Many ideas have been suggested to improve the cooling technology of electronic components with high heat flux generation and compact size. Among these ideas, micro-channel heat sinks drew more attention because of high heat transfer coefficients and low coolant requirements. For optimization of micro-channel heat sinks, different algorithms and methods have been used. One of these methods is the constructal theory. Electrokinetic effects are important for micro- and nano-scale traort applications, so they should be considered. First part of the thesis is about the geometric optimization of an array of circular and non-circular ducts. As optimal dimensions were independent of the array configuration, the numerical simulation was performed on a unit cell. Numerical optimization for circular, square and isosceles right triangle cross-sections of channels was performed.The second part reports the numerical geometric optimization of three-dimensional micro-channel heat sinks with rectangular, elliptic and isosceles triangular cross-sections. 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. Considering the constraints and geometric parameters for the optimization of the present study, it was revealed that the micro-channel heat sinks with rectangular and elliptic cross-sections have similar performances while micro-channels with isosceles triangular cross-sections show weaker performances. The optimal shapes of all three kinds of the channels were achieved numerically and compared with the approximate results obtained from scale analysis which good agreements were observed.In the third section, in addition to the external structure, internal structure of the micro-channel was allowed to vary. In fact in this section, the optimum possible geometry of the micro-channel heat sink was acquired numerically by 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. Finally the effect of Electrokinetic on the aspect ratio, channel hydraulic diameter and peak temperature was investigated Keywords: Constructal, non-circular micro-channel, heat sink, optimal shape, Electrokinetic.
