A scientific instrument requires mercury to be cooled from 50°C to 5°C using a iced-water bath kept at 0°C The flow rate of mercury is 0.45 kg/s. Assume the inner surface of the tube carrying mercury is at the same temperature of the bath.

(a) Assuming the flow is fully-developed, which of the following tubing would you recommend and why: (A) thin tube with a circular cross-section of 25 cm diameter, (B) thin tube with a square cross-section of 30 cm sides, or (C) thin tube with a rectangular cross-section of 15 cmx30 cm.

(b) Is the thermally fully-developed assumption justified? If not, without any calculation, argue how would your choice of tubing change.