Water flowing at a rate of 10 kg/s through 50 tubes double-pass shell and tube heat exchanger heats air that flows through the shell side. The length of the brass tubes is 6.7 m and they have an outside diameter of 2.6 cm and an inside diameter of 2.3 cm. The heat transfer coefficient of the water and air are 470 W/(m2 K) and 210 W/(m2 K), respectively. The air enters the shell at a temperature of 15°C and a flow rate of 16 kg/s. The temperature of the water as it enters the tubes is 75°C. Calculate (a) the heat exchanger effectiveness, (b) the heat transfer rate to the air, and (c) the outlet temperature of the air and water.

Question

GIVEN

• Shell-and-tube heat exchanger - one shell, two tube passes

• Water in brass tubes, air in shell

• Water flow rate ( m w)= 10 kg/s

• Number of double passes (N) = 50

• Tube length (L) = 6.7 m

• Tube diameters

? Do = 2.6 cm = 0.026 m

? Di = 2.3 cm = 0.023 m

• Heat transfer coefficient

? Water ( )ih = 470 W/(m2 K)

? Air ( )oh = 210 W/(m2 K)

• Air inlet temperature (Ta,in) = 15°C

• Air flow rate ( m a)= 16 kg/s

• Water inlet temperature (Tw,in) = 75°C

FIND

(a) Effectiveness (e)

(b) The heat transfer rate (q)

(c) Outlet temperatures (Ta,out, Tw,out)

ASSUMPTIONS

• Tube length includes both passes

SKETCH



OPERTIES AND CONSTANTS

the specific heat of water at 75°C (cpw) = 4190 J/(kg K)

the specific heat of air at 15°C (cpa) = 1012 J/(kg K)

the thermal conductivity of brass (kb) = 111 W/(m K)

Answer 1

The heat capacity rates are



(a) The overall heat transfer coefficient is



The transfer area is A = N(? Do L) = 50[? (0.026 m)(6.7 m)] = 27.36 m2 The Number of transfer units is



for Cmin/Cmax = 0.4 and NTU = 0.235, e ? 0.20 = 20% (b) The rate of heat transfer is



(c) For the water



For the air