In this paper, exergy destruction is regarded as the irreversibility of heat transfer and a method to optimize the convective heat transfer is proposed by set exergy destruction rate as optimization objective and fixed fluid power consumption as a constraint condition. This paper will derive the optimum velocity field equation for steady laminar convective heat transfer by taking Lagrange functional variation on the objective equation. The optimumvelocity field equation will be numerically solved and the form of the velocity field will be found out. The optimumvelocity field will offer a guidance for selecting and designing an appropriate enhancement unit.