Temperature distributions, critical conditions and scaling for exothermic materials under different boundary conditions. Part 2.—Intermediate boundary conditions (arbitrary biot number) and bodies of low symmetry

Abstract

An approximate method enabling rapid calculation of critical size as a function of the ambient temperature for bodies of arbitrary shape under generalized boundary conditions is given. These boundary conditions apply when there is resistance to heat transfer both within and at the surface of the reactant. The approach uses the same size and shape factors R₀ and j as before and invokes two lengths, l_in and l_ex, which are fixed by the ambient temperature, reactant composition and heat-transfer characteristics. Our results allow small-scale experiments to be used to give safe predictions for larger systems. This is important as conventional methods may err on the dangerous side.

Also given are simple routes to obtaining close bounds on the critical size for more complicated systems. These extra complications arise from bodies which are subject to different boundary conditions on different faces, have very low symmetry or have complicated surfaces. In the latter two cases discussion is restricted to Frank-Kamenetskii boundary conditions.

Example calculations are given.