Thermal explosion during the flow of a viscous liquid

Abstract

Frank-Kamenetskii has discussed a steady-state formulation of thermal explosions [1]. Bostandzhiyan et al. [2] and Bostandzhiyan and Chernyaeva [3] have shown, for the flow in a cylindrical tube of Newtonian and non-Newtonian liquids having a strong (nonlinear) temperature dependence of the viscosity, that a phenomenon analogous to thermal explosion may occur during the flow of a chemically inert liquid. Bostandzhiyan et al. [4] have also studied Couette flow and the flow between two rotating circular cylinders of a Newtonian liquid having the same temperature dependence for its viscosity. It was shown that, although the heat balance equation reduces to the equations of the steady-state theory of thermal explosion for the corresponding region, hydrodynamic thermal “explosion” was not observed in these cases. This phenomenon was found to be characteristic of only pressurized flows.

Below, we study thermal explosions during the Poiseuille flow of a viscous, chemically reactive liquid in an infinite circular cylindrical tube, and during the motion of the liquid between infinite rotating cylinders. The combined effect of chemical and mechanical heat cources are considered.