The LMTD is the temperature difference at one end of the heat exchanger less the temperature difference at the other end, divide by the natural logarithm of the ratio of these two differences. This calculator computes the ideal and true mean temperature differences for one or more shell-and-tube heat exchanger in series. The hot and cold fluids are assumed to be flowing countercurrent to each other.
The ideal LMTD applies to the double-pipe heat transfer arrangement where the convective heat transfer coefficients are more or less constant. For more complex heat exchanger arrangements involing multiple tubes, several shells passes and crossflow, it is necessary to apply a correction factor, usually read from graphs and charts.
Here, the correction factor is derived via Bowman's solution for an exchanger with multiple shell passes. The number of shell passes is automatically incremented until the resulting correction factor just exceeds the minimum desired. This task is accomplished by the iterative solution of the following Equations:
where
LMTD = Log mean temperature difference
CLMTD = Corrected Log mean temperature difference
F = Correction factor
Th1 = hot fluid inlet temperature
Th2 = hot fluid outlet temperature
Tc1 = cold fluid inlet temperature
Tc2 = cold fluid outlet temperature
N = number of shell passes = shell passes per shell x number of shell units in series
P = temperature efficiency
R, X = terms for convenient grouping of variables
All temperatures are in same units (i.e. all ° F or all ° C).
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