Length of exchanger
Length of exchanger
FIG. 11-1 Temperature profiles in heat exchangers. (a) Countercurrent. (b) Cocurrent.
UomATm to use in Eq. (11-4) is [Colburn, Ind. Eng. Chem., 25, 873 (1933)]
Uom A Tm
for countercurrent flow, where U'O is the overall coefficient evaluated when the stream temperatures are t1 and tj and U'Q is evaluated at tj and t" The corresponding equation for cocurrent flow is
Uom A Tm
.U'0(t'2 - t£), where U'„ is evaluated at t2 and t"2 and U" is evaluated at t1 and t". To use these equations, it is necessary to calculate two values of Uo. *
The use of Eq. (11-6) will frequently give satisfactory results even if Uo is not strictly linear with temperature difference.
Reversed, Mixed, or Cross-Flow If the flow pattern in the exchanger is not completely countercurrent or cocurrent, it is necessary to apply a correction factor FT by which the LMTD is multiplied to obtain the appropriate MTD. These corrections have been mathematically derived for flow patterns of interest, still by making assumptions 1 to 5 [see Bowman, Mueller, and Nagle, Trans. Am. Soc. Mech. Eng., 62, 283 (1940) or Hewitt, et al. op. cit.]. For a common flow pattern, the 1-2 exchanger (Fig. 11-2), the correction factor FT is given in Fig. 11-4a, which is also valid for finding FT for a 1-2 exchanger in which the shell-side flow direction is reversed from that shown in Fig. 11-2. Figure 11-4a is also applicable with negligible error to exchangers with one shell pass and any number of tube passes. Values of FT less than 0.8 (0.75 at the very lowest) are generally unacceptable because the exchanger configuration chosen is inefficient; the chart is difficult to read accurately; and even a small violation of the first assumption underlying the MTD will invalidate the mathematical derivation and lead to a thermodynamically inoperable exchanger.
Correction-factor charts are also available for exchangers with more
than one shell pass provided by a longitudinal shell-side baffle. However, these exchangers are seldom used in practice because of mechanical complications in their construction. Also thermal and physical leakages across the longitudinal baffle further reduce the mean temperature difference and are not properly incorporated into the correction-factor charts. Such charts are useful, however, when it is necessary to construct a multiple-shell exchanger train such as that shown in Fig. 11-3 and are included here for two, three, four, and six separate identical shells and two or more tube passes per shell in Fig. 11-4b, c, d, and e. If only one tube pass per shell is required, the piping can and should be arranged to provide pure countercurrent flow, in which case the LMTD is used with no correction.
Cross-flow exchangers of various kinds are also important and require correction to be applied to the LMTD calculated by assuming countercurrent flow. Several cases are given in Fig. 11-4f g, h, i, andj.
Many other MTD correction-factor charts have been prepared for various configurations. The FT charts are often employed to make approximate corrections for configurations even in cases for which they are not completely valid.
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