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A tree-like network heat sink with diverging–converging channel is designed, and effect of flow rate, channel diverging-converging angles on the flow and heat dissipation performance of the tree-like network heat sink is analysed and compared by numerical simulation. Results show that the diverging– converging angle of 2° can reduce the pressure drop by 14% when inlet mass flow rate is 0.00499kg/s. And the maximum temperature, the temperature difference between the maximum and minimum of the heat sink increases by 0.63K and 0.92K respectively. As the diverging-converging angle increases to 4°, however, it only reduces the pressure drop by 13% and can not bring more pressure drop due to formation of flow recirculation inside the tree-like network heat sink channel. Therefore, the diverging–converging fractal micro-channel heat sink with 2° has good heat dissipation performance with obvious lower pumping power.