In this paper, an approximate analytical solution for Frank-Kamenetskii equation modeling a thermal explosion in a sphere, is obtained. The approximate solution is obtained by perturbation methods in terms of small and large distance parameter. The approximate solution is compared with the numerical solution obtained from an initial value problem formulation to the original boundary value problem. The approximate solution obtained is valid for all values of the distance parameter. For the original boundary value problem and for a given Frank-Kamenetskii parameter, a nonlinear algebraic equation needs to be solved to be able to apply the approximate solution.
Soliman, Moustafa A., "Approximations to the Solution of the Frank-Kamenetskii Equation in a Spherical Geometry" (2014). Chemical Engineering. 52.