Question: Helium flows through a thin-walled 1.25 cm diameter circular tube at a mean velocity of 6 m/s under the following conditions at a particular point along the tube:

P = 345 kPa,   t_m = 200°C

The tube is exposed on one side to an infinite plane that emits black-body radiation at 300°C, while the remainder of the surrounding space is effectively nongraduating. Assuming that the tube wall is sufficiently thin that peripheral conduction in the Wallis negligible, assuming that the outer-wall surface is a black body, and evaluating radiation from the tube as if the entire tube were at a uniform temperature of 300°C (re-radiation will be relatively small and an exact solution would require iteration), calculate the net heat flux to the tube and estimate the temperature distribution in the wall around the tube. Assume that the heat-transfer resistance of the wall is negligible in the radial direction and that fluid properties are constant.