Based on the analysis of the irreversibility of heat transfer process, a physical quantity called enerty is introduced to establish an equilibrium equation which is different from conventional energy conservation equation. Comparing to minimum entropy generation and minimum entransy dissipation, an approach of minimum heat consumption is proposed to optimize heat transfer process. The transport efficiency, a criterion to evaluate heat transfer performance, is proposed based on the definition of heat consumption rate. By setting minimum heat consumption as optimization objective and fluid power consumption as constraint condition, a momentum equation with additional volume force is constructed through functional variation to numerically simulate convective heat transfer in coupling with energy equation. The results disclose that longitudinal swirl flow with single vortex or multi-vortexes appears in the flow field, which leads to heat transfer enhancement. Additionally, a sub-area method is developed to enhance convective heat transfer characterized by relatively higher Nu number, which can be applied to optimize flow field in a circular tube and guide the design for tube insert. The results further indicate that the area ratio and the intensity of additional volume force affect the distribution of temperature and velocity fields. A comparison among minimum heat consumption (MHC), minimum entransy dissipation (MED) and minimum power consumption (MPC) is conducted. The results show that heat transfer performances are close to each other for using the three approaches, which indicates that the proposed MHC approach is effective in designing tube insert or heat transfer unit. (C) 2012 Elsevier Ltd. All rights reserved.