Over the last four years $400 million (US) losses by fire have occurred in a total of seven instances of containerships carrying materials prone to spontaneous self-heating and ignition. In all these cases calcium hypochlorite was present in quantity and is believed to be responsible, but the problem is a wider one arising from the modern practice of shipping kegs of such materials inside containers. The container itself prevents effective dissipation of the heat generated by the kegs which therefore interact more strongly with each other by a positive feedback mechanism. The critical (or spontaneous ignition) temperatures of such kegs can be and are measured directly and are in the region of 60C - well above the likely shipping temperatures, even in the tropics. Recently one of us (BFG) commenced an investigation of the interaction of such kegs with each other and the effect that this interaction could have on the spontaneous ignition temperature.
These tests showed that whereas a single keg ignited at 65C the assembly of 18 by 14kg kegs actually ignited at 55C! In the shipping situation over 400 40kg kegs are transported in a single container and individually they have a critical temperature of 60C, so the expected critical temperature for the assembly would be expected to be significantly lower. Full scale tests are far too dangerous and time consuming to carry out so mathematical modelling comes into its own with a vengeance in such a case. Zeroth order semi-quantitative modelling indicates that the critical temperature for an assembly of 400 kegs is in the region of 35C, well within the realistic ships hold temperature range. This modelling also shows a correspondingly lengthened time-scale for the full-size case.
It is clear that the safest and quickest way to investigate the realistic case of 400+ kegs interacting with each other is to use numerical methods in addition to more sophisticated analytical modelling and experimental testing. This work, and direct visualization of the experimental data, are ongoing.
See also the School mathematical combustion page.