Micro- and Nanoscale Conductive Tree-Structures for Cooling a Disk-Shaped Electronic Piece

In this research, we consider the generation of conductive heat trees at microscales and nanoscales for cooling electronics which are considered as heat-generating disk-shaped solids. With the advent of nanotechnology and the production of electronics in micro- and nanoscales in recent years, designing workable systems for cooling them is considered widely. Therefore, tree-shape conduction paths of highly conductive material including radial patterns, structures with one level of branching, tree-with-loop architectures, and combination of structures with branching and structures with loops are generated for cooling such electronic devices. Furthermore, constructal method which is used to analytically generate heat trees for cooling a disk-shaped body is modified in the present work, that we call it modified analytical method. Moreover, every feature of the tree architectures is optimized numerically to make a comparison between numerical and analytical results and to generate novel architectures. Since there are some constructal tree architectures which are not possible to be generated analytically, numerical approach is used for optimization. When the smallest features of the internal structure are smaller than mean free path of the energy carriers, heat conductivity is no longer a constant and becomes a function of the smallest dimension of the structure. Therefore, we consider models which were proposed for estimating conductivity of small scale bodies.