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Constructal analysis of tree-shaped microchannels for flow boiling in a disc-shaped body has been carried out to achieve an energy efficient design for chip cooling. n 0 channels touch the center and np channels touch the periphery. Three different complexities have been investigated: the radial flow pattern where n 0 = np; the one pairing level flow pattern where 2n 0 = np; and the two pairing level flow pattern where 4n 0 = np. The fluid is R-134 a evaporating at a temperature of 300 K. The fluid enters under a saturated state at the inlet and exits at the periphery. Throughout this paper, the constraints are the total volume of ducts V and the radius of the disc R. The degrees of freedom are the number of channels touching the center n 0, the number of peripheral channels np, and the mass flow rate. The disc, made of copper, is subjected to a heat flux on both its faces. Heat conduction has been simulated in the disc in the radial and angular directions combined with the boiling heat transfer coefficients and the pressure drops along the channels. The temperature field has been calculated and it can be observed that the highest temperature is located where the distance between two microchannels is the largest (most often at the periphery). For characterizing successive diameter ratios for complex structures, Murray's law is shown to be the best solution when using the homogeneous model for calculating the pressure drops. As a first conclusion, we can say that increasing the number of channels decreases the thermal resistance, whatever the complexity is. It is shown that the use of a radial structure with 2n 0 central channels is more efficient than a one pairing level design with n 0 central channels. Deeper analysis leads to different conclusions. For low pumping power, the radial flow pat- - tern presents the lowest thermal resistance. For medium pumping power, one pairing level design shows the lowest pumping power. For higher pumping power, the design with two pairing levels exhibits the best solution. Finally, complexity is not necessarily the best solution.