A Note on the Determination of Shearing Stress and Heat Flux around the Perimeter of a Duct

Extract

Graphical and experimental methods exist for the determination of the local shearing stress and heat flux on the boundary of a duct of constant cross section in a fully developed turbulent flow. While the graphical method (see for example Ref. 1) is simple to effect, the premise on which it is based is questionable and even so a high order of drawing accuracy is necessary for reliable results. In the graphical method, it is assumed that there is no turbulent stress on surfaces which are perpendicular to the w-velocity contours (see Fig. 1). The shearing forces on the elemental area which is subtended at the boundary are then equated to the difference between the pressure forces acting over the elemental area of the duct cross section. This is a clever technique, but the use of surfaces across which the w-velocity gradient is zero for the calculation of the boundary stress needs more justification. Similarly, for heat flux distribution by a graphical method, it is difficult to determine the planes in the duct across which there is no turbulent heat transfer. As for the stress, surfaces across which there is no temperature gradient are not necessarily coincident with surfaces of zero heat flow. For the experimental determination of the wall stress, the ingenious Preston tube is available, but for the heat flux there is no simple counterpart. Heat meters (and their associated instruments) which are sometimes used are difficult to manufacture and their data must be treated with care.