Convective heat transfer plays an important role in both the fundamental research and the development of high-performance heat exchangers. Inspired by blades of grass vibrating in the wind, we developed a self-agitator for convective heat transfer enhancement. Because of fluid-structure interactions, the agitator, with self-sustained vibration, can generate strong vortices to significantly break the thermal boundary layer and improve fluid mixing for enhanced convective heat transfer. In particular, we establish a methodology to link the vorticity field at a preferred frequency to the optimal improvement in the convective heat transfer. To identify the self-agitator preferred frequency, mode analysis is performed with simulation results using dynamic mode decomposition. Experimental results are also obtained to further validate the proposed approach. These results show that the proposed self-agitator design can improve the convective heat transfer by 120% in a conventional heat exchanger without additional pumping power requirements and can achieve a Nusselt number of up to 30 within the laminar flow region, which is improved by 200% with the same Reynolds number compared to the clean channel.