Synergistic enhancement of temperature uniformity and energy efficiency in roll flame heating via CFD and multi-dimensional metrics

• Validated 3D model with P-control developed for roll flame heating process. • Hot belt mechanism revealed: transverse vortex creates hot spot at stagnation point. • Novel multi-metric system quantifies temperature uniformity. • Optimization boosts uniformity 117%, efficiency 36%, cuts process time 23%. A 3D transient fluid–solid coupled heat transfer model was developed and validated to address temperature non-uniformity in roll flame heating—a critical issue affecting energy efficiency and product quality in steel industry. The model incorporates an improved P-control loop for precise temperature holding, with validation based on experimental data. While circumferential uniformity was ensured by roll rotation, axial non-uniformity manifested as a hot belt originating from fluid separation beneath the roll barrel, where sharp velocity gradients near the resulting dead zone induced a transverse vortex. This vortex, whose flow direction opposed the main flow at the 200° generatrix, created a stagnation point that continuously disrupted the thermal boundary layer and locally intensified heat transfer, ultimately forming the hot belt. To resolve this, a multi-dimensional evaluation system was creatively developed, supported by a script for cylindrical-to-planar field transformation, which comprised three metrics: Temperature Difference per Unit Axial Length ( TDA ), Coefficient of Variation in the Axial Direction ( CVA ), and Axial Temperature Non-Uniformity ( U NA ). Results demonstrated the critical need for substantially increasing flue chamber length ( L ) to reduce temperature non-uniformity. In the optimal case ( L = 2.18 m), reductions of 46% in TDA , 62% in CVA , and 78% in U NA were achieved, alongside a 117% improvement in axial uniformity, a 23% shorter process cycle, and a 36% higher energy efficiency, collectively achieving synergistic enhancement of quality, efficiency, and energy consumption. Beyond its theoretical-practical guide for flame heating optimization, this work also establishes a cornerstone for future digital twin and AI-driven research.