Chaotic mechanisms of heat-transfer enhancement governed by bubble-growth dynamics in a bottom-blown multiphase flow

Bottom-blown multiphase stirring is intrinsically nonlinear and remains difficult to optimize using only averaged flow or heat-transfer parameters. This study establishes a visualized hydraulic model to examine how the initial temperature difference, ΔT, and dispersed-phase flow rate, U d , jointly regulate bubble growth, chaoticity, and direct-contact heat transfer. An empirical correlation for the ensemble-averaged equivalent bubble diameter is developed and validated, and the bubble-area time series is analyzed using the correlation dimension, the 0-1 test, and the maximum Lyapunov exponent. Bubble diameter increases with ΔT and U d , and the proposed correlation predicts the ensemble-averaged equivalent diameter with a MAPE of 2.25%, an RMSE of 0.363 mm, and a maximum relative error of 9.91%. Chaotic intensity responds nonlinearly to the operating conditions and reaches a maximum at ΔT = 100 °C and U d = 0.6 kg·s −1 , where Dc = 2.896 and λ max is highest. The ΔT-U d regime map, the Nu-Re reformulation, and the positive correlation between λ max and h (r = 0.847) jointly show that a relatively high temperature difference combined with a moderate flow rate favors both chaos intensification and heat-transfer enhancement. These results clarify the coupled chain linking bubble-structure evolution, chaos intensification, and heat-transfer enhancement, and provide a basis for operating-window optimization in bottom-blown metallurgical processes.