The free convection boundary layer on an insulated wall formed by local internal heating through a modified form of Arrhenius kinetics is considered. It is shown to involve two dimensionless parameters, ϵ\documentclass[12pt]{minimal}
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\begin{document}$$\epsilon $$\end{document} the activation energy and q0\documentclass[12pt]{minimal}
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\begin{document}$$q_0$$\end{document} the rate of local heating. Numerical solutions to the initial-value problem are obtained showing that, for relatively weak internal heating (small q0\documentclass[12pt]{minimal}
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\begin{document}$$q_0$$\end{document}), a nontrivial flow arises at large times, whereas for larger local heating the solution becomes singular at a finite time. This behaviour is also seen to depend on the size of the initial input. The corresponding steady states, being the possible large time solutions to the initial-value problem, are also treated. These show the existence of a critical value q0,crit\documentclass[12pt]{minimal}
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\begin{document}$$q_{0,\mathrm{{crit}}}$$\end{document} of q0\documentclass[12pt]{minimal}
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\begin{document}$$q_0$$\end{document}, dependent on ϵ\documentclass[12pt]{minimal}
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\begin{document}$$\epsilon $$\end{document}. These critical values determined numerically showing that there was a finite region of the ϵ∼q0\documentclass[12pt]{minimal}
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\begin{document}$$\epsilon {\sim }q_0$$\end{document} parameter plane over which steady states cannot be found. Asymptotic forms for both ϵ\documentclass[12pt]{minimal}
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\begin{document}$$\epsilon $$\end{document} and q0\documentclass[12pt]{minimal}
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\begin{document}$$q_0$$\end{document} being small and large are derived.
