The expression of local exergy destruction rate is deduced on the analysis of convective heat transfer. Lagrange function is constructed with local exergy destruction rate set as optimization objective and prescribe flow power consumption as constraint condition. Besides

energy and mass conservation laws are taken into consideration in this Lagrange function. By taking variation on the Lagrange function

optimization equations are obtained. Through numerical simulation

the optimization equations are solved in the convective heat transfer for elliptical tube flow and the optimized velocity and temperature fields are obtained. The results show that the optimum flow structure in the elliptical tube is longitudinal swirl flow with multi-vortexes. Compared with the elliptical tube with general governing equations (Navier-Stokes equations)

the optimized flow has a good heat transfer rate with low increase of flow resistance and the comprehensive performance

(Nu/Nus)/(f/fs)

is 3.21. Furthermore

the distribution of vortexes in the elliptical tube is also obtained which is significant to improve the design of elliptical tubes.