Study on evolution of key internal and external parameters of lithium-ion power battery under different heat transfer conditions

doi:10.11949/0438-1157.20250655

Abstract

Abstract:

The deep application of lithium-ion batteries and the development trend toward high-capacity and high-energy systems have drawn increasing attention to the performance evolution of batteries under non-uniform heat transfer conditions. In this study, a 20 Ah pouch-type lithium iron phosphate battery was investigated by establishing a three-dimensional electrochemical-thermal coupled model of a single cell, considering 48 parallel electrode layers. The model was used to explore the thermal behavior, electrochemical behavior, and electrochemical characteristics of the cell under varying conditions of heat transfer area, convective heat transfer coefficient, and temperature gradient. The study revealed that under different heat transfer areas, at a 4C discharge rate, the temperature gradient varied significantly under different heat dissipation conditions, with a maximum temperature difference reaching 8.54℃ under certain conditions, and under 10C discharge, the temperature difference reached as high as 30℃. However, the temperature differences between the three heat transfer conditions were relatively small and were less affected by the heat transfer area. When varying the convective heat transfer coefficient, single-sided forced convection can effectively controlled overall temperature rise but exacerbated temperature non-uniformity in the thickness direction. At a 10C discharge rate, the cross-sectional temperature difference could reach 5.05℃, which was 1.64 times that under single-sided natural convection. Under different temperature gradients, the solid-phase lithium concentration at the anode during 10C discharge was 6.1 times that at 1C, and the peak anode overpotential increased by 91%. The research work has revealed the evolution law of the internal behavior of batteries under differential heat exchange conditions, providing a reference for the thermal management and safety design of high-rate and large-capacity batteries.

Key words: lithium-ion batteries, non-uniform heat transfer conditions, electrochemical-thermal model, non-uniformity of electrochemical reactions

摘要：

锂离子电池的深度应用和大容量高能量的研发趋势促使电池在差异性换热条件下的性能演变备受关注。本研究以20 Ah的软包磷酸铁锂电池为对象，建立了考虑48层并联电芯的单体电池三维电化学-热耦合模型，探讨了单体电池在差异性的换热面积、对流传热系数和温度梯度条件下电池内外部的热行为、电行为以及电化学特征。研究发现，不同换热面积时，在4C放电时，不同换热条件下的温度梯度差异较大，其中某些条件下温差可达8.54℃，10C放电时的温差可达30℃，但三种换热条件之间温差相差不大，受换热面积影响较小。在不同传热系数时，单侧强制对流虽能有效控制整体温升，却加剧了厚度方向的温度不均匀性，10C放电时横截面温差可达5.05℃，为单侧自然对流的1.64倍。不同温度梯度时，10C放电时负极固相锂浓度是1C时的6.1倍，负极过电势峰值增加91%。研究工作揭示了差异性换热条件下电池内部行为的演化规律，为高倍率、大容量电池的热管理与安全设计提供了参考。

关键词: 锂离子电池, 差异性换热条件, 电化学-热模型, 电化学反应不均匀性

CLC Number:

TM 912

Xiaofei ZHEN, Leiyu HUANG, Yiming SUN, Jia LIU, Wenjiong CAO, Yan HAN, Ti DONG. Study on evolution of key internal and external parameters of lithium-ion power battery under different heat transfer conditions[J]. CIESC Journal, 2025, 76(12): 6644-6657.

甄箫斐, 黄雷雨, 孙一铭, 刘佳, 曹文炅, 韩燕, 董缇. 差异换热条件下锂离子动力电池内外部关键参数演化研究[J]. 化工学报, 2025, 76(12): 6644-6657.

Figures/Tables 15

Fig.1 Schematic of internal and external structure and discharge principle of lithium-ion battery

Table 1 Electrochemical control equations and energy equations

方程名称	控制方程	边界条件
固相电荷守恒	$∂ ∂ x κ s e f f ∂ ∂ x φ s + ∂ ∂ y κ s e f f ∂ ∂ y φ s + ∂ ∂ z κ s e f f ∂ ∂ z φ s - a s j L i = 0$ $a s = 3 ε s R s$	$- κ n e g e f f ∂ φ s ∂ z z = 0 = κ p o s e f f ∂ φ s ∂ z z = L = I A$ $- κ n e g e f f ∂ φ s ∂ z z = δ n e g = κ p o s e f f ∂ φ s ∂ z z = δ n e g + δ s e p = 0$
液相电荷守恒	$∂ ∂ x κ l e f f ∂ φ l ∂ x + ∂ ∂ y κ l e f f ∂ φ l ∂ y + ∂ ∂ z κ l e f f ∂ φ l ∂ z + ∂ ∂ x κ D e f f ∂ ∂ x c l + ∂ ∂ y κ D e f f ∂ ∂ y c l + ∂ ∂ z κ D e f f ∂ ∂ z c l + a s j L i = 0$	$∂ φ l ∂ z z = 0 = ∂ φ l ∂ z z = L = 0$
固相质量守恒	$∂ c s ∂ t j L i = 1 r 2 ∂ ∂ r D s r 2 ∂ c s ∂ r$	$∂ c s ∂ r r = 0 = 0, D s ∂ c s ∂ r r = R s = - j L i a s F$
液相质量守恒	$∂ ε l c l ∂ t = ∂ ∂ x D l e f f ∂ c l ∂ x + ∂ ∂ y D l e f f ∂ c l ∂ y + ∂ ∂ z D l e f f ∂ c l ∂ z + a s j L i F 1 - t + 0$	$∂ c l ∂ z z = 0 = ∂ c l ∂ z z = L = 0$
电极动力学	$j L i = i 0 e x p α a F R T η - e x p - α c F R T η η = φ s - φ l - U$ $i 0 = F k c l α a c s, m a x - c s, s u r f a c e α a c s, s u r f a c e α c$

Table 1 Electrochemical control equations and energy equations

方程名称	控制方程	边界条件
固相电荷守恒	$∂ ∂ x κ s e f f ∂ ∂ x φ s + ∂ ∂ y κ s e f f ∂ ∂ y φ s + ∂ ∂ z κ s e f f ∂ ∂ z φ s - a s j L i = 0$ $a s = 3 ε s R s$	$- κ n e g e f f ∂ φ s ∂ z z = 0 = κ p o s e f f ∂ φ s ∂ z z = L = I A$ $- κ n e g e f f ∂ φ s ∂ z z = δ n e g = κ p o s e f f ∂ φ s ∂ z z = δ n e g + δ s e p = 0$
液相电荷守恒	$∂ ∂ x κ l e f f ∂ φ l ∂ x + ∂ ∂ y κ l e f f ∂ φ l ∂ y + ∂ ∂ z κ l e f f ∂ φ l ∂ z + ∂ ∂ x κ D e f f ∂ ∂ x c l + ∂ ∂ y κ D e f f ∂ ∂ y c l + ∂ ∂ z κ D e f f ∂ ∂ z c l + a s j L i = 0$	$∂ φ l ∂ z z = 0 = ∂ φ l ∂ z z = L = 0$
固相质量守恒	$∂ c s ∂ t j L i = 1 r 2 ∂ ∂ r D s r 2 ∂ c s ∂ r$	$∂ c s ∂ r r = 0 = 0, D s ∂ c s ∂ r r = R s = - j L i a s F$
液相质量守恒	$∂ ε l c l ∂ t = ∂ ∂ x D l e f f ∂ c l ∂ x + ∂ ∂ y D l e f f ∂ c l ∂ y + ∂ ∂ z D l e f f ∂ c l ∂ z + a s j L i F 1 - t + 0$	$∂ c l ∂ z z = 0 = ∂ c l ∂ z z = L = 0$
电极动力学	$j L i = i 0 e x p α a F R T η - e x p - α c F R T η η = φ s - φ l - U$ $i 0 = F k c l α a c s, m a x - c s, s u r f a c e α a c s, s u r f a c e α c$

Table 2 Control equations of thermal model

方程名称	控制方程	初始条件与边界条件
能量守衡方程	$ρ c p ∂ T ∂ t = ∂ ∂ x λ x ∂ T ∂ x + ∂ ∂ y λ y ∂ T ∂ y + ∂ ∂ z λ z ∂ T ∂ z + q t o l q t o l = q r e a + q a c t + q o h m$	$λ x ∂ T ∂ x x = a = h x A T a m b - T s u r f a c e λ y ∂ T ∂ y y = b = h y A T a m b - T s u r f a c e λ z ∂ T ∂ z z = c = h z A T a m b - T s u r f a c e$ $t = 0; T (x, y, z, t) = T 0$
反应热	$q r e a = a s j L i T ∂ U ∂ T$
极化热	$q a c t = a s j L i η$
欧姆热	$q o h m = κ s e f f ∂ φ s ∂ x 2 + ∂ φ s ∂ y 2 + ∂ φ s ∂ z 2 + κ l e f f ∂ φ l ∂ x 2 + ∂ φ l ∂ y 2 + ∂ φ l ∂ z 2 + κ D e f f ∂ l n c l ∂ x ∂ φ l ∂ x + ∂ l n c l ∂ y ∂ φ l ∂ y + ∂ l n c l ∂ z ∂ φ l ∂ z$

Table 2 Control equations of thermal model

方程名称	控制方程	初始条件与边界条件
能量守衡方程	$ρ c p ∂ T ∂ t = ∂ ∂ x λ x ∂ T ∂ x + ∂ ∂ y λ y ∂ T ∂ y + ∂ ∂ z λ z ∂ T ∂ z + q t o l q t o l = q r e a + q a c t + q o h m$	$λ x ∂ T ∂ x x = a = h x A T a m b - T s u r f a c e λ y ∂ T ∂ y y = b = h y A T a m b - T s u r f a c e λ z ∂ T ∂ z z = c = h z A T a m b - T s u r f a c e$ $t = 0; T (x, y, z, t) = T 0$
反应热	$q r e a = a s j L i T ∂ U ∂ T$
极化热	$q a c t = a s j L i η$
欧姆热	$q o h m = κ s e f f ∂ φ s ∂ x 2 + ∂ φ s ∂ y 2 + ∂ φ s ∂ z 2 + κ l e f f ∂ φ l ∂ x 2 + ∂ φ l ∂ y 2 + ∂ φ l ∂ z 2 + κ D e f f ∂ l n c l ∂ x ∂ φ l ∂ x + ∂ l n c l ∂ y ∂ φ l ∂ y + ∂ l n c l ∂ z ∂ φ l ∂ z$

Table 3 Static parameters for simulation

参数	负集流体	负极	隔膜	正极	正集流体
厚度δ/μm	10^③	46^③	20^③	59^③	19^③
密度ρ/(kg·m^-3)	900^①	1437.4^①	1978^①	1260.2^①	385^①
颗粒半径r/μm	—	7.5^①	—	0.6^①	—
固相体积分数ε_s	—	0.45^④	—	0.47^④	—
孔隙率ε_l	—	0.525^④	0.54^④	0.354^④	—
最大锂离子浓度c_s,max/(mol·m^-3)	—	31370^①	—	22806^①	—
初始SOC	—	0.8^④	—	0.13^④	—
初始电解质浓度c_l_,0/(mol·m^-3)	—	—	1200^①	—	—
固相电导率σ_s/(S·m^-1)	—	100^①	—	0.5^①	—
Bruggeman因子p	—	1.5^①	1.5^①	1.5^①	—
负/正极转移系数α_a_,α_c	—	0.5^①	—	0.5^①	—
比热容c_p /(J·kg^-1·K^-1)	385^①	1437.4^①	1978^①	1260.2^①	900^①
热导率λ/(W·m^-1·K^-1)	400^①	1.04^①	0.334^①	1.48^①	238^①
自然对流传热系数h/(W·m^-2·K^-1)	—	—	5^②	—	—
参考温度T_ref/K	298.15^①	298.15^①	298.15^①	298.15^①	298.15^①

Table 4 Material dynamic parameters

描述	参数	正极表达式	负极表达式
固相扩散系数	D_s	$1.18 × 10 - 18 e x p 3.5 × 104 R 1 298.15 - 1 T$	$3.9 × 10 - 15 e x p 3.5 × 104 R 1 298.15 - 1 T$
反应速率常数	k_i	$1.4 × 10 - 12 e x p 3 × 104 R 1 298.15 - 1 T$	$3 × 10 - 11 e x p 2 × 104 R 1 298.15 - 1 T$
平衡电势	U_ref	$3.4323 - 0.4828 e x p - 80.2493 1 - S O C p o s 1.3198 - 3.2474 × 10 - 6 e x p 20.2645 1 - S O C p o s 3.8003 + 3.2482 × 10 - 6 e x p 20.2646 1 - S O C p o s 3.7995$	$0.6379 + 0.5416 e x p (- 305.5309 S O C n e g) + 0.044 t a n h - S O C n e g - 0.1958 0.1088 - 0.1978 t a n h S O C n e g - 1.0571 0.0854 - 0.6875 t a n h S O C n e g - 0.0117 0.0529 - 0.0175 t a n h S O C n e g - 0.5692 0.0875$
熵热系数	$∂ U ∂ T$	$- 0.3537 a 8 + 1.3902 a 7 - 2.2585 a 5 - 0.98716 a 4 + 0.28857 a 3 - 0.046272 a 2 + 0.0032158 a - 1.9186 × 10 - 5$	$344.1347148 e x p (- 32.9633287 b + 8.316711484) 1 + 749.0756003 e x p (- 34.79099646 b + 8.887143624) - 0.8520278805 b + 0.362299229 b 2 + 0.2698001697$
集流体电导率	σ_cc	$- 3.25 T 3 + 3707 T 2 - 1500000 T + 2.408 × 108$	$- 4.889 T 3 + 5465 T 2 - 21800 T + 3.52 × 108$
液相电导率	κ(c_l,T)	$10 - 4 c l × 1.2544 (- 8.2488 + 0.053248 T - 0.00002987 T 2 + 0.26235 × 0.001 c l - 0.0093063 × 0.001 c l T + 0.000008069 × 0.001 c l T 2 + 0.22002 × 10 - 6 c l 2 - 0.0001765 × 10 - 6 c l 2 T) 2$
液相扩散系数	D_l (c_l,T)	$10 - 4.43 - 54 T - 229 - 5 × 0.001 c l - 0.22 × 0.001 c l - 4$
传递系数	$t + 0$	$2.67 × 10 - 4 e x p 833 T C 1000 + 3.09 × 10 - 3 e x p 653 T C 1000 + 0.517 e x p - 49.6 T$

Table 4 Material dynamic parameters

描述	参数	正极表达式	负极表达式
固相扩散系数	D_s	$1.18 × 10 - 18 e x p 3.5 × 104 R 1 298.15 - 1 T$	$3.9 × 10 - 15 e x p 3.5 × 104 R 1 298.15 - 1 T$
反应速率常数	k_i	$1.4 × 10 - 12 e x p 3 × 104 R 1 298.15 - 1 T$	$3 × 10 - 11 e x p 2 × 104 R 1 298.15 - 1 T$
平衡电势	U_ref	$3.4323 - 0.4828 e x p - 80.2493 1 - S O C p o s 1.3198 - 3.2474 × 10 - 6 e x p 20.2645 1 - S O C p o s 3.8003 + 3.2482 × 10 - 6 e x p 20.2646 1 - S O C p o s 3.7995$	$0.6379 + 0.5416 e x p (- 305.5309 S O C n e g) + 0.044 t a n h - S O C n e g - 0.1958 0.1088 - 0.1978 t a n h S O C n e g - 1.0571 0.0854 - 0.6875 t a n h S O C n e g - 0.0117 0.0529 - 0.0175 t a n h S O C n e g - 0.5692 0.0875$
熵热系数	$∂ U ∂ T$	$- 0.3537 a 8 + 1.3902 a 7 - 2.2585 a 5 - 0.98716 a 4 + 0.28857 a 3 - 0.046272 a 2 + 0.0032158 a - 1.9186 × 10 - 5$	$344.1347148 e x p (- 32.9633287 b + 8.316711484) 1 + 749.0756003 e x p (- 34.79099646 b + 8.887143624) - 0.8520278805 b + 0.362299229 b 2 + 0.2698001697$
集流体电导率	σ_cc	$- 3.25 T 3 + 3707 T 2 - 1500000 T + 2.408 × 108$	$- 4.889 T 3 + 5465 T 2 - 21800 T + 3.52 × 108$
液相电导率	κ(c_l,T)	$10 - 4 c l × 1.2544 (- 8.2488 + 0.053248 T - 0.00002987 T 2 + 0.26235 × 0.001 c l - 0.0093063 × 0.001 c l T + 0.000008069 × 0.001 c l T 2 + 0.22002 × 10 - 6 c l 2 - 0.0001765 × 10 - 6 c l 2 T) 2$
液相扩散系数	D_l (c_l,T)	$10 - 4.43 - 54 T - 229 - 5 × 0.001 c l - 0.22 × 0.001 c l - 4$
传递系数	$t + 0$	$2.67 × 10 - 4 e x p 833 T C 1000 + 3.09 × 10 - 3 e x p 653 T C 1000 + 0.517 e x p - 49.6 T$

Table 5 Basic parameters of LiFePO4 battery

参数	数值
标称容量/Ah	20
标称电压/V	3.3
充电截止电压/V	3.6
放电截止电压/V	2.0
外形尺寸/(mm×mm×mm)	227×160×7.5
质量/g	496

Fig.2 Battery charge-discharge testing platform

Fig.3 Validation results of model voltage and temperature

Fig.4 Schematic diagram of the internal state and operating conditions of the battery

Fig.5 Variation of average temperature of the battery under different heat transfer area conditions

Fig.6 Three-dimensional temperature distribution: (a)—(c) Case1 condition; (d)—(f) Case2 condition; (g)—(i) Case3 condition

Fig.7 Distribution of maximum temperature, minimum temperature, and temperature difference at the end of discharge

Fig.8 Two-dimensional temperature distribution at the middle cross-section in the y-direction at the end of discharge: (a)—(c) Case3 condition; (d)—(f) Case4 condition; (g)—(i) Case5 condition

Fig.9 Solid-phase lithium concentration distribution at the end of discharge: (a)—(c) Case 6 condition; (d)—(f) Case 7 condition; (g)—(i) Case 8 condition (initial values for anode and cathode: 2971.8 and 25096 mol·m-³, respectively)

Fig.10 Anode overpotential distribution at the end of discharge: (a)—(c) Case6 condition; (d)—(f) Case7 condition; (g)—(i) Case8 condition

References 32

[1]	陈国贺, 吕培召, 李孟涵, 等. 锂离子电池热失控传播特性及其抑制策略研究进展[J]. 储能科学与技术, 2024, 13(7): 2470-2482.
	Chen G H, Lyu P Z, Li M H, et al. Research progress on thermal runaway propagation characteristics and suppression strategies of lithium-ion batteries[J]. Energy Storage Science and Technology, 2024, 13(7): 2470-2482.
[2]	李晋, 王青松, 孔得朋, 等. 锂离子电池储能安全评价研究进展[J]. 储能科学与技术, 2023, 12(7): 2282-2301.
	Li J, Wang Q S, Kong D P, et al. Research progress on safety evaluation of lithium-ion battery energy storage[J]. Energy Storage Science and Technology, 2023, 12(7): 2282-2301.
[3]	Ren D S, Liu X, Feng X N, et al. Model-based thermal runaway prediction of lithium-ion batteries from kinetics analysis of cell components[J]. Applied Energy, 2018, 228: 633-644.
[4]	Liao Z W, Lv D Z, Hu Q Y, et al. Review on aging risk assessment and life prediction technology of lithium energy storage batteries[J]. Energies, 2024, 17(15): 3668.
[5]	Dong T, Huang L Y, Liu J, et al. Advances and challenges in obtaining internal temperature for lithium-ion batteries[J]. Journal of Power Sources, 2025, 651: 237571.
[6]	Hollinger A S, McAnallen D R, Brockett M T, et al. Cylindrical lithium-ion structural batteries for drones[J]. International Journal of Energy Research, 2020, 44(1): 560-566.
[7]	Chen Z F, Jia L, Yin L F, et al. A review on thermal management of Li-ion battery: from small-scale battery module to large-scale electrochemical energy storage power station[J]. Journal of Thermal Science, 2025, 34(1): 1-23.
[8]	Wu X G, Du J Y, Guo H Q, et al. Boundary conditions for onboard thermal-management system of a battery pack under ultrafast charging[J]. Energy, 2022, 243: 123075.
[9]	Wang J L, Zhang Y M. Research on cooling characteristics of power battery fast-charging of refrigerant-based direct cooling system[J]. IOP Conference Series: Earth and Environmental Science, 2021, 696(1): 012007.
[10]	Zhang Y, Mei W X, Qin P, et al. Numerical modeling on thermal runaway triggered by local overheating for lithium iron phosphate battery[J]. Applied Thermal Engineering, 2021, 192: 116928.
[11]	Zhou Z Z, Li M Y, Zhou X D, et al. Investigating thermal runaway triggering mechanism of the prismatic lithium iron phosphate battery under thermal abuse[J]. Renewable Energy, 2024, 220: 119674.
[12]	Hu X S, Zheng Y S, Howey D A, et al. Battery warm-up methodologies at subzero temperatures for automotive applications: recent advances and perspectives[J]. Progress in Energy and Combustion Science, 2020, 77: 100806.
[13]	He C X, Yue Q L, Wan S B, et al. Experimental and numerical investigations of liquid cooling plates for pouch lithium-ion batteries considering non-uniform heat generation[J]. Applied Thermal Engineering, 2025, 258: 124777.
[14]	Wu W X, Wu W, Qiu X H, et al. Low-temperature reversible capacity loss and aging mechanism in lithium-ion batteries for different discharge profiles[J]. International Journal of Energy Research, 2019, 43(1): 243-253.
[15]	黄瑞, 汪铭磊, 吴启超, 等. 不同换热环境对电池性能影响的试验研究[J]. 实验室研究与探索, 2022, 41(11): 45-48, 52.
	Huang R, Wang M L, Wu Q C, et al. Experimental study on the influence of different heat transfer environments on battery performance[J]. Research and Exploration in Laboratory, 2022, 41(11): 45-48, 52.
[16]	宋缙华, 丰震河, 郭向飞, 等. 基于多尺度的空间锂离子蓄电池单体电-热耦合模型[J]. 上海航天, 2021, 38(5): 17-24.
	Song J H, Feng Z H, Guo X F, et al. Multi-scale electro-thermal coupled model of space lithium-ion battery cell[J]. Shanghai Aerospace, 2021, 38(5): 17-24.
[17]	Mei W X, Duan Q L, Zhao C P, et al. Three-dimensional layered electrochemical-thermal model for a lithium-ion pouch cell(part Ⅱ): The effect of units number on the performance under adiabatic condition during the discharge[J]. International Journal of Heat and Mass Transfer, 2020, 148: 119082.
[18]	张赛, 汪振毅, 胡世旺. 基于电化学-热-力耦合模型的锂离子电池热失控研究[J]. 安全与环境学报, 2024, 24(2): 551-559.
	Zhang S, Wang Z Y, Hu S W. Study on thermal runaway of lithium-ion batteries based on electrochemical-thermal-mechanical coupled model[J]. Journal of Safety and Environment, 2024, 24(2): 551-559.
[19]	Jiang G W, Zhuang L, Hu Q H, et al. An investigation of heat transfer and capacity fade in a prismatic Li-ion battery based on an electrochemical-thermal coupling model[J]. Applied Thermal Engineering, 2020, 171: 115080.
[20]	孙祺明. 基于电化学-热耦合模型的大容量磷酸铁锂电池热特性分析[D]. 武汉: 武汉理工大学, 2021.
	Sun Q M. Thermal characteristic analysis of large-capacity lithium iron phosphate batteries based on an electrochemical-thermal coupled model[D]. Wuhan: Wuhan University of Technology, 2021.
[21]	Wu X K, Song K F, Zhang X Y, et al. Safety issues in lithium ion batteries: materials and cell design[J]. Frontiers in Energy Research, 2019, 7: 65.
[22]	Sung C, Kim H, Kim C S, et al. Improvement of thermal stability of lithium ion pouch type cell[J]. ECS Meeting Abstracts, 2018, MA2018-01(3): 366.
[23]	Fuller T F, Doyle M, Newman J. Simulation and optimization of the dual lithium ion insertion cell[J]. Journal of the Electrochemical Society, 1994, 141(1): 1-10.
[24]	Doyle M, Newman J. Modeling the performance of rechargeable lithium-based cells: design correlations for limiting cases[J]. Journal of Power Sources, 1995, 54(1): 46-51.
[25]	Doyle M, Fuller T F, Newman J. Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell[J]. Journal of the Electrochemical Society, 1993, 140(6): 1526-1533.
[26]	Azuaje-Berbecí B J, Ertan H B. A model for the prediction of thermal runaway in lithium-ion batteries[J]. Journal of Energy Storage, 2024, 90: 111831.
[27]	陈昊鹏. 锂电池热电耦合特性分析与热行为仿真研究[D]. 长春: 吉林大学, 2023.
	Chen H P. Analysis of thermoelectric coupling characteristics and thermal behavior simulation of lithium batteries[D]. Changchun: Jilin University, 2023.
[28]	Mi J P, Liu X L, Zhu D M, et al. The exploration of the internal homogeneities for a LiFePO₄ pouch lithium-ion battery with a 3D electrochemical-thermal coupled model[J]. Next Energy, 2024, 4: 100127.
[29]	韦雪晴. 动力锂离子电池模组的热特性建模与支撑结构优化设计[D]. 长沙: 中南大学, 2023.
	Wei X Q. Thermal characteristic modeling and support structure optimization design of power lithium-ion battery modules[D]. Changsha: Central South University, 2023.
[30]	Panchal S, Dincer I, Agelin-Chaab M, et al. Transient electrochemical heat transfer modeling and experimental validation of a large sized LiFePO₄/graphite battery[J]. International Journal of Heat and Mass Transfer, 2017, 109: 1239-1251.
[31]	Qian G N, Zan G B, Li J Z, et al. In-device battery failure analysis[J]. Advanced Materials, 2025, 37(10): 2416915.
[32]	孟德超, 马紫峰, 李林森. 锂离子电池介尺度电化学反应非均匀性[J]. 化工进展, 2021, 40(9): 4869-4881.
	Meng D C, Ma Z F, Li L S. Non-uniformity of mesoscale electrochemical reactions in lithium-ion batteries[J]. Chemical Industry and Engineering Progress, 2021, 40(9): 4869-4881.