Non-probabilistic set-theoretic models for transient heat conduction of thermal protection systems with uncertain parameters

Thermal protection systems (TPS) play a key role in the development of hypersonic aircrafts and the performance of TPS is directly in connection with its temperature field, thus a number of analytical and experimental studies have been conducted to study heat transfer analysis. Due to the existence of uncertain parameters in the temperature field, it is imperative to adopt the approaches involving uncertainty analysis to obtain reliable results. The non-probabilistic set-theoretic models, compared with the probabilistic approach, only require a small amount of experimental samples to process the study of uncertainties. Interval analysis method (IAM), classical convex model (CCM) and novel convex model (NCM) are applied to quantify uncertain parameters in TPS and then combined with finite elemental differential equation of transient thermal analysis to study the effects of uncertain parameters on temperature field response by means of Taylor series expansion. Moreover, the thermal responsive bounds in both CCM and NCM are yielded by the Lagrange multiplier method. A ceramic TPS is performed to illustrate the application of the present method and the results show that NCM can reduce the space of temperature field responses. Besides, the non-probabilistic set-theoretic methods can serve for the design of TPS.