Simplified thermal stability analysis of diffusion-reaction problems using surrogate modeling

Abstract

Thermal stability analysis of problems involving temperature-dependent heat generation, for example, due to Joule heating or chemical reactions is of much practical interest for the safety of Li-ion cells, chemical reactors and similar systems. There remains an important need for thermal stability analysis of such diffusion-reaction heat transfer problems using simplified methods for practical use. This work presents surrogate modeling based thermal stability analysis of diffusion-reaction problems. Instead of deriving expressions for the transient temperature distribution, an approximate model for total energy of the body as a function of time is used for deriving conditions that cause divergence at large times. Results are shown to agree well with previously reported results based on eigenvalue analysis, and also with independent numerical simulations. Under special conditions, results are shown to reduce to past work on diffusion-reaction and pure-diffusion decay problems. A practical problem related to thermal management of an encapsulated Li-ion cell is analyzed, highlighting the role of intra-cell thermal conduction and convective heat removal at the boundary. Compared to past work, this work offers a mathematically simpler, yet accurate technique for thermal stability prediction. This work extends the state-of-the-art in thermal stability analysis and may benefit a number of engineering systems.