Historical investigation into the first burning model of a solid fuel and the origin of the Crank–Nicolson numerical method

Current numerical models for the burning of solid fuels have reached a level of complexity that enables researchers to study and predict the intricate thermochemistry involved in various combustion problems, ranging from polymers like PMMA and foams like PU to natural fuels such as timber and vegetation. Yet they share a common mathematical formulation and numerical method that can be traced back to the first solid-burning model, developed for wood combustion during the 1940s. In this paper, we investigate the origins, formulation, and historical context of this model. Developed during the Second World War, it brought together a team of five scientists, Phyllis Nicolson, John Crank, Douglas Hartree, Clement Bamford, and David Malan, from the University of Manchester, the University of Cambridge, and the Special Operations Executive, a British espionage and sabotage organisation. Their task was to solve the governing equations and apply them to improve small incendiary devices for the war effort. The model consists of the heat diffusion equation with a source term representing an Arrhenius-type pyrolysis reaction. The stiffness of the resulting partial differential equation made it difficult to solve with the techniques of the time. This challenge led the team to develop the second-order accurate semi-implicit Crank–Nicolson scheme. This breakthrough not only transformed numerical analysis but also laid the foundations for computational fluid dynamics, modern heat transfer modelling, and advances in combustion and fire science. Overall, we highlight the historical roots of the first solid-fuel burning model, which, though born of wartime combustion research, has had a profound and lasting influence on today’s models and numerical methods. • We investigate the origins, formulation, and historical context of the Crank–Nicolson method. • The first burning model of a solid fuel, the heat diffusion equation with an Arrhenius-type source was solved by Phyllis Nicolson during the Second World War to develop incendiary devices. • The solution led to develop the Crank–Nicolson method, having a profound and lasting influence computational modeling and CFD.