Combined conduction, convection, and radiation effects in optically thin tube flow

The author gives a general formulation for determining the gas and surface tempeature distributions for laminar flow in a circular tube. The analysis allows for arbitrary wall heat generation and radiation effects in the gas and at the tube surface. The analytical development is applicables to more general radiation situations than optically thin radiation to any gas for which the relevant properties are known, and to fluids with heat sources due to effects other than radiation. Numericalresults for a variety of parameters are compared with results obtained for nonparticipating gases (surface radiation effects considered). For a prescribed wall heat generation, the nonparticipating gas solution represents a poor estimate of the wall temperature distribution as well as the gas bulk temperature variation. Introducing a so- called '%'quasi- one- dimensional'%' approximation for the radiation term in the energy equation simplifies the computational procedures without sacrificing accuracy.