The pieces with micro and nano scales are used in many industries such as electronic, design of cooling channels in computers and electromechanic systems. The performance of these pieces is directly related to their temperature; therefore, they should be kept under the favorite temperature. Microchannels are an efficient way to absorb the high heat generation of the small electronic pieces. For the optimization geometry characteristics of microchannels, constructal theory is a good means. This theory finds the best structure by predicting the procedure of various designs. In this study, the arrived heat flux to the bottom surface of microchannel was considered as step function. Optimum geometry of the rectangular micro-channel has been determined in such a way that rectangular micro-channels configuration would have maximum heat transfer in the unit volume. The numerical simulation was performed on a unit cell . Numerical optimization for rectangular cross-section was performed. Based on the results of this investigation, some correlations were proposed to predict the optimal hydraulic diameter and the dimensionless heat transfer per unit volume. Rectangular micro-channel heat sinks were geometrically optimized to find the highest heat conduction of channels. Actually, the purpose of the geometric optimization was to determine the optimal values of these parameters in such a way that the peak temperature of the wall was minimized. The output results were verified by the previous results where good agreements were observed. The effects of solid volume fraction, aspect ratio, hydraulic diameter and heat flux from parallel and serial flows upon the peak temperature of the mentioned micro-channels are investigated. Moreover, these micro-channel heat sinks are compared with each other at their optimal conditions. The optimal shapes of rectangular channels were achieved numerically and compared with the approximate results obtained from scale analysis where good agreements were observed. In addition to the external structure, internal structure of the micro-channel was allowed to vary. In fact, the optimum possible geometry of the micro-channel heat sink was acquired numerically considering another degree of freedom of the micro-channel heat sink. Using the intersection of asymptotes method, some equations were derived to calculate the internal dimension of microchannel. The rectangular microchannel heat sinks with a non-uniform heat fluxes were investigated. Considering a fixed length and a fixed volume a 3D numerical simulation was performed. The analytical equations showed that the usage of non-uniform heat flux caused changes in the channel internal dimensions. The external dimensions of channel were different for various heat flux values, even in the optimum situation. Moreover, it was observed that the maximum temperature in the parallel flow was less than its peer in the serial flow. Key words :Constructal Theory, Rectangular Micro-Channel Heat sink, Optimization, Non- Uniform Heat Flux
