A. Introduction

Centrifugal forces in a fluid flowing through a curved pipe cause secondary flows that circulate outward into the core region of the pipe to form a pair of symmetric vortices. The combination of the main and secondary flows creates a flow pattern in which the maximum velocity is shifted outward from the center of the tube. The secondary flow produces a transverse transport of the fluid over the cross section of the pipe. This additional convective transport increases the heat transfer and the pressure drop when compared to that in a straight tube. The differences are particularly apparent in laminar flows.

B. Definitions

Figure 1 shows the geometry of a coil. The intensity of the secondary flow depends on the relative curvature \((d/D)\) of the coil, where d is the inner diameter of the tube and D the diameter of the curvature. The diameter of the curvature D is related to the diameter \(D_{c}\) and the pitch h of the helical coil by

\[\label{eq1} D=D_{c}\left[1+\left(\frac{h}{\pi D_{c}}\right)^{2}\right]\tag{1}\]