A two-stage decoupled framework for sequential prediction of thermal conductivity and surface heat flux in nonlinear inverse heat conduction problems

Purpose The prediction of both temperature-dependent thermal conductivity k(T) and surface heat flux in extreme aerothermal environments is severely ill-posed, particularly when material properties must be extrapolated into unmeasured high-temperature regions. This study aims to develop a robust, physics-guided and computationally efficient framework to address the extrapolation instability inherent in conventional coupled inverse methods. Design/methodology/approach A two-stage decoupled strategy is proposed. In Stage I, k(T) is estimated via a modified Levenberg–Marquardt algorithm using interior sensor data, with Chebyshev polynomial parameterization enforcing strict physical constraints (k > 0, dk/dT = 0) to ensure stable extrapolation. In Stage II, surface heat flux is reconstructed noniteratively via a space-marching algorithm integrated with a frequency-optimized Gaussian filtering technique. The framework is validated using Al2O3 as host material under multipulse thermal loads with 2% measurement noise. Findings The framework achieves a heat flux Relative Root-Mean-Square Error (RRMSE) of 4.75% and a surface temperature RRMSE of 0.92%. Physics-guided constraints eliminate unphysical oscillations in extrapolated conductivity up to 1,800 K. The decoupled framework reduces runtime from approximately 1,500 to 0.15 s – a 104-fold speedup over conventional iterative methods. This acceleration reduces a typical surface-heat-flux reconstruction from the order of minutes to a fraction of a second on a standard workstation, enabling near-real-time monitoring in applications such as hypersonic thermal protection and on-line diagnostics. Originality/value This work addresses the “extrapolation dilemma” in high-temperature thermal characterization through sequential prediction of material properties and boundary conditions. The combination of solid-state physics constraints with a noniterative space-marching scheme ensures thermophysical consistency and computational efficiency, offering an effective tool for development and evaluation of thermal protection systems.