Errors Found in Expressions Given by Schaeffer and by Selph for Radiation Flux in Rectangular Straight Duct

Abstract

Assuming the entrance of a rectangular straight duct to be uniformly covered with a film of radiation source, and the radiations to be emitted into the duct at intensities proportional to cos2θ (θ : Angle of radiation incidence), the unscattered component of radiations along the duct axis is shown to be expressed by where φ0 is the total flux from the radiation source, while a, b are non-dimensional parameters representing the perspective angle of radiation source vertical and horizontal spreads. This consequently proves the fallacy of the expressions given by Schaeffer and by
Selph for the same assumptions, i.e.
and which are widely cited in textbooks, handbooks and reports.