This paper is focused on the analysis of interaction of free convection and exothermic chemical reaction. As a consequence of the chemical reaction, free convection effects can result. It is difficult to perform an analytical bifurcation analysis of the full nonlinear governing equations; however, Fourier expansion combined with a Galerkin approximation results in a small set of ordinary nonlinear differential equations (initial-value problem) that are amenable to analysis. Conditions for branching of the solution can be determined in an analytical way. A continuation algorithm makes it possible to calculate the branches of stability. The results of the approximative analysis are supported by the numerical integration of the full governing nonlinear equations.