Dimensionless-index framework for delayed cooling coordination in PCM–liquid hybrid battery thermal management over wide ambient temperatures

Hybrid battery thermal management systems (H-BTMSs) that combine composite phase change materials (CPCMs) with liquid cooling can reduce auxiliary energy consumption, but the effectiveness of delayed cooling depends strongly on ambient temperature, PCM melting-point matching, and discharge rate. Here, experiments were conducted on a compact 20-cell 18,650 lithium-ion battery module with 3 mm cell spacing using three CPCMs, namely C18-CPCM, C20-CPCM, and C22-CPCM, based on n-octadecane, n-eicosane, and n-docosane, respectively, over ambient temperatures of 15-45 °C and multiple discharge rates. Clear climate-matched PCM selections were identified: C18-CPCM performs best in temperate conditions (15-25 °C), C20-CPCM in subtropical conditions (25-35 °C), and C22-CPCM in tropical conditions (35-45 °C). Delayed liquid-cooling activation can maintain safe module temperatures while significantly reducing pump energy, although the admissible delay decreases as ambient temperature rises. To generalize the experimental observations, a control-oriented three-node grey-box thermal model of the cell-PCM-cooling-tube assembly was developed and validated against 212 experimental cycles, yielding an overall RMSE of 1.7 °C and R2 of 0.96. Based on this model, three dimensionless indicators—melting proximity index (MPI), latent endurance number (LEN), and passive feasibility ratio (PFR)—together with the latest safe pump-on time (LSPT), were proposed to quantify melting-point matching, latent-heat sufficiency, passive cooling capability, and admissible cooling delay. Across 34 representative operating conditions, the resulting framework achieved a decision accuracy of 94% and an average pump-energy saving of 57%. The MPI-LEN-PFR-LSPT framework therefore provides a compact, physically interpretable, and climate-adaptive basis for PCM selection and delayed-cooling coordination in hybrid PCM–liquid BTMS.