Water flows through a long tube, which has a 2 m long heated segment, as shown in Figure P 8.2. The tube inner diameter is 5 cm. The temperature and Reynolds number of water prior to entering the...

Water flows through a long tube, which has a 2 m long heated segment, as shown in Figure P 8.2. The tube inner diameter is 5 cm. The temperature and Reynolds number of water prior to entering the heated segment are 20°C and 20,000, respectively. The flow is hydrodynamically fully developed upstream from the heated segment.

a. The heat flux through the wall is adjusted such that the mean water temperature at the exit of the heated segment reaches 50°C. Assuming a smooth tube wall, calculate the wall heat flux and the wall temperature at the middle and exit of the heated segment.

b. Inspection shows that the tube surface is in fact rough, with a characteristic dimensionless surface roughness of
Repeat the calculations in Part a.

 c. Due to poor manufacturing, it is found out that water leaks out through the wall over a 5 cm long central segment of the heated segment, at the rate of 0.01 kg/s. Assuming that the heat flux and other conditions remain the same as Part b, estimate the surface temperature at the middle of the heated segment. For simplicity, assume that the leakage mass flux is uniform over the 5 cm long central segment of the heated segment