Page 196 - Chemical process engineering design and economics

178 Chapter 4

value of 2.5xlO~ 4 for the fouling resistance for raw water and a low value of IxlO" 4
for the fouling resistance for distilled water, which is clean. Thus, the overall heat-
transfer coefficient,

3
3
4
4
U 0 = l/[2.5xlQ- + (l/5.0xl0 ) + (l/5.0xl0 ) + l.OxKT ]
2
3
2
= 1.333 x 10 W/m -K (235 Btu/h-ft -°F)
This value for the overall heat-transfer coefficient appears to be on the high side.
Ludwig (4.15) reports a range of coefficients of 170 to 225 Btu/h-ff^F (965 to
1280 W/m2-K) for raw water in the tubes and treated water in the shell. We will
use the value of the coefficient calculated above, and then, correct the area calcula-
tion by using a large safety factor.
For a cooler, select from Table 4.4 an approach temperature difference of
5.0 °C, which is an economic rule-of-thumb. This approach is selected rather than
the upper limit of 50.0 °C to conserve heat, but the surface area will be larger for
the 5.0 °C approach. From Equation 4.5.8, the exit raw-water temperature, t2,
equals 29 °C. Because the raw water has a tendency to scale, it is located on the
tube side. At a water temperature of about 50 °C and above, scale formation in-
creases so that the exit water temperature should never exceed 50 °C (122 °F).
From Equation 4.5.5, the logarithmic-mean temperature difference is

(30-23)-(34-29)
(At) LM =——————————— = 5.944 °C (10.7 °F)
(30 - 23)
hi —————
(34 - 29)

Next, calculate the logarithmic-mean temperature difference correction fac-
tor, F, from Equation 4.5.4. Calculate F either from Equation 4.10 or use plots of
Equation 4.10 given in the chemical engineering handbook [1]. In either case, first
calculate the parameters R and S. R and S are defined in Figure 4.7.
34-30
R = ———— =0.6667
29-23

29-23
S =———— =0.5455
34-23

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