Indirect Method of the Critical Parameters of Frank-Kamenetskii Equations in Spontaneous Combustion Theory

The steady state heat balance equation in Frank-Kamenetskii model is one of the basic models of spontaneous combustion. For a non-uniform temperature exothermic reaction system met the Arrhenius law, the reaction heat term of the heat balance equation can be described by a simple nonlinear term. The simplified spontaneous theoretical model equation is a typical bifurcation problem. The governing equation of bifurcation points is generally Nonlinear Ill-posed Equation. To solve this kind of equation, usually we divide it into three steps to complete: regularization, difference and iterative. Homotopy-Newton hybrid method is a typical direct method to solve it. However, this direct method for a specific problem, deterministic and convergence of solutions are not guaranteed. In this paper, a kind of effective indirect method is introduced. This shooting method by control parameter can effectively improve the convergence.