Solve the following problem:
Q: Air at 3 atm and 100°C is discharged from a compressor into a vertical receiver of 2.5-m height and 0.75-m diameter. Assume that the receiver wall has negligible thermal resistance is at a uniform temperature, and that heat transfer at its inner and outer surfaces is by free convection from a vertical plate. Neglect radiation exchange and any losses from the top.
(a) Estimate the receiver wall temperature and the heat transfer to the ambient air at 25°C. To facilitate use of the free convection correlations with appropriate film temperatures, assume that the receiver wan temperature is 60°C.
(b) Were the assumed film temperatures of part (a) reasonable? If not, use an iteration procedure to find consistent values.
(c) Now consider two features of the receiver neglected in the previous analysis: (i) radiation exchange from the exterior surface of emissivity 0.85 to large surroundings, also at 25°C; and (ii) the thermal resistance of a 20-mm-thick wall with a thermal conductivity of 0.25 W/m. K. Represent the system by a thermal circuit and estimate the wall temperatures and the heat transfer rate.
