The advanced heat flux manipulating structures inspired by TO-based spatial mapping have aroused wide interests owing to huge potential in high-efficient thermal energy utilization. However, most researches are limited to the realization of single function in one specific structure and appropriate evaluation of the energy transfer process is relatively lacking. In this work, based on time-dependent two-dimensional heat conduction equation, a co-effect structure capable of accomplishing concentration and rotation functions simultaneously is established and validated by finite element simulations compared with the conventional single concentrator and singe rotator. In addition, from the perspective of thermodynamics, the transformed local entropy production rate and total entropy production are theoretically derived and applied to evaluate the quality of energy transfer processes. The proposed co-effect structure can help to explore other potential mass/flux manipulating devices and the evaluation method is valuable for the further manufacturing as well as optimization of these devices in engineering applications.