A second law comparison for optimum shape of duct subjected to constant wall temperature and laminar flow

Various cross sectional duct geometries were compared from the point of view of entropy generation and pumping power requirement in order to determine the possible optimum duct geometry which minimizes the exergetic losses within the range of laminar flow conditions and constant wall temperature. Duct geometries used are; circular, square, equilateral triangle, rectangle with aspect ratio 1/2 and sinusoidal with aspect ratio √3/2. It is shown that the optimum duct geometry for constant thermophysical properties depends on the Reynolds number, however, the circular duct geometry is found to be the favorable one especially when the frictional contribution of entropy generation becomes dominant. Triangular and rectangular duct geometries are in general the worst choices for both entropy generation and pumping power requirement.