PROBLEM 3

Problem 10.23. Helically coiled tubes are used in heat exchangers in air conditioning systems, nuclear

steam generators, and many other applications. For natural convection on the outside of vertical helical

coils, based on experiments with water with tube diameter of 13.5 and 15.8 mm, and helical coil pitches

in the range 13.5 to 47.4 mm, Prabhanjan et al. (2004) have proposed the following correlation:

Nu = 0.0749 Ra421;9x10°

where H is the total coil height.

Ali et al. (1994) proposed the following correlation for natural convection on the outside of a vertical coil:

Nu = 0.257 Ra23;6×10³ < Ra<3×10¹¹

(b)

(a)

The tube radius in Ali et al's data was 12 mm and tube radius-to-coil radius ratio covered the range 0.08

to 0.101.

Consider a vertically oriented helically coiled tube. Assume that the coiled tube has an inner diameter of

13 mm and water flows into the coiled tube with a Reynolds number of Re, = 9700. Also,

R/R = 0.08. Water inlet temperature for the flow inside the coiled tube are 300 K, and the total length

of the coiled tube is 4.09 m. The pitch for the coiled tube is 21 mm. The coiled tube is inside a large tank

that contains stagnant water at a temperature of 365 K. Calculate the mean water temperature at the exit

of the coiled tube. For simplicity neglect the thermal resistance of the coiled tube's wall.