Effect of Specularly Reflecting Gray Surface on Thermal Radiation Through a Tube and From Its Heated Wall

An analysis was made of specular radiation exchange within a circular tube open at both ends and in vacuum. The tube is exposed to thermal radiation from an environment at each end and can have a uniform heat flux supplied at its wall. The external surface of the tube wall is insulated, while the internal surface is a gray, specular (mirrorlike) reflector for thermal radiation. The integral equations governing the radiation exchange are solved to determine the internal surface temperature and the amount of heat transmitted through the tube from the environment at one end to the other. Specular reflections were found to reduce the maximum surface temperature of the heated wall as compared with diffuse reflections, and in some instances the maximum temperature was below the value for a black surface. The energy transmitted through the tube was larger for the specularly reflecting wall than for diffuse reflections. It was also shown that the energy transmitted for a diffusely reflecting gray wall is the same as for a black wall.