We develop a constructal approach that is capable of finding constructal microstructure of nanofluids for constructal system performance. The approach converts the inverse problem of optimizing the microstructure for the best system performance into a forward one by first specifying a type of microstructures and then optimizing system performance with respect to the available freedom within the specified type of microstructures. The approach is applied to constructal design of nanofluids with any branching level of tree-shaped nanostructures in a circular disc with uniform heat generation. The constructal configuration and constructal system thermal resistance have some elegant universal features for both cases of given aspect ratio of the periphery sectors and given the total number of slabs in the periphery sectors, respectively. While our focus is on the constructal design and optimization of nanofluids microstructure, the methodologies and results are equally valid for other problems such as heat conduction optimization for cooling a disc-shaped area. (C) 2010 Elsevier Ltd. All rights reserved.