Thermal Resistance Network Model Research Articles

Numerical and thermal resistance analysis on the cryogenic porous medium heat exchanger with liquid channel

The porous medium heat exchanger has been increasingly utilized in cryogenic applications, especially in the milli-Kelvin region. This study focuses on the porous medium heat exchanger with liquid channel commonly used in the dilution refrigerator and proposes a numerical model, which applies the local thermal non-equilibrium (LTNE) model coupled with N–S equations and Brinkman-Forchheimer model. Comparing with literature results validates the numerical model. By analyzing the heat transfer characteristics of the heat exchanger, a thermal resistance network model is developed to capture the heat transfer mechanism. The results show that the total thermal resistance mainly depends on the fluid conductive thermal resistance and Kapitza thermal resistance inside the porous medium. The fluid conductive thermal resistance dominates at higher temperature while the Kapitza thermal resistance dominates at lower temperature. The expression of critical temperature is derived to determine the priority of reducing thermal resistance. At cryogenic temperatures, the porous medium serves to bypass the significant Kapitza thermal resistance by introducing much lower thermal resistances, while at normal temperatures, the porous medium reduces the overall thermal resistance by incorporating a parallel thermal resistance but without magnitude difference.

Modeling and Simulation of a Gas-Exhaust Design for Battery Thermal Runaway Propagation in a LiFePO4 Module

The release of flammable gases during battery thermal runaway poses a risk of combustion and explosion, endangering personnel safety. The convective and diffusive properties of the gas make it challenging to accurately measure gas state, complicating the assessment of the battery pack exhaust design. In this paper, a thermal resistance network model is established, which is used to calculate the battery thermal runaway propagation. Gas accumulation after thermal runaway venting of a LiFeO4 module is studied using ANSYS Fluent under different venting schemes. The results show that the scheme of battery inversion and simultaneous exhaust from the side and bottom of the module is optimal. The methods and results presented can guide the design of LiFeO4 cell pack runners.

In situ monitoring of flip chip package process using thermal resistance network method and active thermography

Flip chip technology has been used extensively in microelectronic packaging due to the high density, fine spacing, smaller size. However, the size and spacing of the solder bumps are decreasing gradually, defect detection is getting more and more difficult. Thus, the growing demand for high reliability has generated considerable attention on the importance of defect inspection. This paper proposes an in-situ infrared thermography monitoring method with in situ monitoring system bases on modified thermal resistance network model that added the phase transition for the non-destructive analysis of packaging process. The different defects, such as missing bump and pad, missing bump, and bridge are inspected with an accuracy of up to 90 % based on in situ monitoring system. The maximum error between the model and the experiment is 27.6 %, while the minimum error is 13.6 %. The experiment results show that the max temperature of missing bump and pad, missing bump is 35.43 °C and 6.13 °C higher than normal, and the bridge is 0.44 °C lower than normal, respectively. The maximum amplitude by the Fourier transform is used to inspect due to the max temperature of normal and bridge are indiscernible, the results show that the bridge is 4 lower than normal. The model and experimental results show that the in-situ infrared thermography monitoring method is effective for detecting defects in high density electronic devices. The proposed method of in situ monitoring is expected to provide a new strategy for next generation of three-dimensional heterogeneous integrated chips defect inspection.

Parametric optimization of ambient and cryogenic loop heat pipes using multiple linear regression method

In the design and optimization of ambient and cryogenic loop heat pipes (ALHPs and CLHPs), the cost for optimizing every parameter may be very high. Additionally, in cryogenic spacecraft applications, the resources allocated to the thermal control system are very limited. Therefore, it is crucial to identify and optimize the parameters that have a greater impact on the overall performance. In this paper, a thermal resistance network model for LHP was established. The model was validated experimentally using an ethylene-CLHP and by using experimental data of an ammonia-ALHP and a nitrogen-CLHP reported in the literature. The model was then used to comprehensively investigate the impact of boundary and inherent parameters on the operational performance of nitrogen-CLHPs in the 70–110 K temperature range, ethylene-CLHPs in the 150–250 K temperature range, and ammonia-ALHPs in the 250–400 K temperature range. Standardized coefficients were obtained by multiple linear regression to compare the relative importance of the influence of each parameter on the evaporator temperature, serving as an optimization criterion for identifying the most significant parameters for LHP optimization with different working fluids. It was found that most parameters affect the operating performance in the same manner for ALHPs and CLHPs, while the length of wick and compensation chamber had opposite effects on ALHPs and CLHPs. Finally, modified strategies for parameter optimization and design of ALHP and CLHP were proposed and an optimization case for an ethylene-CLHP was presented.

Numerical investigation on thermal behavior of high temperature heat pipe based on thermal resistance network model

High-temperature heat pipes are often used as heat exchangers in nuclear reactors because of their remarkable advantages in terms of thermal conductivity, isothermal properties, and self-actuation. To ensure the safe operation and efficient heat transfer of a reactor system, it is necessary to analyze the transient heat transfer performances of heat pipes. The working temperature range of the high-temperature heat pipe is 800–1,300 K when sodium is selected as the working fluid. A network system consisting of the thermal resistances can be used to analyze heat pipe transients. For a high-temperature thermosiphon, the existence of a liquid pool and a liquid film will affect the overall thermal resistance and temperature distribution. In this paper, a thermal resistance network model including convection and phase changes was established, a linear differential equation was established based on the energy conservation equation, and code was developed based on this differential equation to solve the thermal resistance and temperature field equations of the heat pipe. It was found that the temperature of numerical calculation in each region was in good agreement with the experimental results. To simulate a complex reactor environment, a power wave was introduced to explore the influence of the heat source on the thermal resistance and temperature field. It is found that with the increase of heating power, the temperature of each region of the heat pipe also increases, and the time required for the heat pipe to reach equilibrium decreases. In addition, the variations of the thermal resistance and temperature field with different heat pipe sizes and cooling modes at the condensation section under variable-power conditions were explored.

Thermal resistance capacity model for the cold release characteristics of cemented paste backfill with phase change materials

A new method based on thermal resistance and capacity (RC) network model for fast predicting cold release characteristics of the cemented paste backfill with phase change materials is developed. The simplified heat transfer calculation model was established, and temperature variation was calculated by MATLAB. The RC model and program were validated by experimental results and numerical heat transfer simulations. Based on the verified RC model, the influence law of the initial ice-water ratio and slurry concentration were analyzed. With the increase of initial ice-water ratio and the decrease of slurry concentration, the cooling ability was enhanced and the cold release process was extended. Furthermore, the cemented paste backfill with ice and paraffin were compared. The cooling release effect of slurry containing ice grains was better than that of slurry containing paraffin throughout the melting process. Compared with the numerical heat transfer simulation method, RC model can effectively improve the calculation efficiency under the premise of satisfying the accuracy. This study is of great significance in providing a timely forecast of the cold release characteristics of the cemented paste backfill with phase change materials in engineering design and practice.

Multi-objective optimization of thermal modules in high heat flux laptops

The thermal module, as an important cooling pathway for chips, is a major factor affecting the performance of laptops. However, thermal analysis and optimization of the whole thermal module of a laptop is absent. Moreover, cost is also a major consideration in the design of a laptop’s thermal module. In this study, based on the thermal module of a high heat flux prototype laptop, we constructed an efficient thermal resistance network model and a cost model to evaluate the impact of different components. Furthermore, we employed NSGA-II (non-dominated sorting genetic algorithm II) to enhance the thermal module's heat dissipation capacity while minimizing cost. By obtaining Pareto solutions that provided optimal thermal resistances for the components in the thermal module, we then utilized LINMAP (linear programming technique for multidimensional analysis of preference) as a decision-making method to determine the best compromise solution. The best compromise solution focuses on reducing the thermal resistances of the thermal interface material on the high heat flux APU side, the shared heat pipe, and heatsinks to enhance the heat dissipation capacity of the thermal module. To control cost, sacrifices were made in the heat transfer performances of the thermal interface material on the GPU side and the independent heat pipes. Comparing the best compromise solution with the prototype, the cooling capacity is improved by 24% and cost is reduced by 9%. The efficient model coupled with optimization method may provide a new theoretical guideline for the laptop designers.

Experimental study on the thermal performance of a liquid-cooled heat sink integrating heat pipes for dual CPU servers

The increasing power consumption of server CPUs poses a challenge for data center cooling. In this work, a liquid-cooled heat pipe heat sink (LHPHS) with compactly arranged heat pipes is designed and fabricated for CPU cooling in dual CPU servers. Water is selected as the working fluid in the heat pipes. Experiments are conducted to explore the heat dissipation potential of LHPHS under high inlet coolant temperature and high heat load conditions, and to investigate the operational stability of LHPHS under the conditions of uneven heat generation between two CPUs. Furthermore, a one-dimensional thermal resistance network and numerical model of the LHPHS are established to quantitatively analyze the thermal resistance distribution of LHPHS and the variation of thermal resistance with coolant flow rate. The results show that, firstly, the LHPHS operates stably under high inlet coolant temperature and high heat load conditions, meeting the heat dissipation requirements of up to 37.5 W/cm2 with a coolant flow rate of 1 L/min and inlet coolant temperature of 35℃. Secondly, the LHPHS exhibits excellent performance in controlling temperature difference between CPUs and even when there is discrepant heat generation between them. Thirdly, the LHPHS performs a low thermal resistance, measuring 0.044 ℃/W at a coolant flow rate of 0.5 L/min, and this resistance further decreases as the flow rate increases. Additionally, it is observed that the thermal resistance of the liquid-cooled plate decreases with the increasing flow rate, and heat transfer within the heat pipes becomes a critical aspect under high coolant flow rates. Therefore, reducing the thermal resistance of the heat pipe is crucial for the thermal performance improvement of the LHPHS.

Study on the effect of carbon fiber ply angle on thermal response of CFRP laminate based on the thermal resistance network model

AbstractCarbon fiber reinforced polymer (CFRP) exhibits different heat transfer phenomena along the fiber direction and the transverse direction during the heat transfer process due to its anisotropic thermo‐physical properties, which makes it difficult to quantitatively analyze the overall thermal performance of CFRP with different ply angles. A thermal resistance network model of composite material considering fiber ply angle and heat transfer direction was developed based on the series–parallel resistance computing method, and it was applied to describe the test results measured by the thermal response tests of unidirectional carbon fiber laminates. Thermal resistance Rx along the heat transfer direction and Ry transverse to the heat transfer direction calculated by the proposed model, which are related with the thermal response of the specimen, can be utilized to reflect the temperature values and temperature distribution maps. It was found that as the fiber ply angle θ increases from 0° to 45°, thermal resistance in the x‐axis direction increases from about 0.13 K/W to 2.56 K/W, while thermal resistance in the y‐axis direction decreases about 48.7%. As a result, major axis of quasi‐ellipse temperature profile changes by about +45° relative to the x‐axis.Highlights A CFRP thermal resistance network model considering ply angle was proposed. The series–parallel thermal resistance method is used to calculate Rx and Ry. The ply angle from 0° to 45°, Rx increases several times and Ry decreases by half. Major axis of elliptic temperature curve changes by +45° relative to the x‐axis.

Analytical thermal resistance network model for calculating each mean die temperature of the multi-chips module combined with quad flat no-leads packaging

With the rapid advancement of next-generation communication technology, traditional Quad Flat No-leads (QFN) packaging is facing challenges to meet functional requirements. Due to its high integration and excellent thermal performance, the Multi-chips Module combined with Quad Flat No-leads (MCM-QFN) packaging is gaining popularity. However, the structural complexity of MCM-QFN packaging and the thermal coupling effect between multiple dies make it challenging to analyze the steady-state thermal distribution of MCM-QFN packaging, which is necessary for assessing the reliability and optimizing the layout design of the multi-chips module. By analyzing the heat dissipation path from each die to the ambient, this paper proposes an analytical thermal resistance network model for calculating each mean die temperature of MCM-QFN packaging. The thermal coupling effect among the multi-chips, the thermal spreading resistance between critical layers, and the boundary conditions and cooling conditions are all considered. All thermal resistances in the model are expressed analytically, and the mean temperature of each chip can be calculated within 0.1 s using MATLAB programming. To validate the accuracy of the proposed model, finite element method (FEM) simulations are conducted to provide a reference for the mean temperature of each chip under four sets of thermal conditions. The data comparison demonstrates that the analytical model is fast and accurate in calculating each mean die temperature of MCM-QFN packaging, with a maximum error of 3.72%, and the calculation speed increased by about 600× compared to that of FEM simulation. Furthermore, the analytical model is able to offer a direction for optimizing the layout design and material selection of MCM-QFN packaging.

Optimization analysis of multi-layered microchannel heat sink

Microchannel heat sinks with a large specific surface area are widely applied to the heat dissipation of microelectronic devices. In this work, a multi-layered microchannel heat sink with a size of was proposed based on the microchannel of the Printed Circuit Heat Exchanger (PCHE). The thermal resistance network model was established for the multi-layered heat sink with a semi-circular cross-section microchannel. Then, the Genetic Algorithm(GA) was employed to optimize the structure and operation parameters of the heat sink based on the thermal resistance network model. The optimized parameters and the corresponding thermal resistance under various power consumption were obtained. The optimization results show that the thermal resistance decreases rapidly with the increase of power consumption. When the power consumption is large, the trend of thermal resistance reduction is gradually flat. When the power consumption increases to 0.8 W, the optimal value of channel layers is up to 12, and the thermal resistance of the heat sink is 0.322 °C/(W/cm2). As the power consumption further increases from 0.8 W, the optimal value of layers remains constant at 12, and the ratio of the channel radius to the plate thickness remains at about 0.56. Three-dimensional numerical simulation is performed to verify the thermal resistance network model, and the results of the thermal network model agree well with the simulation.

Low cost energy-efficient preheating of battery module integrated with air cooling based on a heat spreader plate

Integration of heating and cooling functions has aroused increasing interest for the automotive battery modules. The proposed cylindrical 18650 battery module is equipped with an external sleeved spreader plate (SHSP), which features low thermal resistance and a large exchange area as an efficient heat transfer medium. The transient temperature characteristics of the battery module were experimentally investigated in both cooling mode and heating mode, respectively. In cooling mode, the temperature characteristics of the battery module equipped with SHSP were examined. With an inlet velocity of 1 m/s and a discharge rate of 3 C, the temperature rise and temperature difference are only 12.9 °C and 2.83 °C at an ambient temperature of 25 °C, respectively. In heating mode, the heat-up characteristics of the battery module were experimentally examined at a subzero temperature of −20 °C under three different heating protocols: continuous heating, fast-rest-slow heating, and slow-rest-fast heating. Immune from potential effects on the battery internal degradation, the heating rate of the battery module in a continuous heating protocol could reach 6.98 °C/min with a heating efficiency of 69.8%, which outperforms the existing external heating modes.Additionally, the fast-rest-slow heating protocol has clear-cut advantages in terms of heating rate while maintaining a smaller temperature difference during the heating phase. Finally, a simplified thermal resistance network model for the cell is established based on the analysis of the one-dimensional steady state heat transfer. According to projections, the thermal resistance of the present heating model is 2.03 K/W, which is less than the hot air convection heating model by 5.24 K/W. The proposed method exhibits excellent performance and provides a low-cost, highly efficient design solution for the battery module under varying conditions.

Improving the Sierpinski carpet model arithmetic to accurately predict the thermal conductivity of fatty acid/carbon composite phase-change materials

The effective thermal conductivity is an important physical parameter of composite phase-change materials (PCMs). In this study, a new analytic expression of the dimensionless thermal conductivity is proposed to predict the dimensionless thermal conductivity of fatty acid–carbon materials composite PCMs based on the Sierpinski carpet model and the thermal resistance network model of a fractal geometry combined with the principle of the weighted average. The new analytical expression can be used to overcome the issue of the predicted values deviating considerably from the experimental results when the fractal series n is too small. At the same time, an accurate solution for the dimensionless ratio (t+) of the width of the carbon materials to the side length of the Sierpinski carpet is presented. Compared with the general solution algorithm proposed by Song, the commonly used quadratic parallel (QP) prediction model, and the Maxwell–Eucken model, this algorithm is more reliable. The proposed prediction model can be used to predict the effective thermal conductivity of fatty acid–carbon materials.

Realizing the Accurate Measurements of Thermal Conductivity over a Wide Range by Scanning Thermal Microscopy Combined with Quantitative Prediction of Thermal Contact Resistance.

Quantitative thermal performance measurements and thermal management at the micro-/nano scale are becoming increasingly important as the size of electronic components shrinks. Scanning thermal microscopy (SThM) is an emerging method with high spatial resolution that accurately reflects changes in local thermal signals based on a thermally sensitive probe. However, because of the unclear thermal resistance at the probe-sample interface, quantitative characterization of thermal conductivity for different kinds of materials still remains limited. In this paper, the heat transfer process considering the thermal contact resistance between the probe and sample surface is analyzed using finite element simulation and thermal resistance network model. On this basis, a mathematical empirical function is developed applicable to a variety of material systems, which depicts the relationship between the thermal conductivity of the sample and the probe temperature. The proposed model is verified by measuring ten materials with a wide thermal conductivity range, and then further validated by two materials with unknown thermal conductivity. In conclusion, this work provides the prospect of achieving quantitative characterization of thermal conductivity over a wide range and further enables the mapping of local thermal conductivity to microstructures or phases of materials.

Numerical modelling and heat transfer optimization of large-scale multi-tubular metal hydride reactors

Heat management during the absorption/desorption process is a key aspect in improving the performance of large-scale hydrogen storage systems. In this article, the absorption and desorption performance of a multi-tubular hydride reactor is numerically investigated and optimized for 60 kg mass of LaNi5 alloy. The 90% absorption with 7, 14, and 19 tubes is achieved in 985, 404, and 317 s with an overall reactor weight of 78.46, 88, and 88.2 kg, respectively. The 14-tube reactor performance is investigated by introducing the longitudinal fins inside the tubes. The reactor performance is enhanced by allocating fins into different pairs of half and full fins constrained by overall fin volume. A thermal resistance network model is presented to investigate the effect of fin distribution and coolant velocity on equivalent resistance of the metal hydride reactor. Storage performance obtained from numerical model validates the thermal resistance analysis from heat transfer viewpoint. With six full fins, 90% hydrogen absorption is achieved in 76 s. However, tubes with 6, 8, and 12 pairs of half and full fins require 74, 58, and 54 s, respectively. The 14-tube reactor with 8 pairs of half and full fins is used for quantifying the augmentation in the absorption performance in response to operating conditions (supply pressure and heat transfer fluid temperature). A design methodology is outlined for the development of a large-scale multi-tubular hydride reactor based on a heat transfer optimization strategy.

Experimental study and numerical analysis of vacuum thermal characteristics of brush DC motor

Brush direct current (DC) motors have several qualities that make them very attractive for space flight applications. Considering the high reliability requirements of aerospace missions, the thermal characteristics and thermal failure of the brush DC motor in the space environment were studied. Using a motor thermal resistance network model, a special thermal test method was determined and combined with a thermal conductivity analysis model, the thermal parameters were obtained via item-by-item stripping, and the motor temperature field was constructed. By introducing the arc discharge factor to evaluate the electric-corrosion heat consumption, the numerical analysis results were in good agreement with the test results under the conditions of stalled rotor, normal rotation, single brush, and multiple brushes. The analysis and test results show that continuous operation for 110 s will lead to melting of the brush solder joints, and electrical corrosion heat consumption is one of the main factors that cannot be ignored. The reliability model of vacuum applications should be established in the normal working mode of at least two brushes in both the positive and negative electrodes. To improve the reliability, a sealed air-filled structure of the motor was proposed, a heat-flow co-simulation model of a continuous medium flow with a large curvature and constant without a gravity field was established, and the temperature and velocity fields under different sealed pressures were obtained. The results show that the temperature of the single brush reduced to below 140 °C from 204.5 °C in vacuum, which can meet the long-term continuous working requirement of high reliability of brush motors in space missions. In addition, it was found that with the decrease in pressure, the effect of convective heat transfer gradually weakens, the temperature gradually increases and converges to the unique heat conduction process of the gas, while the effect of convection is negligible. As the pressure continues to decrease, the sealed gas evolves from continuous medium flow to transitional and free molecular flow, and the heat conduction effect of the gas weakens again until it approaches the singleness solid conduction process.

Thermal modeling and analysis of 3-D integrated circuits with irregular structure

Considering the manufacturing and packaging process, 3-D integrated circuits design often requires irregular chip structures. The 3-D integrated circuits with irregular structures can facilitate differentiated chip design and reduce manufac?turing costs. Highly complex through-silicon vias have not been considered in past thermal modelling and analysis of irregularly structured 3-D integrated circuits. Thus, a detailed model of a three-layer irregularly structured 3-D integrated circuit with through-silicon vias and microbumps is developed, and an analytical method based on the thermal resistance network model is proposed to extract the equiv?alent thermal conductivity of through-silicon vias and microbumps, the accuracy of which is verified by a 3-D finite element simulation method. The results show that the maximum temperature and temperature gradient obtained by the equivalent model simulations agree well with the detailed model results, proving the validity of the equivalent model. To save the computational cost, the effects of heat source area, power setting and through-silicon vias structure parameters on the maximum temperature are studied by numerical simulation method based on the equivalent model. Heat source area equal to the overlap between chip layers, high power chips close to the heat sink, and reducing through-silicon vias pitch can better reduce the maximum temperature. The results provide a reference value for thermal design and optimization of 3-D integrated circuits with irregular structures.

The Electrical and Thermal Characteristics of Stacked GaN MISHEMT.

To study the working performance of 3D stacked chips, a double-layer stacked GaN MISHEMTs structure was designed to study the electro-thermal characteristics and heat transfer process of stacked chips. Firstly, the electrical characteristics of double-layer and single-layer GaN MISHEMTs are compared at room temperature. Under the same conditions, the output current of double-layer GaN MISHEMTs is twice that of single-layer GaN MISHEMTs, but its off-state current is much higher than that of a single-layer device. Meanwhile, there is no significant difference between the threshold voltages of the double-layer and single-layer GaN MISHEMTs. Then, the effect of temperature on the electrical characteristics of double-layer GaN MISHEMTs is also investigated. When the temperature increased from room temperature to 150 °C, the device's threshold voltage gradually shifted negatively, the output current of the device decreased, and the off-state current of the device increased. Furthermore, a thermal resistance network model has been established to analyze the thermal characteristics of the stacked GaN MISHEMTs. The relative error between the results calculated according to the model and the experimental results does not exceed 4.26%, which verified the correctness and accuracy of the presented model to predict the temperature distribution of the stacked GaN MISHEMTs.

Thermal-mechanical dynamic interaction in high-speed motorized spindle considering nonlinear vibration

The neglection of thermal-mechanical interaction of the high-speed motorized spindle system may lead to modeling errors of thermal and dynamic characteristics. In this work, the thermal-mechanical interaction mechanism is analyzed, and a closed-loop iterative modeling method for thermal and dynamical characteristics is proposed to improve the modeling accuracy. The nonlinear dynamic model with thermal effects of the spindle system under unbalanced magnetic pull and unbalanced mass excitation is established to evaluate its transient dynamic behavior. A multi-node thermal resistance network model of the motorized spindle system considering the nonlinear vibration of the spindle system is established to evaluate transient thermal behavior. Based on the load-displacement relationship, the nonlinear stiffness and restoring force model of bearing considering thermal effects and nonlinear vibration is established. The heat generation of the bearing and the built-in motor are calculated by Palmgren's formula and the equivalent circuit model of the induction motor, respectively. The bearing heating is improved considering the comprehensive effects of lubricant viscosity change, bearing thermal expansion, and nonlinear dynamic load. The mechanical power loss of the motorized spindle is analyzed to calculate the electrical parameters required to study the spindle dynamics and motor heat generation. The accuracy and effectiveness of the proposed theoretical method are experimentally verified. Numerical simulations show that the thermal and mechanical effects in the motorized spindle system exhibit a non-negligible dynamic interaction.

An electrochemical-thermal coupling model for prismatic lithium-ion batteries over wide temperature range

Accurate and rapid prediction of battery thermal behavior can provide accurate basis for making battery use plan, which is beneficial for alleviating the influence of thermal effect on battery life and safety. A fast numerical solution method of electrochemical-thermal coupling model for prismatic lithium-ion batteries is proposed in this work. Firstly, based on an existing electrochemical single particle model and one-dimensional thermal resistance network, analytical expression of thermal resistance network model in two-dimensional space is obtained by theoretical formula derivation. Then, to calibrate the model parameters at different temperatures, temperature range is divided into several intervals, and optimal parameter sets at different intervals are obtained by excitation response analysis method and multi-group particle swarm optimization algorithm. Finally, to realize the accurate numerical simulation of the model, a double adaptive extended Kalman filter method is applied to further optimize the parameters in real time. Seen from the simulation results over wide temperature range, mean absolute errors of voltage and temperature are less than 30 mV and 0.12 K at −5–55 °C respectively, which indicates the capability of the developed model for high-precision numerical simulation over temperature range for prismatic lithium-ion batteries.