Fractional-order heat transfer characteristics and prediction of blast furnace cooling staves

To address the problem that traditional integer-order models exhibit prediction deviations due to non-local thermal memory and transient multi-scale coupling characteristics in the heat transfer process of blast furnace cooling staves, the research aims to construct an accurate heat transfer analysis and dynamic prediction model, providing theoretical and methodological support for the intelligent regulation of cooling systems. The research establishes an unsteady heat transfer model based on the Caputo fractional derivative, which is solved using a Grünwald-Letnikov discretization scheme modified by the short-memory effect to characterize the thermal memory properties of refrac‑tory materials. A physics-informed neural network（PINN） architecture embedded with fractional-order operators is designed, combined with receding horizon optimization and transfer learning strategies, to achieve efficient inversion of time-varying thermal conductivity, heat source terms, and fractional-order parameters, as well as dynamic predic‑tion of temperature fields. Through molecular dynamics and phase-field multi-scale simulations, the microscopic effects of Al_2O 3-SiO₂ lattices and microcrack networks on heat conduction are analyzed. A health early warning framework for cooling staves is established based on the mapping relationship between fractional-order parameters and microstructures. The results show that the model converges stably; when the optimal fractional-order α = 0. 8, the global temperature prediction root mean square error(R_MSE) reaches 0. 99 ℃, which is significantly better than that of the integer-order model, and the temperature field simulation is consistent with actual working conditions. Multi-scale simulations reveal that the power-law relaxation characteristics of Al₂O₃-SiO₂ lattices and the non-local thermal diffusion induced by microcrack networks are consistent with the characteristics of the fractional-order model. The established health early warning framework can realize quantitative classification of risk levels. The research confirms the advantages of the fractional-order-PINN model in characterizing heat transfer in blast furnace cooling staves, providing a high-precision tool for the intelligent operation and maintenance of blast furnace cooling systems, and promoting the interdisciplinary application of fractional-order theory and deep learning in industrial heat transfer fields.