One Dimensional Steady Flow of a Radiating Gas Past a Heat Source

Abstract

One dimensional steady flow of a grey gas past a grey non-reflecting heat source is studied. This linearized problem is not only a model of radiative furnace but also one of the simplest problems which concern the interaction between the convection and the thermal radiation. The conductivity and the viscosity are neglected. The kernel substitution solution is obtained and its correction is tried. The exact form for weak radiation and near the heat source for arbitrary radiation strength, the solution by diffusion approximation without slip and numerical results are obtained and compared with each other. The temperature profile shows almost symmetric feature for weak radiation. But when radiation is strong, it gradually shifts far up-stream against the convective cooling and rapidly attains its asymptotic value downstream. Radiation slips are also calculated.