Analytical solution for multi-component pyrolysis simulations of thermal protection materials

This paper provides the analytical solution to a one-parameter Šesták–Berggren kinetic model for thermoanalytical study of pyrolysis reactions involving multiple independent parallel reactions. Such are widely used, instance, in modeling thermal protection materials used heatshields spacecraft during atmospheric entry phase. Solving inverse problems infer parameters through optimization techniques or Bayesian inference methods uncertainty quantification may require large number evaluations response and its sensitivities (derivatives with respect parameters). Moreover, case equations, Arrhenius can exhibit strong dependence that further an accurate parameter calibration. The interest this is reduce computation cost while having high accuracy perform calibration from experiments sensitivity analysis. We propose use exponential–integral functions express temperature integral, we derive reaction both constant (isothermal) heating rate conditions. validated on six-equation using inferred previous work experimental data phenolic-impregnated carbon ablator material, compare computational implemented numerical solution. Our results show such function significantly reduces compared