Critical initial conditions for spontaneous thermal ignition

Critical initial conditions for thermal ignition are calculated numerically for planar, cylindrical and spherical geometries. In each case a comparison is made on the bifurcation diagram with the intermediate steady state(s). It is clearly seen that the actual critical initial condition which depends upon the initial temperature profile, is partly below the intermediate steady state(s). The variation with ambient temperature, exothermicity and Biot number are all explicitly shown. The results are important for calculations relevant to the critical hot product assembly problem where a hot manufactured organic product is packed into containers or stockpiled at a subcritical ambient storage temperature. An example calculation for an interesting case study (milk powder) is given to illustrate the utility of our results.