Self-similar piston problems with radiative heat transfer

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Abstract
A differential approximation for the equations of radiative transfer in a grey gas is applied in a study of the effects of thermal radiation upon the classical problem of the compressive action of a plane, cylindrical or spherical piston. The ambient gas ahead of the precursor shock wave is supposed cool and the shock wave transparent, whilst the piston is taken to be neither an emittor nor reflector of radiative energy. It is shown that self-similar flow patterns may arise if the ambient density and piston speed are both non-uniform with variations linked to the absorption coefficient which is assumed to be density and temperature dependent. Detailed flow patterns are obtained in the case of general opacity and also in the transparent limit from which it is deduced that under certain conditions the approximation provided by the latter may be rather dubious.

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