Compact Heat Exchangers

Appendices

A.1 Derivation of Fourier Series Mathematical Equation

The heat exchanger core frontal face is a rectangular domain having edges 2a, 2b in x‐y plane as shown in Figure 4.10b and will be a square domain when a = b. The sides of the rectangle are along the straight lines x = a, x = −a, y = b and y = −b.

The Navier‐Stokes equations are,

(A‐1)

(A‐2)

(A‐3)

(A‐4)

(A‐5)

(A‐6)

Consider that the cold fluid flows in the z‐direction, which is parallel to the wall of the rectangular duct. There is no cross flow for the cold fluid. Hence

(A‐7)

(A‐8)

Inertial terms drop out from the full Navier–Stokes equations. There is a constant pressure gradient in the z‐direction and = constant. ...