Topology Optimization of an Air-Cooled Heat Sink for Transient Heat Dissipation using a Homogenization Approach

A homogenization approach to topology optimization is utilized to optimize the thermal performance of air-cooled heat sinks. Under the homogenization approach, partial densities are physically represented as square air ducts of varying sizes concentric to the grid cell. This formulation allows the calculation of local heat transfer coefficients using correlations for flow inside a duct. Because many electronics applications require transient thermal management solutions due to time-varying or periodic workloads, a subroutine is discussed to characterize and improve the transient performance indicators of heat sinks using a steady optimization toolbox. This subroutine aims to improve the transient thermal performance of a heat sink by imposing a solid region over the heat input of the optimization domain. This increases the thermal capacitance of the heat sink to address transient spikes in heat input. Heat sinks with increasingly thick solid regions are optimized under a steady average heat load, and then the thermal performance of these optimized designs is evaluated in response to a transient heat load profile. The heat sink thermal performance is evaluated using thermal resistance for the steady heat load and peak and time-averaged maximum domain temperatures for a pulsed periodic heat load. It was observed that the time-averaged maximum domain temperature is directly related to the optimized thermal resistance under a steady heat load boundary condition. There exists an optimal solid region thickness at which the transient performance is most improved in terms of peak or time-averaged maximum domain temperatures. The work demonstrates an approach for heat sink topology optimization for managing thermal fluctuations under a periodic heat load.