Bayesian-Calibrated Enthalpy Modeling for Thermal Regulation of Phase-Change-Assisted Electric Heat Tracing Systems

<title>Abstract</title> <p> Low-temperature pipelines are prone to rapid heat loss and local freezing after interruption of electric heat tracing, which limits the reliability of conventional thermal protection methods. In this study, a phase-change-material-assisted electric heat tracing system was developed for low-temperature pipeline thermal regulation. A multilayer pipeline test section consisting of a 304 stainless-steel pipe, electric heating tape, annular phase change material layer, aluminum encapsulation shell and polyurethane insulation layer was established in a programmable low-temperature chamber. A two-dimensional axisymmetric transient heat-transfer model was constructed using the enthalpy method, and Bayesian calibration was introduced to update key parameters including solid and liquid thermal conductivity, latent heat, convective heat-transfer coefficient and contact thermal resistance. Under the baseline condition of 40 W heating power, -20°C ambient temperature, 17.5 mm PCM thickness and 20 mm insulation thickness, the PCM formed a melting plateau near 10.1°C and a solidification plateau near 9.4°C, with a phase-change hysteresis of 0.7°C. The average liquid fraction increased from 0.18 at 10 min to 0.99 at 90 min, indicating progressive melting of the PCM layer. Compared with the uncalibrated model, the Bayesian-calibrated model reduced the mean RMSE of six temperature sensors from 1.85°C to 0.82°C, with a mean MAE of 0.59°C and a mean R ² of 0.990. The PCM-assisted system increased the retention time above 10°C from 12.6 min to 42.1 min and the retention time above 5°C from 31.5 min to 78.4 min compared with conventional electric heat tracing. Multi-condition analysis showed that heating power mainly controlled startup and melting time, ambient temperature governed boundary heat loss, PCM thickness determined latent heat capacity, and insulation thickness reduced post-heating cooling. A reasonable operating region was identified as 40–50 W heating power, 17.5–20 mm PCM thickness and 20–30 mm insulation thickness. The results demonstrate that the proposed system improves low-temperature pipeline thermal regulation through the coordinated action of active electric heating, latent heat buffering and boundary heat-loss suppression. </p>