In this research, we consider the generation of conductive heat trees at micro and nano scales for cooling electronics which are considered as heat-generating disc-shaped solids. Due to the development of nano technology and its role in the production of small scale electronics in recent decades, the necessity of designing cooling systems for them will be revealed more than any other time. 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 loop 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-shaped architectures is optimized numerically to make a comparison between numerical and analytical results and to generate novel architectures. When the smallest features of the internal structure are so small, the conventional description of conduction breaks down. Hence, the effective thermal conductivity exhibits the “size effect”, and is governed by the smallest structural dimension which is comparable with the mean free path of the energy carriers. Therefore, we consider a model which was proposed for small-scale bodies in order to evaluate conductivity of heat trees.

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