The core challenge the researchers confronted is one of boundary characterization. Every battery thermal model depends on assumptions about how heat leaves the cell’s surface, and at sea level those assumptions are well rehearsed. Air density, dynamic viscosity, and thermal conductivity are treated as constants or simple functions of temperature, and convective heat-transfer coefficients follow familiar correlations. But when atmospheric pressure drops from 100 kilopascals to 50 kilopascals, the air density falls by roughly half, and the viscosity and thermal conductivity of the gas shift in ways described by Sutherland’s law and related temperature-correction formulations. A simulation that ignores these corrections will systematically misjudge how effectively the surrounding air can carry heat away from the cell, and the error compounds at higher discharge rates when more heat is being generated in the first place.

To build a model adequate to this environment, the team anchored their electrochemical description in the Newman–Tiedemann–Gu–Kim, or NTGK, framework, a semi-empirical approach that represents the battery through parameters related to the equilibrium potential and the equivalent conductance of the cell. The NTGK model is prized in battery engineering because it captures the essential electrochemistry without the computational burden of full porous-electrode theory, making it practical for the multi-scale multi-domain simulations needed to resolve temperature fields across an entire cell. The researchers embedded this electrochemical core within a coupled thermal-fluid simulation, and then made the crucial modification: at the convective heat-transfer boundary, they corrected the air density and viscosity for the actual ambient pressure and temperature, so that the fluid exchanging heat with the battery behaved like the thin air it truly was.

Validation came from experiment. The team compared their simulation predictions against measured battery surface temperatures and found an absolute error of less than 1.5 kelvin and a relative error of less than 5 percent in predicting the maximum surface temperature. The simulated temperature-rise trends tracked the experimental curves closely across the tested conditions. In a field where thermal models of batteries under nonstandard atmospheres often carry uncertainties several times larger, this level of agreement matters. It means engineers can now trust the model’s output when designing thermal management systems for aircraft battery packs or high-altitude installations, rather than treating the simulations as rough qualitative guides requiring extensive physical retesting.

The quantitative findings carry a message that is both reassuring and cautionary. Under identical atmospheric pressure, when the discharge rate increased from 0.5C to 2C, the battery’s temperature rise grew by 7.42 to 8.21 kelvin. That is a substantial thermal penalty for pushing a cell harder, and it confirms that discharge rate is the dominant lever on battery thermal response. By contrast, under the same discharge rate, when atmospheric pressure fell from 100 to 50 kilopascals, the overall battery temperature increased by only 0.49 to 1.37 kelvin. The effect of halving the ambient pressure is real but modest, roughly an order of magnitude smaller than the effect of quadrupling the discharge current.

Perhaps more intriguing is what the pressure change did not do. The temperature difference between the interior and exterior of the battery remained essentially constant at approximately 1.5 kelvin across the tested pressures, showing minimal impact from the reduced atmosphere. This is a technically significant observation. It suggests that low pressure does not dramatically alter the internal thermal gradients within the cell, which are governed mainly by the cell’s own thermal conductivity and the distribution of heat generation. Instead, the primary mechanism by which reduced pressure harms battery thermal performance is external: thinner air convects heat away less effectively, so heat accumulates at the surface and the whole cell runs slightly hotter, but the interior-to-surface temperature difference stays largely intact.

The physics behind this asymmetry is worth unpacking. Convective heat transfer at a battery surface scales with the properties of the boundary-layer air, and as density decreases, the mass flow of air available to absorb and transport heat diminishes even if the flow velocity is unchanged. The specific heat capacity per unit volume of the air drops in proportion to its density, so each cubic meter of thin air carries away less thermal energy than the same volume at sea level. Meanwhile, the heat generated inside the cell, which the NTGK model partitions into irreversible contributions from electrochemical resistance and reversible contributions from entropy change, depends on the discharge current and the cell’s state of charge, not on the ambient pressure. Discharge rate therefore controls the heat input directly, while pressure controls only the efficiency of heat rejection, which explains why the former dominates the thermal response.

For the emerging field of electric aviation, these results arrive at a critical moment. Battery thermal runaway hazards at cruise altitudes have become a focus of intense research, with prior studies documenting how cylindrical and pouch cells behave under the low pressures typical of civil aircraft flight, and how thermal runaway propagates differently in modules at reduced ambient pressure. The new work complements that hazard-focused literature by providing a validated predictive tool for normal operating conditions, the regime in which thermal management systems must function every flight. A designer of an air-cooled battery pack for an electric aircraft can now use the corrected convective boundary conditions to estimate how much extra temperature margin is needed at altitude, and the answer, according to this study, is on the order of one kelvin per halving of pressure at moderate discharge rates, a manageable but non-negligible correction.

The study also speaks to a broader methodological debate in battery modeling. Computational fluid dynamics approaches to battery thermal management have proliferated, covering pouch cells, prismatic cells, and full modules with liquid cooling and phase-change materials. But many of these studies implicitly assume sea-level atmospheres, and the authors’ demonstration that pressure-corrected air properties must enter the convective boundary to achieve sub-1.5-kelvin accuracy is a warning that extends well beyond low-pressure applications. Any simulation of an air-cooled battery system operating in a hot, dry climate, at elevation, or inside a pressurized cabin with altered air composition should apply the same rigor to its boundary conditions. The framework’s modular structure, combining the NTGK electrochemical core with corrected fluid properties, makes such extensions straightforward.

Funded by the National Natural Science Foundation of China and the Natural Science Foundation of Hunan Province, the work from the Hunan University of Technology and its collaborators provides a quantitative foundation for a question that has lingered as batteries have taken to the skies. The takeaway is crisp: if you want to keep a lithium-ion battery cool, the discharge rate you demand from it matters far more than the altitude at which you fly it, but thin air will quietly erode your cooling margin, and now you can calculate exactly by how much. As electric aircraft move from prototypes to passenger service, models like this one, validated against experiment and honest about their boundary conditions, will be part of the safety case that makes that transition possible.

Subject of Research: Thermal behavior and convective heat-transfer modeling of lithium-ion batteries under low-pressure conditions

Article Title: Convective heat-transfer boundary characterization and numerical simulation of lithium-ion batteries under low-pressure conditions

Article References: Zhang, Y., Huang, Z., Liu, S., Jiang, Y., & Shen, S. (2026). Convective heat-transfer boundary characterization and numerical simulation of lithium-ion batteries under low-pressure conditions. Ionics. https://doi.org/10.1007/s11581-026-07553-5

Image Credits: AI Generated

DOI: 10.1007/s11581-026-07553-5

Keywords: lithium-ion batteries, low pressure, convective heat transfer, NTGK model, multiphysics simulation, thermal management, electric aircraft, discharge rate, air density, battery temperature, numerical simulation, heat dissipation