Even though most internal flow heat transfer experiments and correlations of data have been done in pipes with circular cross sectional areas, there is an equation to find out a hydraulic diameter for almost any geometric shape. The equation for the hydraulic diameter is,

where Ac is the cross sectional area and P is the wetted perimeter. After using this equation to find the hydraulic diameter, the rest of the problem can be approached in the same manner as if it were circular pipe.

The steady-state forced convection in a an air-cooled horizontal equilateral triangular duct was investigated experimentally under a hydrodynamic fully developed turbulent flow condition. The length of the duct was 2.4 m and the cross sectional area of the duct consisted of an equilateral triangle with side length of ??. Heat exchangers that consist of ducts with triangular cross sectional area have a very high ratio of heat transfer area to overall volume, therefore they are a good choice when compactness is important. However its major disadvantage is relatively poor performance in heat transfer per unit area. The purpose of the experiment was to maximize the heat transfer per unit area by using different surface finishes in the inside of the duct. In the analysis of the data only the data acquired from the smooth duct will be used. The Prandalt number and thermal conductivity of the fluid were assumed to be constant, Pr = ?? , k = ?? .

T. T. Wong and C.W. Leung "Forced-Convection Augumentation of Turbulent Flow in a Triangular Duct with Artificially Roughened Internal Surface" Experimental Heat Transfer vol. 15 : pp. 89-106, 2002

1. Given the dimensions of the triangular duct, determine the hydrodynamic diameter.
2. Plot the given data Nud vs. Red and fit it with a power trendline.
3. Display the equation of the trendline that fits the data and compare it with the equation given in the book for turbulent flow. ( Nud=0.023Red4/5Prn ) where n=0.4 for heating of the fluid.