The fast development of computing technology has led to the miniaturization and density integration of electronic devices. However, this miniaturization involves more heat generation per unit area. Consequently, the working temperature of the electronic components may exceed the desired temperature level. Since the performance of equipment has a direct relationship with its temperature, it is important to keep it at an acceptable temperature level. Among proposed methods to improve cooling technology of electronic equipment ,micro-channel heat sinks have attracted more attention because of low coolant requirements and high heat transfer coefficient . Different methods are used in optimizing micro-channels, one of which is constructal theory. The purpose of the current project is optimization of an array of circular ducts and geometric optimization of single-layer, double-layer and multi-layer circular micro-channel heat sinks. Proposed system consists of a fixed volume which is cooled by laminar forced convection. In the geometric optimization of an array of circular ducts, optimal dimensions were determined using an approximate method and a numerical method, so that the dimensionless heat transfer per unit volume was maximized. Air was considered as the coolent fluid and the pressure difference along a unit cell was fixed. It was found that the optimal size of the channel is independent of the array configuration and only depends on the length constraint and the pressure drop. Geometric optimization of circular micro-channel heat sinks was performed in two different conditions: when air flow was entered from one side of the channel (one-sided entrance flow) or from both sides of the channel (two-sided entrance flow). The purpose of geometric optimization was to reach maximum overall thermal conductance. Cooling fluid was considered water and the pressure difference was fixed. Also, length of micro channel and its volume were constant. The uniform heat flux arrives at the bottom surface of micro-channel heat sink. Optimization was performed for four different volume fractions. Optimal dimensions for single-layer, double-layer and multi-layer circular micro-channel heat sinks were determined so that the maximum temperature of the system is minimized. Results showed that effect of thickness ratios on maximum temperature of the system is not considerable. Also, extent of closing channels to each other and to the bottom surface of heat sinks depends on mechanical strength of the system and it has to be studied more. Eventually, it was found that a double-layered micro-channel heat sink had a better cooling performance than a single-layer micro-channel heat sink and adding a middle layer did not improve cooling performance. By studying the effect of applying two-sided entrance flow, it was observed that double-layer micro-channel heat sink with two-sided entrance flow has better cooling performance than a micro-channel heat sink with one-sided entrance flow. Two different cases ? and ?? for multi-layer circular micro-channel heat sinks were investigated. Results showed that among multi-layer micro-channel heat sinks with one-sided and two-sided entrance flow, micro-channel heat sink with two-sided entrance flow ,case ?, provides the best cooling performance. Key words : Constructal theory, Multi-layer circular micro-channel, Heat sink, Optimization
