H Theorems for One-Dimensional Combustion of a Gas

Abstract

The equations for unsteady one‐dimensional combustion processes are derived under very justifiable physical assumptions. The combustion equations dictate that a functional of the temperature distribution, called H, always decreases with time at an increasing absolute rate. This H theorem is used to determine the critical size of a pocket of gas which can instigate combustion waves. For the case of ``normal'' diffusion, the asymptotic combustion equation implies that a second functional of the temperature distribution, called H^*, always decreases with time at a decreasing absolute rate. This second H theorem is associated with a dynamical principle equivalent to the full content of the asymptotic combustion equation.