On the Thermal Decomposition of Reactive Materials of Variable Thermal Conductivity and Heat Loss Characteristics in a Long Pipe

In this article, we investigate the thermal decomposition of a stockpile of reactive material undergoing a steady-state exothermic chemical reaction inside a long pipe with heat loss characteristics at its surface. It is assumed that the thermal conductivity (k) of the material varies exponentially with temperature and the pipe surface exchanges heat with the ambient following Newton's law of cooling. The nonlinear differential equation governing the problem is tackled analytically using a regular perturbation technique (RPT) coupled with a computer-extended series solution (CESS) and a special type of Hermite-Padé approximation. The effects of various thermophysical parameters on the temperature field together with critical conditions for thermal ignition represented by turning points on the bifurcation diagram are obtained and discussed quantitatively. An increase in critical behavior is observed with a decrease in the material's thermal conductivity. However, the stability of the material is enhanced by an increase in the material's thermal conductivity.