Effect of the geometrical parameters of a solid with a constant surface temperature on the critical conditions of thermal explosion

The problem of the effect of the geometry of a sample on the critical conditions for thermal explosion in an arbitrarily shaped solid with a constant surface temperature has been studied. The geometrical factors affecting the location of the hot spot and the critical conditions have been analyzed. It has been shown that the location of the hot spot is related to the dimension of the problem and can be quite accurately determined for a body with any shape. The concept of an equivalent ellipse or ellipsoid, which provides a higher accuracy than the concept of an equivalent sphere used in engineering calculations, has been introduced. Expressions for the critical conditions of a thermal explosion of two- and three-dimensional solids of an ellipsoidal shape and some other configurations have been derived to illustrate the application of the proposed approach.