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Research Papers

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

[+] Author and Article Information
Mohammad Reza Salimpour

e-mail: salimpour@cc.iut.ac.ir
Department of Mechanical Engineering,
Isfahan University of Technology,
Isfahan 84156-83111, Iran

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received April 25, 2012; final manuscript received October 20, 2012; published online February 14, 2013. Assoc. Editor: Giulio Lorenzini.

J. Heat Transfer 135(3), 031401 (Feb 14, 2013) (10 pages) Paper No: HT-12-1189; doi: 10.1115/1.4007903 History: Received April 25, 2012; Revised October 20, 2012

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.

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Figures

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Fig. 1

Highly conductive heat trees with (a) branched, (b) loop, and (c) combined structures embedded in a heat-generating disk-shaped body, for N = 6

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Fig. 2

Elemental volume: circular sector with high-conductivity blade on its centerline

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Fig. 3

Structure with one level of branching

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Fig. 4

Geometry of (a) a structure with one level of branching, (b) a structure with loop, and (c) a combined architecture

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Fig. 5

Minimal thermal resistances of branched structures of the present study (numerical results) compared with those reported in Ref. [8]

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Fig. 6

Minimal thermal resistance of elemental volumes versus λ¯, in radial structures

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Fig. 7

Optimal values of D¯ and D¯/n in (a) bb region, (b) bn region, and (c) nn region

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Fig. 8

Minimal thermal resistance with respect to R¯ at different values of ϕ in (a) bb region, (b) bn region, and (c) nn region

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Fig. 9

Optimal profile of half of the thickness of the blade with respect to r for radial structures with optimal blades shape

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Fig. 10

Minimal thermal resistances of radial structures with optimal blades shape obtained using kmodel-1 and kmodel-2

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Fig. 11

Optimal profile of half of the thickness of central blade with respect to r for branched structures with optimal blades shape

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Fig. 12

Minimal thermal resistances of branched structures with embedded optimally varying-thickness blades evaluated based on (a) kmodel-1 and (b) kmodel-2

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Fig. 13

Minimal values of thermal resistance for branched structures obtained based on numerical, analytical and modified analytical results for (a) R¯ = 4, (b) R¯ = 6, and (c) R¯ = 8

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Fig. 14

Minimal thermal resistances of branched architectures with optimally varying-thickness blades obtained based on analytical, modified analytical and numerical methods using (a) kmodel-1 and (b) kmodel-2

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Fig. 15

Minimal values of thermal resistance obtained based on numerical approach

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Fig. 16

Minimal thermal resistances of structures with branched pattern, loop pattern, and combined pattern for (a) λ˜ = 0.001 and (b) λ˜ = 0.1

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