The three dimensional integrated circuit (3D-IC) brings new challenges to chip thermal management due to its high power density. Micro-channel based liquid cooling shows great potential in removing high density heat in 3D circuits. The current micro-channel heat sink designs spread the entire surface to be cooled with micro-channels. This approach, though might provide sufficient cooling, requires quite high pumping power. In this paper, we investigate designing of nonuniformly distributed micro-channel cooling systems which provide sufficient cooling with less pumping power. Using the proposed non-uniform micro-channel heat sink, dynamic thermal management is also investigated by tuning the pressure drop across the micro-channels. The experiments show that, compared with the conventional design which spreads microchannels all over the chip, our non-uniform micro-channel design and thermal management achieves more than 70% pumping power savings.