The Three-Dimensional Analytical Modeling of Lightning-Induced Heat Diffusion: The Critical Roles of the Continuing Current and Lightning Channel Radius in Structural Damage

The utilization of metal roofing as natural air terminals is a standard practice in lightning protection; however, the risk of thermal perforation and subsequent ignition of internal hazardous atmospheres remains a critical safety concern. While current standards (e.g., IEC 62305) primarily focus on material thickness and total charge (Q), this study demonstrates that these parameters alone are insufficient for predicting burn-through failure. We present a comprehensive electrothermal analysis based on the method of images to simulate three-dimensional heat diffusion in finite-thickness plates (0.5–7 mm) made of aluminum, copper, and steel. Unlike simplified 1D models, our approach considers the spatial distribution of the heat source and the varying depth of the thermal penetration. The results confirm that the continuing current component (Qlong≈200 C) is the primary driver of volumetric melting. Crucially, the sensitivity analysis reveals that the lightning channel radius (rmbo) acts as a governing factor for perforation risk; a reduction in the lightning channel radius from 5 mm to 2 mm can shift the outcome from minor surface heating to complete perforation for thin sheets (0.5 mm), even under identical charge conditions. This paper identifies a “safety gap” in current engineering practices, demonstrating that neglecting this parameter constriction effect results in an underestimation of the thermal threat. The proposed analytical model provides a precise tool for determining the safety margins of natural air terminals, offering direct applicability for designing lightning protection systems in high-risk industrial facilities.