HEAT TRANSFER 177
Thus, assuming one shell pass, two tube-side passes, from Figure 9.71:FD 0 .82 and
mFD
0. 82 ð 180 D 147 .6K
Thus, in equation 9.212:AD
417. 4 ð 103 /
30 ð 147. 6 D 94 .3m^2 and:
total length of tubingD
94. 3 / 0. 1005 D938 m.Using standard tubes 2.44 m long, number of tubesD
938 / 2. 44 D384 or
384 / 2 D
192 tubes/pass.
The cross-sectional area for flow would then be
192 ð 0. 00050 D 9. 61 ð 10 ^2 m^2
and the air velocityD
4. 03 / 9. 61 ð 10 ^2 D 41 .9m/s.
This is not excessive providing the minimum acceptable pressure drop is not exceeded.
The nearest standard size is 390ð32 mm o.d. tubes, 2.44 m in a 940 mm i.d. shell
arranged on 40 mm triangular pitch in two passes.
PROBLEM 9.45
A large block of material of thermal diffusivityDHD 0 .0042 cm^2 /s is initially at a
uniform temperature of 290 K and one face is raised suddenly to 875 K and maintained
at that temperature. Calculate the time taken for the material at a depth of 0.45 m to
reach a temperature of 475 K on the assumption of unidirectional heat transfer and that
the material can be considered to be infinite in extent in the direction of transfer.
Solution
This problem is identical to Problem 9.2 except for slight variations in temperature, and
reference may be made to that solution.
PROBLEM 9.46
A 50% glycerol – water mixture is flowing at a Reynolds number of 1500 through a 25 mm
diameter pipe. Plot the mean value of the heat transfer coefficient as a function of pipe
length, assuming that:NuD 1. 62
Re Pr d/l ^0.^33.
Indicate the conditions under which this is consistent with the predicted valueNuD 4. 1
for fully developed flow.
Solution
For 50% glycerol – water at, say, 290 K:D 0 .007 N s/m^2 ,kD 0 .415 W/m K andCpD
3135 J/kg K.
∴
hð 0. 025 / 0. 415 D 1 .62[
1500 ð 3135 ð 0. 007 / 0. 415
0. 025 /l ]^0.^33
∴ hD 26. 89
1983 /l ^0.^33 D 330 /l^0.^33 W/m^2 K
his plotted as a function oflover the rangelD0 – 10 m in Fig. 9d.
WhenNuD 4 .1:hD 4. 1 k/dD
4. 1 ð 0. 415 / 0. 025 D 68 .1W/m^2 K.
Taking this as a point value,lD
330 / 68. 1 3 D 113 .8m