Based on entransy theory, this paper proposes a new mathematical model for multi-scale data center thermal management. A comparison of heat transfer optimizing is made first, using exergy/entropy method and entransy dissipation, to verify the fitness of entransy theory. Based on which, a complete model of entransy dissipation for data center heat transfer is built, from CPU level to data center room level, with detailed computational derivation. Specifically, the calculating method of entransy dissipated by undesired air mixing has been derived, which can give quantitative evaluation on air mixing to the entire thermal performance of data center. A case study of a CFD simulation and a CRAC retrofitting engineering have been performed to verify the entransy model. In the case study, the temperature penalty caused by undesired air mixing is calculated using the entransy analysis model and testified by the retrofitting test, which directly reduces the free cooling potential and decrease data center energy performance. This entransy theory based model offers a new method to better optimize the thermal management and gives specific measures to improve the thermal performance of data centers.