144 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS
With this value, the mean air and waste gas temperatures are 330 K and 440 K respec-
tively. These are within 10 deg K of the assumed values in each case. Such a difference
would have a negligible effect on the film properties and recalculation is unnecessary.
PROBLEM 9.14
Oil is to be heated from 300 K to 344 K by passing it at 1 m/s through the pipes of a shell-
and-tube heat exchanger. Steam at 377 K condenses on the outside of the pipes, which
have outer and inner diameters of 48 and 41 mm respectively, though due to fouling, the
inside diameter has been reduced to 38 mm, and the resistance to heat transfer of the pipe
wall and dirt together, based on this diameter, is 0.0009 m^2 K/W.
It is known from previous measurements under similar conditions that the oil side
coefficients of heat transfer for a velocity of 1 m/s, based on a diameter of 38 mm, vary
with the temperature of the oil as follows:
Oil temperature (K) 300 311 322 333 344
Oil side coefficient of heat transfer (W/m^2 K) 74 80 97 136 244
The specific heat and density of the oil may be assumed constant at 1.9 kJ/kg K and
900 kg/m^3 respectively and any resistance to heat transfer on the steam side may be
neglected.
Find the length of tube bundle required?
Solution
In the absence of further data, this problem will be worked on the basis of one tube.
Heat load
Cross-sectional area at the inside diameter of the scaleD
$/ 4
0. 038 2 D 0 .00113 m^2.
∴ volumetric flowD
0. 00113 ð 1. 0 D 0 .00113 m^3 /s
and: mass flowD
0. 00113 ð 900 D 1 .021 kg/s
∴ heat load,QD 1. 021 ð 1. 9
344 300 D 85 .33 kW
Temperature driving force
1 D
377 300 D77 deg K, 2 D
377 344 D33 deg Kand, in equation 9.9: mD
77 33 /ln
77 / 33 D52 deg K
Overall coefficient
Inside:
The mean oil temperatureD 0. 5
344 C 300 D322 K at which
hi based ondiD 0 .038 m D97 W/m^2 K.