Safety monitoring of exothermic reactions using time derivatives of temperature sensors

• Relationships between heat flux and temperature on cylindrical walls.
• Heat flux as indicator for thermal runaway processes.
• Low-order time derivatives of temperature as approximation for the heat flux.

We propose a new method of safety monitoring for overheating in exothermic reactions that is applicable to detection of thermal runaway in Li-ion batteries. The proposed method is based on the solutions of a one-dimensional heat conduction problem across the wall thickness of a cylinder. The problem is known as an Inverse Heat Conduction Problem (IHCP) since heat is conducted outwards while monitoring sensors only have access to the outside surface. We first obtain the transfer functions relating the inner and outer boundaries through Laplace transform. We then use Hadamard factorization theorem to express the transfer functions in terms of infinite product of polynomials. Truncations of the polynomial transfer functions represent time domain relationships between physically accessible measurements and the heating inside a cylindrical wall. These relationships lead us to propose time derivatives of temperature as better indicators for safety monitoring in exothermic processes.