In the last few decades, scientific developments and daily increment needs for design and manufacturing of the smaller devices with stronger capability have changed international public direction of the investigations, technology and industry for using of new devices in micro and nano dimensions. These devices are used for different aspects such as electronic and cooling of the circuit which are applied in design and manufacturing of the computers and electro-mechanic systems. Inasmuch as working condition of this equipment is directly related to its temperature, keeping it in the safe temperature limitation is vital. Many different methods have been proposed to improve the cooling process of the electronic systems with massive heat flux production and compacted size. Among these methods, micro-channel heat sinks have attracted more glances because of the high heat transfer coefficient and low need of cooling fluid. Different algorithms and methods are used for dimensional characteristics optimization of the micro-channels; Contructal theory is one of these methods. In the first and second parts of the present project, some aspects of Constructal theory and its point of view about optimization in biological systems and also its usage in micro-channels and advanced manmade equipment have been presented. In the third section, optimum geometry of the trapezoidal micro-channels with the side angles of 30, 45, 60 and 75 degree has been determined in such a way that trapezoidal micro-channels configuration would have maximum heat transfer in the unit volume. As optimal dimensions were independent of the array configuration, the numerical simulation was performed on a unit cell. Numerical optimization for trapezoid cross-section with different side angles was performed. Based on the results of this investigation, some correlations were proposed to predict the optimal hydraulic diameter and dimensionless heat transfer per unit volume. In addition to examining the effect of pressure drop on these parameters, it was showed that among the different geometries of this study, trapezoid cross-section with the side angle of 75 o has the most efficiency for a given volume. In the fourth section, trapezoidal micro-channel heat sinks are geometrically optimized finding the highest heat conduction of channels. The cross-sectional areas of the mentioned micro-channels can change regarding to the degrees of freedom, i.e. the aspect ratio and the solid volume fraction. Actually, the purpose of the geometric optimization is to determine the optimal values of these parameters in such a way that the peak temperature of the wall is minimized. The effects of solid volume fraction and pressure drop upon the aspect ratio, hydraulic diameter and 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 all trapezoidal channels were achieved numerically and compared with the approximate results obtained from scale analysis which good agreements were observed. In the last section, 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. It was noteworthy that the effect of variation of coolant fluid thermophysical properties on the characteristics of fluid flow and heat transfer was also considered. Key words Constructal theory, Trapezoidal micro-channel, Heat sink, Optimization.