OPTIMAL DESIGN OF THREE-DIMENSIONAL ORTHOTROPIC SUBSTRATES

摘要

Three-dimensional heat conduction within an orthotropic substrate subjected to a uniform heat flux over a portion of one surface is considered. The surface opposite the heated side is cooled by a uniform environment while the remaining surfaces are insulated. A mathematical model for the design of an optimal substrate is developed based on optimization theory. The temperature inside the substrate is minimized with respective to the heated area aspect ratio. The effects of varying the substrate dimensions and the Biot numbers typical of microelectronic applications are investigated. Graphical results are presented for the minimum temperature and the corresponding thickness over a wide range of substrate physical dimensions. The optimization model provides a design tool for electronic component design engineers to quickly and accurately perform three-dimensional analyses of orthotropic substrates.