AIR-COOLED HEAT EXCHANGER DESIGN

THEORY  &   FORMULAE

Sizing of Air-Cooled Heat Exchanger

Heat exchangers are systems that transfer heat between fluid mediums. The fluids or gases in a heat exchanger can be mixed or the energy transference can go through a conductive wall that keeps them separate. Heat exchangers are found in car radiators, furnaces, refrigerators, air conditioning, space heating, refining and chemical processing systems. Air-cooled heat exchangers typically have rectangular bundles containg several rows of tubes. The hot fluid enters at the top of the bundle, while air is blown by fans vertically upwards across the tube bank, i.e. counter current flow.

The calculator here is based on the correlations presented by Smith and Brown, and the series of equations presented by Blackwell to fit the graphs and tables of Smith and Brown. In brief, the method begins with the first equation, hinges on the iterative solution of the second equation below, and ultimately leads to the third equation, as described by Coker:
    
where
     R = number of tube rows
     U = overall heat transfer coefficient
     Q = exchager duty (heat load)
     C_i^'s = correlation constants
     t₁ = air outlet temperature
     t₂ = air inlet temperature
     T₁ = process fluid outlet temperature
     T₂ = process fluid inlet temperature
     A_f = face area of bundle
     V_f = face velocity of air
     W = tube bundle width
     L = tube width

Heat Exchanger Design & Log Mean Temperature Difference

THEORY  &   FORMULAE

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
     T_h1 = hot fluid inlet temperature
     T_h2 = hot fluid outlet temperature
     T_c1 = cold fluid inlet temperature
     T_c2 = 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).