A Note on a Two-Step Reactive-Diffusive Equation with Variable Pre-Exponential Factor

摘要

To study the steady-state solutions for the exothermic chemical reactions (two-step Arrhenius reactions), taking the diffusion of the reactions in a slab into account and assuming an Arrhenius dependence with variable pre-exponential factor to determine the effects of Frank-Kamenetskii parameter and some thermo physical properties on temperature of a giving system. Steady state energy equation was transformed to non-dimensional form. Numerical solutions of the resulting equation were done by the use of shooting method. We discovered that there are certain values for n, m, r and can accommodation for solution to be stable. Similarly, Frank-Kamenetskii parameter 1, 2 must not exceed some values for the solution to exist and at the same time stable. Finally, the Frank-Kamenetskii parameter must not exceed the critical value for the solution to have physical implication or application and r must not be large for convergence of the solution (i.e., r< 1). The results of this study will serve as baseline information to combustion engineering in designing combustion equipments or manufacturing of chemical to aid complete combustion reactions and to burn fuel more efficiently to avoid knocking of engines.