Innovative numerical optimization methodologies for the design of high-performance heat sinks.

The cooling of electronic devices is essential to guarantee their functional performance and operational lifetime. Due to continued miniaturization and integration of transistors in packaged chips, the heat dissipation rate has surpassed the limits of classical air-cooled heat sinks. This has triggered a lot of research towards alternatives for high heat flux cooling. 
Liquid cooling with micro heat sinks is one ofthese candidate solutions. Cold liquid flows through microscopic channels to extract heat from the chip. These microchannels are manufactured in a heat sink attached on top of the chip, or even in the chip itself, to minimize the conduction path. By using very small flow channels, high heat transfer rates can be achieved as demonstrated by Tuckerman and Pease using a heat sink with parallel channels. However, these small channels lead to elevated pressure drops.
The design of flow paths in microheat sinks plays a crucial role in harmonizing high cooling rates with moderate pumping requirements. This is traditionally approached by optimizing the size of the channels. Furthermore, alternative layouts involving a topological change of the flow network have been proposed. 
Advanced design optimization methods such as shape optimization and topology optimization have proven their virtue in other engineering disciplines such as aerodynamics and structural mechanics. These methods can beuseful in heat sink design to exploit further improvement potential andautomate the design process in a systematic and flexible way.
In this thesis advanced numerical design methods for micro heat sinks are developed. Two approaches have been investigated: shape optimization of single microchannels, and topology optimization of heat sinks. 
The first part of this thesis focusses on microchannel shape optimization. The streamwise width distribution of a single microchannel element is optimized using a correlation-based analytical model. This work continues on the work of Bau by considering more degrees of freedom. It is shown inthis thesis that optimized microchannels can be used to reduce thermal resistance by 8% compared to a microchannel with constant width, or alternatively to eliminate non-uniformities in the source temperature. 
In the second part of this thesis, a topological heat sink design method is developed. A two-dimensional model of partial-differential equations for the simulation of fluid flow and heat transfer in the heat sinkis presented. The hybrid nature of this model enables to distinguish solid material from fluid by tuning a fictitious porosity. The topology optimization problem is solved by optimally controlling this porosity. Theminimization of the objective functional is performed by the method of moving asymptotes, which is a robust gradient-based optimization algorithm. The set of adjoint equations corresponding to the heat sink model equations is derived. The solution of these equations provides an efficient means for calculation of the objective gradient.
The topological design method is appliedto two test cases with different boundary conditions to represent the heat source. The first case considers a constant temperature source, which admits a simpler heat sink model. The secondcase involves a constant flux heat source. Both cases show a significant thermal resistance reduction of respectively 50% and 30% with respect to an optimized parallel channel heat sink. Typically, the optimized heat sink layouts consist of a branched network of channels. It is concluded that topology optimization is a promising method for automated heat sink design.