Heat and fluid flow are widely used in many industrial applications.With developing the production of micro and nano scale pieces, improvement in their thermal performance is one of the most important topics. These pieces could be used in the electronic, computer and electromechanical systems. The speed of processors in these pieces relates directly to their temperature, so keeping in the appropriate temperature is necessary. The target is to reach the maximum heat transfer rate with considering some limitations such as cooling channels volume, constant heat flux, and the actual temperature of the piece. Various methods were suggested for optimization of electronic systems with high heat flux production. One of the useful methods to improve heat transfer in electronic devices in various configurations is the use of channels with smaller dimensions down to micro and nano scales because of high heat transfer coefficient. For example, using forced convection inside the micro-channels as the heat sink has been proposed for cooling the electronic pieces that have a high temperature. The micro-channels arrangement has a sensible effect on heat transfer rate. Constructal theory is a method of geometrical optimization with iire of nature. The constructal theory concepts, which introduced first by Bejan, deals dominantly with shapes and geometry of flow structures. In the constructal theory, flow structure is developed to access the best performance during time. The designer assembles system components to achieve the maximum performance. In this project convective heat transfer cooling of a square shape piece with internal heat generation was considered. The coolant enters at the center of the piece and flows through the diagonal channel path. Distributed fluid is used again for cooling by the second fluid collector network that located below the first microchannels network. Flow enters the reverting channels by vertical interconnections. It merges again successively into a larger channel until it leaves the network through the central region. The purpose of this study is the analysis of the system configuration somehow the thermal resistance reaches its minimum value. In this project, number of branches, length and width ratio in each branch in tree network are investigated. Using of reverting microchannels led to considerable decrement in maximum temperature. The computed results show that the number of branches had a noticeable effect on the maximum value and uniformity of temperature. In the channels with high pressure drop, the contribution of mass flow is lower, so the temperature of zones near these channels increases. Keywords: Constructal theory, Square piece, Convective cooling, geometrical optimization