Question: Helium flows in a thin-walled circular tube of 2.5 cm inside diameter. Down the center of the tube is inserted a 5 mm diameter circular electric heater. The Reynolds number of the flow, based on the hydraulic diameter of the resulting passage, is 30,000. Heat is generated and transferred through the heater surface at a rate of 30 kW/m2 • The outer surface of the outer tube is bare, exposed to an atmospheric environment at 21°C. Heat is transferred from the outer surface to the surroundings by both free convection and radiation. For the free convection, assume a heat-transfer coefficient h of 10Wl(m2 • K). For the radiation, let the surface emissivity be 0.8. At a particular point along the tube the mixed mean fluid temperature is 200°C. Assuming that the gas is transparent to thermal radiation and that the radiation emissivity of the two inner surfaces is 0.8, calculate the surface temperature of the heater and the temperature of the outer tube. Determine the fractions of the original heat generated in the core tube that are ultimately transferred to the helium and to the surroundings. Is radiation a major factor? It may be assumed that the tube is sufficiently long that fully developed conditions are closely approached.