Question

# 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° <Rag <4x10¹¹ 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.  Fig: 1