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

Abstract

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 microand 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.

“Volume-point” heat conduction constructal optimization based on minimization of maximum thermal resistance with triangular element at micro and nanoscales

“…Chen et al [42] optimized the "disc-point" heat conduction disc at micro and nanoscales by taking the minimization of the hot spot temperature as optimization objective, and obtained the optimal constructs of the disc different from the convectional scale. Daneshi et al [43] further carried out constructal optimizations of the discs with tree-shaped and looped-shaped high conductivity channels by using finite element method, respectively, and the results showed that increasing the order of the construct did not always lead to a better heat conduction performance.…”

Constructal Design of an Arrow-Shaped High Thermal Conductivity Channel in a Square Heat Generation Body

“…Bejan [ 1 ] stated the constructal law after further studying the formation of urban street networks, and applied it to the optimization of the heat dissipation structure of an electronic device (ED) [ 2 ]. Since the introduction of the constructal theory [ 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 ], it has been applied to design various heat dissipation bodies, such as rectangular [ 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 ], triangular [ 32 , 33 , 34 , 35 , 36 , 37 ], square [ 38 , 39 , 40 , 41 , 42 , 43 , 44 , 45 , 46 , 47 ] and discal [ 48 , 49 , 50 , 51 , 52 , 53 ,…”

Constructal Optimization for Cooling a Non-Uniform Heat Generating Radial-Pattern Disc by Conduction

“…Neagu and Bejan [28,29] introduced a new geometric feature of variable cross-sectional high conductivity channels into the constructal method with the aim of further minimizing the thermal resistance. Thereafter, many scholars performed constructal optimizations of various heat generating bodies to improve their heat conduction performance (HCP), such as rectangular bodies [30][31][32][33], square bodies [34][35][36][37][38][39][40][41], triangular bodies [42][43][44][45], disc-shaped bodies with radial-pattern [46,47] and tree-shaped HCCs [48][49][50][51][52][53][54], respectively.…”

“…Chen et al [53] re-optimized the disc-shaped body under the circumstances of micro and nano scales, and the results indicated that the constructs with size effects could improve the HCP with authority. Daneshi et al [54] numerically calculated the disc-shaped body with conductive tree-shaped HCCs at micro-and nanoscale, and the results manifested that increasing the number of HCCs didn't appear to necessarily improve the HCP of the disc.…”