Electrochemical-thermal coupled models represent a critical advancement in battery simulation, enabling the analysis of interdependent electrochemical processes and thermal behavior. These models integrate heat generation mechanisms from electrochemical reactions with thermal transport phenomena, providing a comprehensive framework for predicting battery performance under thermal stress. The coupling of these domains addresses the fundamental challenge that electrochemical processes affect temperature distributions, while temperature variations simultaneously influence electrochemical kinetics and transport properties.
The foundation of these models lies in capturing the primary heat generation sources within a battery cell. Joule heating, resulting from ionic and electronic resistances, constitutes a significant contributor. The heat generation rate from Joule heating can be quantified through the potential gradients and current distributions in both the electrolyte and electrodes. Entropic heat, arising from reversible electrochemical reactions, depends on the entropy change of the reaction and the operating current. The sum of these effects, along with additional contributions from side reactions and phase transformations, determines the total heat generation rate, which drives the thermal response of the system.
Multi-domain coupling methods resolve the bidirectional interactions between electrochemical and thermal phenomena. Newman’s pseudo-two-dimensional (P2D) model, originally developed for standalone electrochemical analysis, has been extended to incorporate thermal coupling. In this framework, the electrochemical model solves for lithium concentration in solid and electrolyte phases, potential distributions, and reaction rates, while the thermal model computes the temperature field based on the heat generation terms derived from electrochemical processes. The coupling occurs through temperature-dependent parameters such as ionic conductivity, diffusivity, and reaction rate constants, which are updated iteratively as the temperature evolves.
One widely adopted approach involves solving the electrochemical and thermal domains in a segregated manner, where the two systems are solved sequentially within each time step. The electrochemical model first computes the reaction rates and heat sources, which are then passed to the thermal model to update the temperature distribution. The updated temperature values feed back into the electrochemical model for the next iteration. This method balances computational efficiency with accuracy, though it requires careful handling of the coupling terms to ensure stability.
More advanced implementations employ fully coupled schemes, where the electrochemical and thermal equations are solved simultaneously. These approaches eliminate the lag between domain updates, improving accuracy for scenarios with strong nonlinearities or rapid transients. However, they demand greater computational resources due to the increased complexity of the combined equation system. Numerical techniques such as finite element or finite volume discretization are commonly applied to solve the coupled partial differential equations, with appropriate linearization strategies to handle nonlinear terms.
The thermal transport component typically includes conduction within the cell layers, convection at the boundaries, and sometimes radiation effects for high-temperature applications. The thermal properties of each component, such as the anisotropic thermal conductivity of layered electrodes, must be accurately represented. Cooling conditions, whether passive or active, significantly influence the temperature distribution and must be incorporated into the boundary conditions. The interplay between internal heat generation and external cooling dictates the peak temperatures and gradients that develop during operation.
Validating these models requires experimental data encompassing both electrochemical performance and thermal measurements. Infrared thermography, embedded thermocouples, and calorimetry provide spatially resolved temperature data under various operating conditions. Comparisons between simulated and measured voltage responses under thermal stress further confirm the model's predictive capability. Discrepancies often highlight gaps in material property data or oversimplifications in the coupling mechanisms, guiding refinements to the model.
Practical applications of electrochemical-thermal coupled models include optimizing fast-charging protocols, where excessive heat generation can accelerate degradation or trigger safety hazards. By simulating different current profiles, the models identify conditions that balance charging speed with temperature rise. Similarly, they aid in designing thermal management systems by evaluating the effectiveness of cooling strategies under realistic operating scenarios. In extreme environments, such as high or low ambient temperatures, the models predict how performance limitations arise from the coupled electrochemical-thermal behavior.
Extensions to Newman’s model have incorporated additional physical phenomena to enhance accuracy. For example, some implementations include mechanical effects, where thermal expansion and stress influence porosity and tortuosity, thereby modifying transport properties. Others integrate degradation mechanisms, linking temperature-dependent side reactions to capacity fade. These comprehensive models enable virtual prototyping of batteries, reducing the need for extensive experimental testing during development.
The choice of model fidelity depends on the application requirements. Lumped thermal models, assuming uniform temperature, suffice for small cells or low-rate operations where spatial gradients are negligible. For large-format cells or high-power applications, distributed thermal models with three-dimensional resolution become necessary to capture localized heating effects. Reduced-order electrochemical models, such as single-particle approximations, can be coupled with detailed thermal models to strike a balance between computational cost and predictive power.
Challenges remain in improving the parameterization of these models, particularly for temperature-dependent properties across wide ranges. The inherent variability in material properties due to manufacturing tolerances also complicates precise predictions. Future advancements may leverage high-throughput characterization and machine learning to refine property databases and enhance model adaptability.
Electrochemical-thermal coupled models have become indispensable tools for battery design, operation, and safety assessment. By rigorously integrating heat generation and transport with electrochemical processes, they provide insights that standalone models cannot achieve. Their continued development will support the creation of batteries that are not only higher-performing but also safer and more durable under diverse operating conditions.