In this paper an approximate analytical solution for the Frank-Kamenetskii equation modeling thermal ignition without the depletion of the combustibles in a spherical annulus and non-isothermal zero order reaction in spherical catalyst particle is presented. The approximate solution is compared with the numerical solution and is in good agreement with the numerical solution. The approximate solution obtained is valid for all values of the distance parameter. Multiple solutions occur for some range of Frank-Kamenetskii parameter (λ). The multiplicity is infinite for the case of a solid sphere and λ=2.Interesting relation is obtained for λ at the turning points. For the non-isothermal zero order reaction in a spherical catalyst particle the effectiveness factor was obtained using the approximate solution. The values of the effectiveness factor obtained from the approximate solution are accurate compared with the exact values obtained from numerical computations.
Soliman, Moustafa A., "Approximate Analytical Solution for Mathematical Models of Thermal Ignition and Non-Isothermal Catalytic Zero Order Reaction in a Spherical Geometry" (2019). Chemical Engineering. 80.