Question

Cooling water available at 10°C is used to condense steam at 30°C in the condenser of a power plant at a rate of 0.15 kg/s by circulating the cooling water through a bank of 5-m-long 1.2-cm-internal-diameter thin copper tubes. Water enters the tubes at a mean velocity of 4.75 m/s and leaves at a temperature of 24°C. The tubes are nearly isothermal at 30°C.

The properties of water at the average temperature of (10+24)/2=17°C are:

ρ = 998.7 kg/m³

c_p = 4183.8 J/kg.°C

A.

Determine the average heat transfer coefficient between the water and the tubes.

_________kW/m².°C

B.

If the heat transfer coefficient is 14.3 kW/m².°C, calculate the number of tubes needed to achieve the indicated heat transfer rate in the condenser.

Answer 1

Solution The bulk temperature of water is to Ti + Te. 24+ 10 -17°C 22 diameter of copper tube (dl= 0.012 m A. EX0-012 1.1309 x10m we know m= SAV 998.7 x 1-1309 *104x475 -0.5365 kg/s Heat transfer through one tube Q = mc (Te-T;) -0-5365* 4.183 (24-10) = 31.4173 kw The log-mean temperature will be 4та - лте - 4т: Ate= (30-24) (30-10) en 30-247 I 30-10 Aton = 11063°C] copper tube A - 7dL 7 x 0.012 X 5 The area of = 0.1885 m Since Q - hasaten hier As aten he 31:44173 0.1885 X 1063 ho 14:33 W/m²°C] at 30'c hay = 2431 kJ/kg > Q = mcond y hag Q-0.15 2431 - 364.65 kW :. n. Q total 364•65 = 1.506 31.4173 Ina 12 tubes !