Uncertainty Propagation and Global Sensitivity Analysis of Third-Order Transport Coefficients in Chemically Reactive Nonequilibrium Flows

Third-order Extended Thermodynamics (ET3) introduces additional nonequilibrium moments and nonlinear transport couplings that can improve the representation of rapidly relaxing chemically reactive flows, but these extensions also introduce coefficients whose uncertainty may materially affect model predictions. This study develops a reproducible uncertainty-quantification and global-sensitivity framework for a reduced ET3 reactive-flow model. Five dimensionless inputs—the third-order relaxation time, heat-flux coupling, stress coupling, nonequilibrium-reaction coupling, and Damköhler number—are treated as uncertain. Monte Carlo propagation with 5,000 samples is used to construct predictive intervals for higher-order relaxation, heat flux, reaction progress, and entropy production, while variance-based Sobol indices are estimated with independent pick-freeze samples. A second-order limit is obtained by suppressing the three ET3 coupling coefficients. In the computational illustration, the mean peak heat-flux proxy is 0.0792, the mean peak stress proxy is 0.0453, the mean time to 90% reaction progress is 2.4272, and the mean final cumulative entropy production is 0.7479. Global sensitivity analysis shows that different observables are controlled by different parameter combinations, demonstrating that coefficient identifiability cannot be assessed from a single response variable. The ET3 coupling terms accelerate the median reactive evolution relative to the second-order limit and create non-negligible predictive dispersion. The proposed workflow provides a bridge between kinetic-theory derivation, Bayesian coefficient calibration, and predictive uncertainty assessment. The results are explicitly presented as a computational illustration rather than experimental validation and provide a reproducible basis for subsequent calibration against kinetic, molecular, or laboratory data.