Radiative heat transfer to flow of a combustible mixture in a vertical pipe

The flow of a combustible gas in a vertical cylinder, in the presence of radiative heat transfer, affords the closest model to biomass moving bed gasifier operating at temperatures between 750 and 1500 K. This problem forms the subject matter of the paper under the simplistic assumption of a binary reaction A → B. Under the general differential approximation for radiation, the temperature is perturbed about the wall temperature, and the nonlinear differential equations are subsequently integrated in a closed form. Consequences of the effect of the Arrhenius activation energy are discussed quantitatively.