Local analysis and visualization of convective heat transfer is fundamental for many engineering applications. In fact, the correlation between the flow structure and the transport of heat by advection and diffusion is crucial for designing and optimizing devices undergoing heat transfer, such as heat exchangers. The field synergy principle has been used for more than two decades in order to analyze and enhance the convective heat transfer in different applications. In this paper, the validity of the field synergy principle in elliptic flows is tested for both laminar and turbulent flow regimes. For this end, the flow past a backward facing step is considered for a wide range of Reynolds numbers based on the step height ranging from 36 to 36,000. It is shown that the synergy angle and synergy number both fail to represent the local physics of heat transfer process near the step. This is caused by the assumption of negligible molecular and turbulent thermal diffusivities in this principle. In this paper, it is shown that these diffusivities play a crucial role in heat transfer in elliptic flows and cannot be ignored. Moreover, a global analysis shows that the field synergy number could be used to predict the Nusselt number variation if the elliptic region in the flow is small however, the synergy angle fails here also to characterize the variation in Nusselt number.