The sizing problem was introduced in Section 303. Assume that the factors discussed in that section have led to the selection of surface geometries for each fluid stream. Then, it is necessary to size the heat exchanger for the required thermal duty and fluid temperature, and pressure conditions. The remaining unspecified variables are the velocities for each flow stream. The heat exchanger will require minimum surface area if the velocity is chosen to use all the allowed pressure drop. Two approaches are possible.

The simplest method is to compute designs for a series of velocities that yield pressure losses above and below the allowable value. Each design meets the required thermal effectiveness (ε). Then, a graph of the calculated pressure drops versus the frontal velocity permits selection of the design velocity that meets the specified pressure drops. This approach is ideally suited for a digital computer design program. In essence, the design for each velocity is a rating problem calculation. Because the required thermal duty is known, the average fluid temperature of each stream is known, and the properties are evaluated at these average temperatures. The calculation procedure for a counterflow or parallel-flow heat exchanger is as follows.

1. From the required ε and given C_min /C_max, calculate the required NTU.
   
   
2. Calculate the required U A = NTU C_min.
   
   
3. Follow steps 1, 2, and 4–9 of the rating problem (Section 304).
   
   
4. Using the equation given in step 10 of the rating problem, calculate the required heat exchanger volume.
   
   
5. Calculate heat exchanger length as L = V /A_fr.
   
   
6. The frontal area (A_fr) is directly calculable, since the frontal velocity was initially specified for each stream.
   
   
7. Calculate the pressure drop following Section 305. This procedure is not applicable to a cross-flow design.

For a cross-flow design, independent specification of each velocity fixes the flow depth for each fluid stream. Adaptation of this procedure to cross flow requires setting the velocity for stream 1, and applying the procedure to a range of velocities for stream 2. Then repeat this procedure with a new velocity for stream 1. This will likely require multiple sizing calculations. However, they may be done quickly using a computer.

The second procedure uses the coupled heat transfer and pressure drop equations for each channel. The heat transfer coefficient may be written as