Control of thermal runaway - some mathematical insights

The model problem of a heat generating fluid flowing through a finite length pipe is investigated analytically to study means of controlling the onset and development of thermal runaway. The heat source Q within the fluid is modeled as a linear function of the temperature and it is shown that, when Q is sufficiently large, the temperature will, in general, grow exponentially in time, i.e., thermal runaway will occur. However, even when this is the case, it is shown that thermal runaway can be prevented by imposing certain conditions on: (1) the initial temperature distribution; (2) the time dependent temperature of the ambient fluid surrounding the pipe; or (3) the time dependent boundary conditions. The results are discussed and are illustrated by several examples. (C) 1998 Elsevier Science Ltd. All rights reserved.