The design of a plate-fin heat exchanger requires the use of a special terminology. First, a terminology is required to define the geometric characteristics of a particular surface geometry. Second, certain relations are required to define the geometry of the heat exchanger. The geometric factors needed to specify the fin geometry are (1) the basic surface description, (2) plate spacing b, (3) hydraulic diameter D_h, (4) fin thickness δ, (5) surface area per unit volume between parting sheets β, and (6) fraction of total surface area formed by the fins A_f /A. The derived geometric factors D_h, β, and A_f /A are calculable for each fin surface geometry.

Consider a rectangular fin and parting sheets as shown in Figure 296.1. This material is stacked to make a two-fluid cross-flow heat exchanger as shown in Figure 1a. The fin detail and dimensions are shown in Figure 1b. Its basic geometric dimensions are the plate spacing (b), fin thickness (δ), flow length (L), and center-to-center fin pitch (p_f). Other derived geometric factors are required to define the flow and heat transfer surface geometry for each stream of the heat exchanger. The geometric factors that must be specified for each of the exchanger streams are: A_c (stream free flow area), A_fr (stream frontal area), L (flow length), γ (ratio of stream free flow area to frontal area), and σ (surface area per unit volume). The thickness of the parting sheets is a, and the total heat exchanger volume is V. Defined below are the derived surface and core geometric relations for a specific core channel geometry. The terminology is also defined in the Nomenclature at the end of the section.

Figure 1 (a) Two-fluid heat-exchanger geometry elements; (b) detail of fin cross section

The derived geometrical parameters of a surface geometry are

\[\sigma=\frac{\mbox{Minimum Flow Area}}{\mbox{Wetted Perimeter}}=\frac{A_{c}}{A_{fr}}=\frac{(p_{f}-\delta)(b-\delta)}{p_{f}b}\]