Convective heat transfer optimization based on minimum entransy dissipation is studied in this paper. By setting entransy dissipation as optimization objective and power consumption as constraint condition, optimized fluid momentum equation with additional volume force for convective heat transfer are deduced by variational principle. Numerical investigations for convective heat transfer in a straight circular tube based on optimized governing equations are conducted. The results show that there exist longitudinal swirl flows with multi-vortexes in the tube, which leads to heat transfer enhancement at relatively small flow resistance. The present analysis for heat transfer and flow shows that this kind of optimized flow field can realize a far greater increase in heat transfer than that in flow resistance, which indicates that the investigated optimization method is useful in design of heat transfer enhancement. (C) 2014 Elsevier Ltd. All rights reserved.