) investigated the effect of MgO nanoparticles on the thermal properties of inorganic PCM. The results showed that the thermal conductivity increased to 0.902 W/mK at 0.75% MgO NP concentration. (B Kalidasan et al., 2023) investigated the synergistic effect of car- bon nanoparticles with polyethylene glycol to improve the thermal conductivity and performance of the energy storage device. Lin and Al-Kayiem (Lin and Al-Kayiem, 2016) investigated the effect of the embedded paraffin wax the effect of the number 15 2. Theory of copper nanoparticles on the thermal properties of paraffin wax. The thermal conductivity increased by 14.0%, 23.9%, 42.5% and 46.3% when paraffin wax con- tained 0.5 to 2.0 %wt of copper nanoparticles.Narayanan et al. (Narayanan et al., 2017) investigated a nanocomposite PCM consisting of a eutectic gel and 0.5 wt% of graphite nanoparticles. The nanocomposite PCM was encapsulated in a copper block in a copper block and then wrapped with a copper coil cable. 2.4.3 Metal Foam Metal foam is a hollow material with many internal pores, consisting of a metal matrix filled with a large number of connected or closed pores. Due to this special structure, it has good thermal conductivity, high specific surface area and excellent mechanical properties. Metal foams are widely used in thermal management, energy absorption and cushioning, and structural weight reduction. Figure 2.6 shows a two-dimensional schematic of a metal foam, which shows that there are many pores distributed in the structure. Figure 2.6: Schematic diagram of metal foam structure Porosity is a key parameter describing the internal porosity of the metal foam ma- terial, which indicates the proportion of the pore volume to the total volume, and is an important index for judging the performance of the material in terms of air permeability, thermal conductivity, adsorption capacity and so on. Its expression is as follows. ϕ = Vvoid Vtotal = 1 − Vsolid Vtotal (2.16) Buonomo et al. (Buonomo et al., 2022) investigated the effect of adding a metal foam layer on the tube on the thermal performance of a shell-and-tube LHTES device, and showed that increasing the thickness of the foam layer reduces the melting time. Zhu et al. (Zhu et al., 2018) investigated the effect of the porosity of 96% and 16 2. Theory different pore densities (15 PPI and 30 PPI) on the thermal performance of heat-sink- transient output of PCM and copper foams. Joshi and Rathod (Joshi and Rathod, 2019) numerically investigated the effect of fill rate and foam porosity on the thermal performance of PCM and found that only the lowest fill rate (0.25 of the height) improved the thermal efficiency. In the unfilled metal foam and full volume metal foam configurations, the melting rate was 1.87 and 1.25 times faster at a porosity of 95%, respectively. Marri and Balaji (Marri and Balaji, 2021) combined numerical and experimental approaches to investigate the thermal performance of aluminium foams with different PPIs, porosities, and n-octacosane, the phase change material. The results show that decreasing the porosity or increasing the PPI has a better effect on the thermal efficiency of the heat sink than the case of uniform PPI and porosity.Iasiello et al. (Iasiello et al., 2021) reported simulation and experimental results investigating the effect of aluminium-metal foams on the performance of PCMs with different orientations, porosities, PPIs, and heat flow densities. The results showed that the lower the porosity, the higher the melting fraction, while PPI and orientation had no relevant effect on the melting time. Diani and Rossetto (Diani and Rossetto, 2021) investigated the effect of copper foams with different porosities on the melting of PCM at different melting temperatures (e.g., 42, 55, and 64 °C), and the results showed that the 90.5% porosity of the Copper foam with a porosity of 93.3% performed slightly better than that with a porosity of 93.3%.Li et al. (Li et al., 2012). It was shown that lowering the PPI can improve the temperature uniformity of saturated paraffin in copper foam, as well as lowering the porosity or increasing the natural convection, thus increasing the effective thermal conductivity. Mancin et al. (Mancin et al., 2015) investigated the embedding of copper foam in PCMs with three different melting points, and found that the copper foam acted as a heat sink, resulting in a more uniform temperature distribution and a PCM phase change faster. 17 3 Methods 3.1 Geometry design Figure 3.1 shows a schematic diagram of the various structures in the radiator and the schematic diagram of the cooling system associated with it. Figure 3.1: Cooling system and radiator schematic In our application we needed to optimise an existing radiator. Since the power section of a modern electric car is very compact, we didn’t have much room to add additional structure, so using metal foam became the best option for us. We placed the metal foam and the PCM integrated cooling system in the part of the original radiator above the fins. The picture below shows a three-view of the model used. 18 3. Methods Top View Front View Side View Figure 3.2: The three views of the model In the model, the brown part represents the PCM+MF area, and the rest is the original configuration of the radiator, which has not been changed. 3.2 Numerical procedure and model validation 3.2.1 PCM and MF In this simulation, the PCM we used is RT70HC from RUBITHERM, and its specific parameters are shown in the following table 3.1 Parameter name Numeric Unit Melting area 69-71 ℃ Heat storage capacity 260 KJ/Kg Density solid 0.9 Kg/L Density liquid 0.8 Kg/L Heat conductivity (both phases) 0.2 W/(m·K) Table 3.1: Parameters of the PCM used The melting point of this PCM is close to 70°C, which is close to the temperature at which the chip on the inverter operates normally. In this simulation, copper foam is used, which has a relatively high thermal conductivity, which helps us improve the thermal conductivity of the entire heat dissipation system. 19 3. Methods 3.2.2 Coolant The coolant used in this simulation is from Volvo Cars and its specific parameters are shown in Table 3.2. This coolant will maintain a constant flow rate, which is shown in table 3.2. The typical flow rate of the coolant in the inverter cooling system of an BEV under real working conditions is about 15 L/min. In order to better investigate the role of the PCM in passive thermal management, the coolant flow rate in the simulation is set to 0.5 L/min. The purpose of using this setting is to amplify the dominant role of the PCM in the response to the thermal loads, and to reduce the effect of active cooling on the results. This setting can provide a clearer physical context for structural optimisation and parametric analysis. Parameter Value Unit Heat capacity 3470 J/kg · K Density 1126 kg/m3 Thermal conductivity 0.38 W/m · K Table 3.2: Coolant parameters 3.2.3 Numerical simulation methods The simulation was performed using the finite element analysis software Comsol Multiphysics 6.2. To simulate the energy transfer behavior of the solid-liquid inter- face during the phase change process, this paper uses a phase change model based on the Heaviside function. The advantages of this method are that it avoids explic- itly tracking the phase interface and achieves a smooth transition of the solid-liquid phase change process. By using the Heaviside function, we can effectively bring the latent heat effect into the energy equation, which increases the numerical stability and improves the simulation accuracy, so it is suitable for solving complex geomet- ric structures and unsteady heat transfer problems. In COMSOL, the mathematical expression of Heaviside function is: H(T ) = 1 2 [ 1 + tanh ( T − Tm δT )] (3.1) Where: • T : Current temperature; • Tm: Melting point (or phase change temperature); • δT : Smoothing factor (transition width, controlling the steepness of the phase change transition); • tanh is the hyperbolic tangent function, used to achieve a smooth transition. Thermal properties, including density, specific heat, thermal conductivity, and latent heat, are defined as constant to reduce simulation pressure. 3.2.4 Mesh and time step independent test For the grid independence analysis, we considered three different grids: coarse grid (117975 elements), normal grid (242052 elements) and fine grid (582233 elements), 20 3. Methods with a time step of 1s to reduce its impact on the simulation accuracy. Table 3.3 lists the results of the average operating temperature under three grid conditions when the calculation time is t = 30s. Number of elements Temperature(◦C) Deviation(%) 117975 66.74 2.7% 242052 69.65 1.5% 582233 68.61 0% Table 3.3: Results dependence on grid size variations The maximum variation of the operating temperature is only 1.5%, which is neg- ligible when the grid number is 242,052 and 582,233. Therefore, choosing a grid with a cell number of 242,052 reduces the computation time while maintaining the accuracy of the solution. In order to assess the independence of time steps, simulations were performed with three different time steps (0.1 s, 0.5 s and 1 s) based on 242,052 grids. The results for the 1 s time step were used as a reference. The results show that the average temperature deviation of the inverter at 0.1 s and 0.5 s time steps is only 0.42% and 0.22% with respect to that at 1 s, which is so small that it is negligible. Therefore, the combination of 242,052 grids and 1 s time step was chosen for this study as it provides a good balance between computational accuracy and efficiency. Time steps Temperature(◦C) Deviation(%) 0.1 69.94 0.42% 0.5 69.80 0.22% 1.0 69.65 0% Table 3.4: Results dependence on time step variations 3.3 Hypothesis The following assumptions are made in the simulation model: (a) The PCM used is a homogeneous material with the addition of nanoparticles, also known as NePCM. its phase transition temperature varies over a range of 10 ◦C. (b) The flow of liquid PCM inside the MF is considered to be two-dimensional, Newtonian, laminar, transient, and incompressible. This simplifies the Navier- Stokes equations and is commonly used for modeling thermal systems. How- ever, it may ignore three-dimensional flow effects and turbulence at high flow rates. (c) All open-cell metal foam materials are assumed to be homogeneous and isotropic.Although actual foams may have anisotropic structures, this assumption reduces com- putational costs and is widely used. It may introduce small deviations in 21 3. Methods directional thermal conductivity. (d) The thermophysical properties of the substrate and the metal foam are as- sumed to be constant. This is standard in many simulations, although temperature- dependent properties at larger gradients can produce more accurate results. (e) Except for the density of the PCM, all thermophysical properties of both the PCM and the NePCM are assumed to be constant in each phase. (f) The initial temperature of the PCM, substrate, and metal foam is uniformly set to 45 ◦C. Initially, the PCM is entirely in the solid phase. (g) The coolant enters at a constant temperature of 45 ◦C with a fixed flow rate of 0.5 L/min. (h) Local thermal equilibrium is assumed between the metal foam and the PCM, implying no slip or temperature difference between them. 3.4 Validation of the numerical model Since the research problem involves a complex mechanism, a comprehensive valida- tion study is required to ensure the reliability of the numerical model developed in this paper. To this end, several validations have been carried out, including heat transfer validation and PCM phase transition process validation. 3.4.1 Heat Transfer Validation Firstly, after building the whole cooling plate model, we verified it without adding PCM, focusing on verifying that the material properties, meshing and heat transfer are correct. We compared the model with Volvo’s experimentally validated simula- tion model from the Star-CCM+ and after using the same heat source, the compar- ison results are shown below. 22 3. Methods Figure 3.3: Heat transfer results validation From the results, it can be seen that the model used in this paper has acceptable consistency with the reference model, which indicates that this model can be used for subsequent research 3.4.2 PCM model simulation validation After confirming that the basic heat transfer model is correct, it is necessary to validate the treatment of the PCM in the model of this paper. For this purpose, a numerical model incorporating the PCM was developed and compared and validated with the actual experimental results of Rehman and Park. (Rehman and Park, 2024), as shown in Figure 3.4. 23 3. Methods Figure 3.4: Comparison chart with the results of Rehman and Park From the figure, we can see that our simulation results are basically consistent with their experimental results, which indicates that our modelling parameter settings for the PCM in this paper are reasonable. The consistency of the two results can also further verify the physical accuracy of the thermal management model constructed in this paper and the credibility of the simulation results. 24 4 Results and discussion Our main goal is to reduce or slow down the temperature change of the on-board inverter as much as possible and keep its temperature within the allowable limit. To this end, this study explores the comprehensive impact of integrating PCM on the inverter temperature in the heat dissipation model mentioned above. The melting process, temperature distribution, and liquid fraction of the basic PCM, PCM+MF, and the new design using PCM+MF are studied. 4.1 The effect of PCM What we hope is to use PCM to absorb the heat generated by the on-board inverter whenever there is a sudden heat generation in inverter to achieve the effect of sta- bilizing the temperature. The first thing to do is to verify whether PCM has such a function. 4.1.1 The effect of PCM in simple model The PCM is integrated into the simulation model shown in Figure 4.1. In this model, the hole area is filled with PCM, and the rest of the structure is made of copper. A heat source with a constant power of 100 W is applied to the bottom of the model, and the thermal response of the system is simulated for 100 s. Figure 4.2 shows the temperature change trend of the bottom of the model during this period. 25 4. Results and discussion Figure 4.1: Model diagram Figure 4.2: Temperature response curve over time As can be observed from Figure 4.2, when the temperature reaches the melting point of PCM, PCM begins to undergo phase change. At this stage, the temperature rise rate of the target area slows down significantly and tends to be stable. This shows that PCM maintains a nearly constant temperature while absorbing heat, reflecting its latent heat absorption characteristics and verifying its expected temperature control effect in thermal management. 26 4. Results and discussion 4.1.2 The effet of PCM configuration in the real geometry After verifying the thermal regulation effect of the phase change material PCM in the simplified model, this study further integrated the PCM into the original heat sink structure and applied the time-varying heat source mentioned above to simulate the actual working conditions,figure 4.3 shows how the PCM is integrated in the heat sink,the blue part is the PCM.In the simulation, the coolant flows continuously from the lower left side to the right with an initial temperature of 45°C. At the same time, the MOSFET heat source is located at the top of the structure, and the heat is conducted downward in the vertical direction. The research focuses on the temperature response of the heat source area (i.e., the location of the MOSFET chip). In order to evaluate the thermal management performance of PCM, the thermal responses of the two heat sink structures with and without integrated PCM under the same working conditions were compared and analyzed, and the relevant results are shown in Figure 4.4. Figure 4.3: Heat sink with integrated PCM 27 4. Results and discussion Figure 4.4: Comparison of MOSFET temperature with and without PCM-enhanced radiator However, it can be observed from the results in Figure 4.3 that the temperature of the heat sink with integrated PCM in the MOSFET area is higher than that of the original heat sink without integrated PCM, which is obviously different from the expected cooling effect. Preliminary analysis shows that this phenomenon may be attributed to multiple factors. First, the thermal conductivity of the selected PCM material is low, only 1 W/(m·K), which limits its heat absorption capacity in the early stage of the heat source operation and significantly inhibits the effective conduction of heat to the coolant area. Secondly, the volume of the PCM in the model is relatively small, and its latent heat capacity is limited, which cannot absorb enough heat to significantly reduce the chip temperature. At the same time, due to the continuous heat input, the PCM failed to re-solidify in time after melting, and thus could not achieve the multi-cycle thermal regulation function. These factors together led to the overall thermal management performance not meeting expecta- tions. In order to further reveal the thermodynamic mechanism of the phenomenon, this paper will show 3D simulation results from COMSOL of the temperature field inside the heat sink and the phase transition at critical moments to visually compare the thermal conductivity characteristics of the PCM and its effect on the thermal behavior of the system. 28 4. Results and discussion Figure 4.5: Phase change rate at different times It can be observed from Figure 4.5 that the PCM near the heat source area undergoes phase change first, which indicates that heat conduction starts rapidly in the local area. However, due to the continuous flow of coolant, there are obvious differences in the degree of melting of PCM at different locations. Especially near the coolant inlet, only the PCM close to the heat source melts, while the PCM located below and directly in contact with the coolant is always maintained in a solid state due to continuous cooling, and fails to effectively participate in the heat absorption process, resulting in a waste of thermal management resources. In contrast, in the area far from the coolant inlet, the PCM is basically completely melted within tens of seconds, showing a strong local heat absorption ability. In addition, it can be observed that in the gap between the two driving cycles (such as the 20th and 30th seconds), some PCM re-solidifies. This phenomenon is mainly attributed to the decrease in heat source power during the vehicle deceleration stage, and the coolant takes away part of the accumulated heat, causing the PCM temperature to drop below the phase change temperature, thereby undergoing a phase change back to the solid state. This process reveals the reversible heat storage capacity of PCM under dynamic heat load, which is of great significance for the optimization of subsequent thermal management strategies. 4.2 The effect of metal foam Based on the previous analyses, it was decided to use metal foam in this paper. The metal foam is characterised by high specific surface area and high thermal con- ductivity, which can significantly increase the effective thermal conductivity of the PCM region while maintaining a low volume increment. Its porous structure helps to accelerate the diffusion of heat inside the PCM, thereby enhancing the heat ex- 29 4. Results and discussion change efficiency during the phase change process. In addition, metal foam can also improve the uniformity of temperature distribution inside the PCM to a certain ex- tent, reduce local overheating, and help the system maintain a stable thermal state. Figure 4.6 shows the simulation results after integrating the PCM+MF composite structure into the original radiator structure, and compares the temperature distri- bution without metal foam to further evaluate its thermal regulation performance under dynamic heat load conditions. Figure 4.6: MOSFET temperature variation under different metal foam porosities As can be seen in Figure 4.6, there is a significant difference in the effect of metal foams with different porosities on the MOSFET heat source temperature. Overall, all groups show better results compared to the original heat sink, except for the case with a porosity of 0.9. In particular, in the fifth driving cycle, the metal foam with a porosity of 0.5 can be seen to have significantly lower temperatures compared to the other groups, and a trend towards constant temperatures is seen. This shows that medium porosity has achieved a better balance between thermal conductivity and heat storage capacity. In the case of a porosity of 0.9, its overall thermal con- ductivity is low, and the metal skeleton accounts for a small proportion, making it difficult to effectively export heat from the heat source area, resulting in a decrease in overall heat dissipation performance. However, it is worth noting that in the de- celeration stage of the first two driving cycles, the structure with a porosity of 0.9 is better than the original radiator in short-term temperature performance. This may be because when the heat source power decreases during the deceleration stage, the 30 4. Results and discussion structure can use the latent heat absorption of PCM to delay the temperature rise, and form a temporary "insulation" effect due to its low thermal conductivity. In addition, it can be found from the figure that the temperature curve tends to be stable for a certain period of time during the deceleration phase of each driving cycle, which is the second peak part. This phenomenon indicates that the heat transfer and phase transition rate of the metal foam-PCM composite structure reached a dy- namic equilibrium under the significantly reduced heat input, which made the system temperature temporarily maintained near the PCM phase transition plateau. This property is of positive significance for suppressing the peak temperature fluctuation and improving the thermal stability of the system. Figure 4.7: Temperature at porosity 0.5 Figure 4.7 shows the time trend of the MOSFET heat source temperature in the composite structure of the original heat sink and the integrated metal foam with a porosity of 0.5 under the driving cycle condition. It can be observed that the tem- perature of the structure after the integration of metal foam is significantly lower than that of the original heat sink without metal foam added during the entire sim- ulation period, and the peak temperature is significantly reduced, and the overall temperature fluctuation amplitude is reduced, showing better thermal management performance. This phenomenon can be attributed to the high thermal conductivity skeleton of 31 4. Results and discussion the metal foam, which effectively improves the thermal conductivity of the PCM area, allowing heat to diffuse more quickly in the phase change material, and is also conducive to improving the thermal utilization of the PCM. Compared with the previous structure without the addition of metal foam, this structure can more efficiently conduct the heat generated in the MOSFET area to the cooling medium contact area, thereby reducing the accumulation of heat around the chip. In addi- tion, the three-dimensional interconnected structure of the metal foam also improves the temperature distribution inside the PCM, making it closer to uniform, which helps the continuous phase change process and suppresses local overheating. From the curve fluctuation shape, each peak-valley cycle in the figure corresponds to a typical acceleration-deceleration process, and the temperature drop rate in the deceleration stage is faster and smoother in the structure of integrated metal foam, indicating that the structure has better responsiveness and thermal buffering capacity under dynamic heat load changes. Especially after the fifth cycle, the temperature suppression effect is more obvious, which may be related to the fact that the PCM has partially melted in the early stage and entered the heat capacity platform range. Figure 4.8: Longitudinal section of the MOSFET region 32 4. Results and discussion Figure 4.9: Temperature distribution at t = 100 s along the longitudinal section of the MOSFET region for PCM/metal foam composites with different porosities Figure 4.9 shows the effect of different metal foam porosities (0.1, 0.3, 0.5, 0.7 and 0.9) on the temperature distribution of the PCM+MF composite structure under the same heat source and boundary conditions. The figure shows the temperature field distribution results along the longitudinal section of the MOSFET area at t = 100 s. It can be observed that when the porosity is low (such as 0.1 and 0.3), the over- all temperature level is significantly higher and the high temperature area is larger. This is mainly due to the high proportion of solid skeletons in metal foams. Although they have high thermal conductivity, the volume fraction of PCM they contain is small, resulting in limited phase change heat absorption capacity and difficulty in fully alleviating the temperature rise generated by the heat source. When the poros- ity is 0.5 and 0.7, the temperature field is more uniform as a whole and the high temperature area is reduced, indicating that the porosity within this range achieves a good trade-off between thermal conductivity and heat storage capacity, thereby improving the overall heat dissipation efficiency. When the porosity is further increased to 0.9, although the volume of PCM increases, the proportion of metal skeleton decreases significantly, and the effective thermal conductivity of the composite material decreases, which limits the rapid conduction of heat from the MOSFET area to the cooling area, resulting in heat retention in some areas. In summary, under the medium porosity (0.5–0.7), the PCM+MF structure achieves a balance between the heat conduction path and the phase change heat storage capacity, which can significantly improve the thermal management performance of the MOSFET area, reduce the temperature peak and improve the uniformity of 33 4. Results and discussion the temperature field, verifying the thermal optimization potential of the structure under dynamic heat load conditions. Figure 4.10: The distribution of phase change rate in the PCM region under different porosities (0.1, 0.3, 0.5, 0.7 and 0.9) at t = 100 s Figure 4.10 shows the distribution of phase change rate in the PCM region under different porosities (0.1, 0.3, 0.5, 0.7 and 0.9) at t = 100 s, showing the melting state of the PCM+MF structure under the heat source (MOSFET) in the form of a longitudinal section. The redder the color in the figure, the higher the phase change rate, that is, the PCM has completely melted, and the blue indicates that it is still in a solid state or partially melted. From the overall distribution trend, the phase change area is generally concentrated in the lower right. This is because the coolant flows from left to right. As the distance increases, its temperature increases and the heat transfer capacity decreases. The right area is easier to maintain high temperature, resulting in more complete melting of the PCM. When the porosity is 0.5, although only the PCM in the right half of the figure is completely melted and the phase change degree in the left half is low, this configu- ration shows the lowest MOSFET temperature. This result shows that the quality of thermal management depends not only on the absolute area of the melting range, but also on the efficiency of the thermal conduction path and the heat-fluid synergy mechanism. The structure with a porosity of 0.5 achieves a good balance between the metal foam skeleton and the PCM volume distribution: its skeleton thermal conduction network is sufficient to quickly conduct heat to the bottom, while re- taining enough PCM volume for absorbing heat and forming an effective coupled heat exchange interface with the coolant. This configuration achieves a high thermal 34 4. Results and discussion response efficiency, and can quickly reduce the heat source temperature even if the melting area is not "comprehensive". In contrast, when the porosity is 0.1 and 0.3, the metal foam content is high and the thermal conductivity is strong, but the available PCM content is low and the heat storage capacity is insufficient, resulting in the rapid melting of the PCM but it is difficult to continue the thermal buffering effect, and there is still a high temperature area near the MOSFET; especially when the porosity is 0.1, almost the entire PCM area quickly reaches saturation and loses further heat absorption capacity. When the porosity is 0.7 and 0.9, although the PCM content is sufficient and the latent heat capacity is large, the skeleton heat conduction network is weakened, and the heat is difficult to quickly transfer to the deep part of the PCM. In addition, the heat exchange capacity of the coolant at the right end is significantly reduced, resulting in heat retention inside the PCM, forming a large-scale continuous high- temperature melting area, but it is unable to take away the heat in time, and the MOSFET temperature eventually rises. In summary, although the phase change area is not the largest when the porosity is 0.5, the optimal synergy is formed between its heat dissipation path, heat exchange efficiency and heat storage capacity, which is the configuration option with the best thermal control performance in this study. 4.3 A new design The previous simulation results performed well overall, but there is still room for optimization. We still haven’t seen the temperature remain constant, and the tem- perature on the MOSFET is still changing, which may cause greater thermal stress and accelerate its aging. Therefore, the existing design still needs to be further optimized, and the focus should be on slowing down its temperature rise rate to achieve better thermal management performance and longer device life. 4.3.1 The effect of the cylindrical structure Combined with the above simulation results, it can be seen that although the overall thermal conductivity is improved by introducing the equivalent thermal conductivity of the metal foam enhanced phase change material (PCM) region, there are still certain limitations in the transfer of heat from the heat source to the direction away from the heat source, resulting in uneven temperature field distribution inside the PCM. To be more specific, the PCM on the side close to the heat source melts first, while the area away from the heat source remains in solid state and fails to fully participate in the heat absorption process. This uneven heat distribution limits the utilisation efficiency of the PCM, thus affecting the overall thermal management effect. In order to further improve the coverage of the heat conduction path, this paper introduces a copper cylinder as a high thermal conductivity heat extension element based on the metal foam structure to enhance the ability to transfer heat to 35 4. Results and discussion the area far from the heat source, thereby achieving a more balanced temperature distribution. The structural design is shown in the figure 4.11. Figure 4.11: Cylindrical structure This model can be regarded as a local substructure in the previous PCM+MF com- posite structure model, and its geometric configuration and material parameters are consistent. In order to ensure the comparability and continuity between the simula- tion results, this study uses the heat flux distribution obtained in the previous model as the boundary heat input condition of this model, so that the transient tempera- ture response characteristics of the structure can be analyzed under a unified heat load background. 36 4. Results and discussion Figure 4.12: Comparison of temperature response with and without copper cylindrical structure Figure 4.12 shows the temperature change of the heat source area in the first 100 seconds under two working conditions with and without the copper cylindrical struc- ture. It can be observed that under the same porosity conditions, the introduction of the cylindrical structure significantly reduces the temperature peak at the heat source, reflecting a better initial stage thermal control effect. 4.3.2 Integrating cylindrical structures into realistic models After verifying the effectiveness of the copper cylindrical structure in promoting heat diffusion, this paper further integrates the structure into the radiator system. In order to enhance the modularity of the thermal management structure and pro- vide clearer thermal response analysis conditions for subsequent research, copper partition walls are introduced in the physical structure to divide the PCM area into multiple independent units. This structural design helps control the local heat flow path, enhances the controllability of the system’s thermal response, and lays the foundation for comparative analysis of the heat transfer characteristics of different units. 37 4. Results and discussion Figure 4.13: Integrated cylindrical heat sink Figure 4.13 illustrates the modified heat sink model with the integrated copper pillar structure. The structure introduces longitudinal copper columns as a high thermal conductivity path through which heat can be transferred more quickly to the bottom position of the heat sink. To ensure the comparability of the results, after the model is built, the same boundary conditions (including heat flux, ambient temperature, and convection heat transfer coefficient, etc.) as the aforementioned copper-free structure model are used for simulation calculations to ensure the attributability of thermal response differences between different structures. 38 4. Results and discussion Figure 4.14: Comparison of temperature response of MOSFET devices with and without copper cylindrical structures at different porosity conditions Figure 4.15: Temperature variation on MOSFET with and without cylindrical structure at porosity 0.3 It can be observed from Figure 4.14 that the introduction of the copper cylindrical structure under different porosity conditions has a positive effect on the temperature 39 4. Results and discussion control of the MOSFET device. Compared with the structure without the intro- duction of the copper column, after adding the high thermal conductivity channel, the surface temperature of the MOSFET has decreased to a certain extent at each porosity level, reflecting the universality and effectiveness of the structure in im- proving the thermal diffusion efficiency. In addition, it is worth noting that when the porosity is 0.3, the system thermal management performance shows significant advantages. Specifically, in the fifth driving cycle stage, the temperature of the MOSFET device remained basically stable, maintained at about 103°C, and lasted for about 25 seconds, indicating that the system can effectively suppress the rapid rise and fluctuation of the device temperature under this configuration. This long-term thermal stability can reduce thermal stresses, slow material aging, and improve device operational reliability. Figure 4.16: Temperature distribution of PCM area at each time in the fifth cycle when there is a cylindrical structure 40 4. Results and discussion Figure 4.17: Temperature distribution of PCM area at each moment in the fifth cycle without cylindrical structure In order to compare the thermal management behaviors of different structures in the fifth driving cycle, Figures 4.16 and 4.17 show the cross-sectional temperature distribution of the PCM region at 85 s, 90 s, 95 s, 100 s and 105 s respectively when the porosity is 0.3 and 0.5 with and without the addition of the copper cylindrical structure. It should be pointed out that in this model, the coolant continues to flow, and its flow direction has a certain intersection with the heat transfer path of the PCM region under the heat source. Therefore, the temperature field inside the PCM is affected by both fluid cooling and local thermal conductivity, especially the inhomogeneity of temperature distribution in the flow direction is more obvious. It can be observed from Figure 4.16 that under the condition of introducing the cop- per column structure, although the coolant continues to take away heat, the entire PCM region still maintains a relatively stable temperature field distribution during the above time period. In particular, in the direction of coolant flow, the tempera- ture gradient is significantly suppressed, showing stronger heat diffusion ability and uniformity. Correspondingly, the temperature of the MOSFET device is maintained at about 103℃ for more than 25 seconds, indicating that the system has formed a relatively stable thermal equilibrium in this state. This shows that the copper pillar not only enhances the radial heat diffusion capacity of the PCM area, but also improves the uniformity of temperature distribution along the flow direction, thereby suppressing local heat accumulation and temperature fluctuations. In contrast, the temperature distribution under the copper pillar-free structure shown in Figure 4.17 shows certain dynamic change characteristics. Although the temperature of the MOSFET has been significantly improved compared with the original unfilled PCM structure, its temperature still shows a continuous change 41 4. Results and discussion trend, and the temperature distribution inside the PCM is uneven, especially in the direction of coolant flow. The temperature of the area close to the heat source or the coolant outlet rises rapidly and completes the phase change in advance, while the area far away from the heat source and close to the initial inlet direction of the coolant remains in a low-temperature solid state, indicating that the heat transfer speed in the PCM is limited and the thermal capacity advantage of the entire phase change material cannot be mobilized in time. In summary, the addition of the copper pillar structure not only improves the ther- mal conductivity near the heat source, but also optimizes the thermal uniformity of the PCM area in the direction of coolant flow, significantly prolonging the MOS- FET temperature plateau period, reflecting its effectiveness in regulating the local heat conduction path in a complex cooling environment. This result further demon- strates the considerable potential of the structure we used to improve the thermal management performance of electronic devices. Figure 4.18: Phase change rate diagram of PCM region of integrated copper pillar structure at different time points (85s, 90s, 95s, 100s, 105s) 42 4. Results and discussion Figure 4.19: Phase change rate diagram of PCM region without copper pillar structure at different time points (85s, 90s, 95s, 100s, 105s) After the copper pillar structure was introduced, an obvious temperature platform period was also formed inside the PCM region.Temperature platform refers to the phenomenon that the temperature of a material remains approximately constant while continuously absorbing heat over a period of time. When the copper pillar structure was not set, the PCM phase change process was significantly delayed. The appearance of the temperature platform indicates that the system has entered a thermal equilibrium stage dominated by latent heat absorption, that is, the heat continuously input by the heat source is mainly used to drive the phase change, and the temperature remains constant temporarily, which is consistent with the thermo- dynamic characteristics of the typical PCM phase change process. Upon further examination of the results we found that the melting in the PCM region is higher when a copper column structure is present, especially in the re- gion away from the coolant inlet, where the PCM undergoes essentially a complete phase transition. While when there is no copper pillar structure, there is still a large unmelted area in the same period, and the change over time is more dramatic, reflecting the unevenness of the system in thermal distribution. In particular, the PCM close to the coolant inlet is subject to the strong cooling effect of the coolant, and is prone to local overcooling or incomplete phase change in multiple cycles, resulting in some areas remaining in liquid or solid at the end of the cycle, with the initial state of "uncompleted phase change" remaining. Experimental studies at universities such as Purdue University have verified this cyclic residual effect: if the PCM is not fully solidified at the end of a cycle, the latent heat available to the PCM is reduced during the following warming process, a phenomenon that affects the thermal management efficiency of the system (Ieee.org, 2024). 43 4. Results and discussion In addition, the introduction of copper pillars and copper isolation walls significantly improves the thermal conductivity of PCM. Literature points out that high ther- mal conductivity structures such as copper pillars or metal foams can form a heat conduction network in PCM, which can improve the overall heat transfer efficiency and temperature uniformity by shortening the heat diffusion path, enhancing liquid phase natural convection, and balancing heat capacity distribution (Buonomo et al., 2022). Our results also confirm their theory that the PCM far away from the coolant inlet region can also effectively complete the phase transition after the addition of the copper column structure, showing that the heat can be more uniformly distributed throughout the phase transition region, avoiding localised overheating or unmelting. In summary, the temperature platform phenomenon observed in this study is consis- tent with existing thermodynamic theories and experimental results (Maxa, Novikov and Nowottnick, 2017), reflecting the physical mechanism of temporary balance be- tween latent heat absorption and heat input; at the same time, under the actual working conditions of flow cooling and multiple cycles, local supercooling, incom- plete phase change and thermal residue objectively exist, and the copper column structure effectively alleviates these problems by optimizing the heat diffusion path, improving the thermal response consistency and reliability of the system. The above analysis verifies the importance of structural design in the composite PCM thermal management system, and also provides a theoretical basis and engineering reference for subsequent optimization. 4.3.3 Optimization It is worth noting that in the aforementioned structural optimization scheme, we have achieved some remarkable results. For example, in the 5th driving cycle, we noticed that the system temperature seemed to be nearly constant. However, in practical applications, electronic modules are more susceptible to instantaneous tem- perature rise in the initial heating stage. Therefore, another goal of the optimization in this section is to further reduce its temperature change rate for the first driving cycle and delay the arrival of the peak temperature, thereby improving the initial thermal buffering capacity and system safety. Firstly, since the content of PCM will have an impact on the results of thermal management, we are going to adjust the thickness of the PCM area to change the total amount of PCM..Secondly, considering that the cylindrical structure played a positive role in promoting phase change in the distal region in the previous results, we tried to optimize the radius of the cylinder to further improve the heat transfer efficiency. Changes in the size of the cylinder will directly affect the coverage of its thermal network and the ability to guide heat flow, which may play an important role in balancing heat distribution. In addition, inspired by references Kotb and Wang (2024) and Bian et al( 2024), we introduced a nonlinear gradient porosity structure to explore its performance improvement potential under the condition of coolant flow. Previous studies have 44 4. Results and discussion shown that foam structures along different porosities can significantly improve the heat transfer efficiency and phase change uniformity of PCM. Therefore, combined with the characteristics of continuous flow of coolant in one direction in this model, we try to introduce a gradient porous structure in the PCM region, that is, the PCM region is divided into three sub-regions according to the coolant flow direction, and different porosities are set for each sub-region to achieve segmented optimization and local thermal regulation. This zoning design also takes into account the heat source distribution of the three power modules at the top of the radiator, further improving heat transfer coordination through space matching. In summary, this section will propose and verify a series of optimization schemes from multiple dimensions such as geometric structure, material distribution and heat source coupling to further enhance the thermal management performance of the PCM-coolant coupling system. 4.3.3.1 Parameters As mentioned above, this study selected five key structural parameters as optimiza- tion variables, namely the thickness Th of the PCM region, the radius r of the copper cylindrical structure, and the porosity parameters por1, por2 and por3 of the three sub-regions divided along the coolant flow direction. These parameters were selected to study the effect of porosity distribution, copper cylinder size and PCM content on the overall thermal management effect, and the specific range of values for each parameter is shown in the table 4.1. Figure 4.20 illustrates the spatial distribution of different porosity regions in the porous struc- ture in the geometric model, where Region 1, Region 2 and Region 3 correspond to the upstream, midstream and downstream positions on the coolant flow path, respectively, to achieve gradient structure optimization design that conforms to the flow direction. Parameter name Range Unit Description Th 0.01-0.02 m Thickness of PCM area r 0.001-0.002 m Cylinder radius Por1 0.1-0.9 - Porosity of region 1 Por2 0.1-0.9 - Porosity of region 2 Por3 0.1-0.9 - Porosity of region 2 Table 4.1: Optimization parameters and their value ranges 45 4. Results and discussion Figure 4.20: Schematic diagram of spatial distribution of regions with different porosity 4.3.3.2 Optimization methods and goal setting Our objective is to reduce the rate of change of the surface temperature of the MOSFET during the first heating cycle (0 to 30 seconds) in order to reduce the risk of thermal shock to the MOSFET. To quantify this objective, the following objective function is defined: min (∫ 30 0 ∣∣∣∣∣d TMOSFET(t) dt ∣∣∣∣∣ dt ) (4.1) Among them, TMOSFET(t)represents the average temperature of the MOSFET sur- face at time t, the absolute value operation ensures that the total thermal shock caused by the temperature rise and fall is considered, and the time integral is used to measure the total temperature fluctuation intensity within the entire first cycle. This definition not only helps to keep the objective function in a low dimension, but also effectively reduces the computational burden in the model optimization process. In order to minimise the above objectives, this paper adopts the Boundary Optimi- sation Quadratic Approximation (BOBYQA) algorithm for optimisation.BOBYQA is an iterative optimisation method based on the domain of reliance, which is suit- able for solving the optimisation problems of continuous variables, and is especially suitable for the complex multi-physics field models where the objective function is non-differentiable or difficult to discretise. It shows good stability and convergence speed. Since the thermal simulation model in this study is a nonlinear, strongly coupled transient heat transfer problem, the derivative of the objective function is difficult to obtain explicitly, so the use of BOBYQA can effectively avoid dependence on gradient information and reduce the risk of numerical instability. 46 4. Results and discussion In the optimisation process, the convergence tolerance is set to 0.001 and the max- imum number of iterations is limited to 2000 4.3.3.3 Optimization results Table 4.2 shows the best parameters obtained. Under this parameter combination, the temperature change of the mosfet in the first cycle is the smallest. Parameter name Th r Por1 Por2 Por3 Value 0.015 0.0015 0.58 0.6 0.8 Table 4.2: Optimal parameters Figure 4.21: Comparison of MOSFET Temperature Variation in the First Driving Cycle Before and After Optimization Figure 4.21 shows the comparison of the temperature change of the MOSFET chip area in the first driving cycle before and after optimization. It can be clearly observed from the figure that after the structural parameter optimization, the temperature change rate of the MOSFET has been significantly reduced throughout the cycle. Specifically, in the deceleration stage before optimization (about 17-30 s period), the average temperature of the MOSFET rose by about 13°C in 8 seconds, showing 47 4. Results and discussion an obvious temperature rise jump phenomenon. After multi-parameter joint opti- mization (including phase change material area thickness, copper column radius and porosity partitioning), the temperature in the same time period only rose by about 8°C, and the temperature change rate was reduced by nearly 40% compared with the original structure, indicating that the optimization significantly alleviated the thermal shock effect in the initial stage. In addition, from the perspective of temperature peak, the optimization scheme significantly reduced the temperature change rate without bringing additional peak temperature rise. The maximum temperature of the two schemes is basically the same, indicating that the optimization strategy maintains the overall thermal sta- bility of the system while improving the thermal buffering capacity. The results further validate that this improved structure improves thermal management perfor- mance, especially in the most critical first cycle, successfully controlling the thermal response rate and reducing the thermal shock suffered by the MOSFETs, which helps to prolong the lifetime of the power device. Figure 4.22: Comparison of MOSFET temperature changes from the second to the fifth cycle before and after optimization Figure 4.22 shows the comparison curves of the temperature change of the MOSFET area over time in the second to fifth driving cycles, which correspond to the optimal operating state before structural optimization and the improved scheme after the implementation of multi-parameter structural optimization. 48 4. Results and discussion As can be seen from the figure, although the two groups of working conditions are consistent in the overall temperature evolution trend, the optimized results show better performance in thermal response characteristics in multiple key time periods, especially in the stage of rapid power change. Taking the second to fourth cycles as an example, the temperature change rate of the optimized scheme is significantly lower than that of the situation before optimization. For example, in the cooling section of the second cycle (about 46–52s) and the subsequent heating section of the third cycle (about 60–70s), the temperature rise and cooling rates after optimiza- tion are effectively suppressed, indicating that the transient regulation ability of the thermal management structure is enhanced. However, it should be pointed out that although the optimization scheme effectively reduces the temperature change rate of the first four cycles and improves the sta- bility of thermal regulation, the temperature platform that appeared in the curve before optimization, that is, the phenomenon that the temperature tends to be con- stant for a period of time, is not reproduced in the fifth cycle stage. This may be related to the redistribution of heat capacity distribution and phase change rate by the optimization strategy, indicating the regulatory balance limit of thermal hys- teresis at a specific cycle stage. In summary, the multi-parameter structural optimization scheme proposed in this study significantly reduces the temperature change rate of the MOSFET area within the first driving cycle, showing a certain transient thermal management capability. This makes the optimized structure have stronger thermal relief and temperature rise suppression performance under short-term operation or low-frequency condi- tions. For example, in urban traffic or frequent start-stop conditions, such as buses, taxis or electric delivery vehicles, the operating cycle is short and the thermal shock is frequent. The optimization scheme can effectively reduce local temperature vari- ations, thus extending the service life of power devices and improving system safety. However, from the temperature evolution trend, the optimization scheme did not maintain the temperature platform effect that appeared in the pre-optimization scheme. This may be because the optimized structure sacrificed part of the steady- state heat capacity while improving the response speed, resulting in the inability to maintain thermal balance for a long time in the subsequent heat accumulation stage. Therefore, the original design is more suitable in applications with continuous high load operation, as it shows constant temperature behavior in the fifth cycle, which helps to maintain the thermal stability of the system. Therefore, the structures before and after optimization are complementary under dif- ferent operating conditions: the optimized scheme is more suitable for the working mode with short thermal shock and high frequency, while the design before opti- mization is suitable for the steady-state scenario with high load and long operation. This finding provides a basis for the customized design of the subsequent thermal management strategy, and also suggests that in practical applications, the thermal management structure configuration should be reasonably selected according to the 49 4. Results and discussion vehicle usage mode. 50 5 Conclusion In this study, a systematic thermal management optimisation of a battery electric vehicle (BEV) power inverter is investigated with a focus on improving its transient thermal response. The inverter structure designed in this paper integrates phase change materials (PCMs) and also uses metal foam to exploit the latent heat stor- age properties of the materials. Firstly, this paper constructs a detailed thermal model of the inverter in Comsol and establishes a thermal input model that can dynamically calculate the switching loss and conduction loss of the MOSFET device according to the actual driving conditions in Matlab, which provides a reliable basis for analysing its transient tem- perature rise behaviour. Immediately following this, we explored the combined PCM+MF structure and showed that the system exhibits a significant temperature dr