Thermal ignition of annular layer and its hydrodynamic analog

Abstract

1. Critical conditions of thermal ignition of an annular layer have been investigated, with an arbitrary temperature difference at the cylinder surfaces and also with one surface thermostatted and the other heat-insulated. Transcendental equations determining the critical value of the Frank-Kamenetskii parameter are obtained. 2. With the same temperature boundary conditions, dissipative flow of a viscous liquid with an exponential temperature dependence of the viscosity between two rotating cylinders has been considered, with the value of the tangential stress specified at the surface of the rotating cylinder. An analogy is established between thermal ignition of an annular layer and dissipative liquid flow between two rotating cylinders. 3. In the case of one heat-insulated surface, the analogy exists between the ignition of an annular layer from the inner heat-insulated cylinder and dissipative flow with a heat-insulated outer cylinder, and conversely. 4. For these cases, there is a simple relation between the critical values of the Frank-Kamenetskii parameter of hydrodynamic thermal explosion and thermal explosion of chemical explosion; see Eq. (39).