Battery thermal management for high power applications such as electrical vehicle (EV) or hybrid electrical vehicle (HEV) is crucial. Modeling is an indispensable tool to help engineers design better battery cooling systems. While computational fluid dynamics (CFD) has been used quite successfully for battery thermal management, CFD models can be too large and too slow for repeated transient thermal analysis, especially for a battery module or pack. A state space model based on CFD results can be used to replace the original CFD model. The state space model runs approximately two orders of magnitude faster and yet under some conditions obtains equivalent results as the original CFD model. The state space model is based on linear and time-invariant (LTI) system theory. The main limitation of the method is that the method applies strictly speaking to systems that satisfy both linearity and time invariance conditions. General battery cooling problems unfortunately do not strictly satisfy those two conditions. This paper examines quantitatively the amount of error involved if these two conditions are not met. It turns out that these conditions can be relaxed in some ways while preserving satisfactory results for non-linear and time-varying battery thermal systems. This paper also discusses non-linear curve fitting needed for the method.

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