Low Reynolds number flow irreversibility inside straight channels with irregular crossection

A widespread conviction has been established that the two competing irreversibilities in a duct flow with heat transfer always lead to the existence of an optimum that characterizes a minimum of an objective function related to entropy generation. This paper clearly shows that when an objective function is represented by the entropy generation rate per unit heat capacity rate of the fluid, the thermodynamic optimum flow regime represents a rather rare occurrence in the laminar region of irregular ducts. The analysis is performed for selected ranges of relevant geometric, flow, and thermal parameters. The study has been conducted for a set of straight ducts with irregular free flow area cross-sections. The following geometries were investigated: sine duct, circular duct, elliptical duct, moon shaped ducts, and four cusped duct. The range of Reynolds numbers has been established between O(10²) and O(10⁴). The existence of this objective function minima is confirmed for ducts with irregular crossection only for very small hydraulic diameters. These minima are relatively weak, and as a general rule, the set of optimal parameters is close to the onset of turbulence or possibly in the transitional or turbulent regions. The most pronounced extrema are found for the four cusped duct geometry.