Topology optimization modifies the material distribution in the design domain to produce micro-channel structure with improved thermal performance. In this work, five heat dissipation micro-channel structures with various design domain aspect ratios are optimally designed based on the bi-objective topology optimization method. The optimal design variable fields, temperature fields, and pressure fields are subsequently obtained for each operating condition, and the flow heat transfer effect and the enhanced heat transfer mechanism are investigated under various working conditions. On this basis, the flow heat transfer impact of micro-channels under various operating situations is optimized and studied by combining the field synergy concept and entransy dissipation theory. The findings show that when the Reynolds number rises in the laminar flow region, the complexity of the topological flow channels also rises. The average temperature, Tave,decreases, Nusselt number rises, the inlet and outlet pressure drop, ΔP, gradually increases, the integrated enhanced heat transfer factor PEC gradually decreases, the field synergy number, Fc, increases, the pressure drop synergy angle, θ, gradually increases, the entransy dissipation, Evh, increases, and the flow heat transfer performance of each heat dissipation channel is also enhanced due to the complex channels and high Reynolds number in the domain. The investigation of micro-channels with various topologies revealed that the micro-channels with the same boundary conditions and a design domain aspect ratio of 25/64 had the best synergy effects of velocity-pressure gradient and velocity-temperature gradient, the best heat transfer effect, and the best flow characteristics.