Operational Temperature Optimization in Hydrogen Turbine Blades via Time-Fractional Conformable Sensitivity Analysis

This study focuses on optimizing the thermal performance of hydrogen turbine blades through a sensitivity analysis using generalized fractional calculus. The approach is designed to capture the transient temperature dynamics and optimize thermal profiles by analyzing the influence of a fractional-order parameter on the system’s behavior. The model was implemented in Python, using Monte Carlo simulations to evaluate the impact of the parameter on the temperature evolution in different thermal regimes. Three distinct regions were identified: the Quasi-Uniform Region (where fractional effects are negligible), the Sub-Classical Region (characterized by delayed thermal behavior), and the Super-Classical Region (exhibiting enhanced heat accumulation). Regression analyses reveal quadratic and cubic dependencies of blade temperature on the fractional-order parameter, confirming the robustness of the model with R2 values greater than 0.96. The study highlights the potential of using fractional calculus to optimize the thermal response of turbine blades, helping to identify the most suitable parameters for faster stabilization and efficient heat management in hydrogen turbines. Furthermore, it was found that by adjusting the fractional-order parameter, the system can be optimized to reach equilibrium more rapidly while achieving higher temperatures. Importantly, the equilibrium is not altered but rather accelerated based on the chosen parameter, ensuring a more efficient thermal stabilization process.