Aspects of the temperature distribution in a Frank-Kamenetski sphere

Abstract

This thesis includes derivations of the following: (1) The boundary value problem for a Frank-Kamenetski sphere from its defining properties. (2) A 'determinant' and a 'Cauchy product' recursive relation for the coefficients of the Taylor series of the solution. (3) Upper and lower bounds on the coefficients and hence on the radius of convergence of the Taylor series. (4) Properties of the solution including its transcendentality. (5) An upper bound on the solution. (6) The shape of the bifurcation diagram.