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Transient combustion of a gaseous sphere of fuel is examined in the flame-sheet limit. The gas is considered thermally expandable, the Lewis numbers are taken as unity and a temperature-dependent thermal diffusivity is allowed. Evaluation of some approximations used in forming the model are evaluated by examining a spherical, nonlinear thermal conduction problem first. Mathematica is used to solve the PDEs arising from both problems by a Method of Lines. The solutions for the combustion problem show the expansion and subsequent collapse of the flame-sheet trajectory, the sharp initial temperature spike at the flame front and its later diffusive spreading, and the early peaked expansion velocity, followed by a double humped velocity profile.
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