Hot water is to be heated from 10 to 30°C, at the rate of 300 kg/s by atmospheric pressure steam in a single-pass shell-and-tube heat exchanger consisting of 1-in. schedule 40 steel pipe. The surface coefficient on the steam side is estimated to be 11,350 W/(m2 K). An available pump can deliver the desired quantity of water provided the pressure drop through the pipes does not exceed 15 psi. Calculate the number of tubes in parallel and the length of each tube necessary to operate the heat exchanger with the available pump.

Question

GIVEN

Single-pass shell-and-tube heat exchanger Water is heated by atmosphere steam Water temperatures

? Tw,in = 10°C

? Tw,out = 30°C Water flow rate ( m w)= 300 kg/s Inner tube: 1 in. schedule 40 steel pipe Maximum water pressure drop (?p) = 15 psi = 103,422 N/m2 Steam side heat transfer coefficient ( oh ) = 11,350 W/(m2 K)

FIND

(a) The number of tubes in parallel (N)

(b) The length of each tube (L)

ASSUMPTIONS The tube is smooth The tube is 1% carbon steel Uniform pipe surface temperature Fully developed flow in pipe Water flow is turbulent to insure good heat transfer

SKETCH



PROPERTIES AND CONSTANTS

for 1 in. schedule 40 pipe

Inside diameter (Di) = 1.049 in. = 0.0266 m

Outside diameter (Do) = 1.315 in. = 0.0334 m

the saturation temperature of steam at 1 atm = 100°C

for water at the average temperature of 20°C

Absolute viscosity (?) = 993 × 10–6 Ns/m2

Density (?) = 998.2 kg/m3 Specific heat (cpw) = 4182 J/(kg K)

Thermal conductivity (kw) = 0.597 W/(m K)

Prandtl number (Pr) = 7.0,

the thermal conductivity of 1% carbon steel (ks) = 43 W/(m K).

Answer 1

The Reynolds number for the water flow through the pipes is



The friction factor for turbulent flow through smooth tubes for 105 < Re < 106 is



The pressure drop through the tube is



The heat capacity rate of the condensing steam is essentially infinite, therefore, Cmin/Cmax = 0. The effectiveness, is



NTU ? 0.25



The overall heat transfer coefficient (Uo) is



For fully developed turbulent flow with constant surface temperature, the Nusselt number in the pipe is



Substituting these and L = 2.75 × 10–4 N1.8 m into the expression for NTU



Canceling all units



By trial and error, N = 220

Therefore