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Optimizing the design of nanostructures for improved thermal conduction within confined spaces.

Kou J, Qian H, Lu H, Liu Y, Xu Y, Wu F, Fan J - Nanoscale Res Lett (2011)

Bottom Line: Maintaining constant temperature is of particular importance to the normal operation of electronic devices.Branched structure made of single-walled carbon nanotubes (CNTs) are shown to be particularly suitable for the purpose.It was found that the total thermal resistance of a branched structure reaches a minimum when the diameter ratio, β* satisfies the relationship: β* = γ-0.25bN-1/k*, where γ is ratio of length, b = 0.3 to approximately 0.4 on the single-walled CNTs, b = 0.6 to approximately 0.8 on the multiwalled CNTs, k* = 2 and N is the bifurcation number (N = 2, 3, 4 ...).

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Affiliation: College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, PR China. wfm@zjnu.cn.

ABSTRACT
Maintaining constant temperature is of particular importance to the normal operation of electronic devices. Aiming at the question, this paper proposes an optimum design of nanostructures made of high thermal conductive nanomaterials to provide outstanding heat dissipation from the confined interior (possibly nanosized) to the micro-spaces of electronic devices. The design incorporates a carbon nanocone for conducting heat from the interior to the exterior of a miniature electronic device, with the optimum diameter, D0, of the nanocone satisfying the relationship: D02(x) ∝ x1/2 where x is the position along the length direction of the carbon nanocone. Branched structure made of single-walled carbon nanotubes (CNTs) are shown to be particularly suitable for the purpose. It was found that the total thermal resistance of a branched structure reaches a minimum when the diameter ratio, β* satisfies the relationship: β* = γ-0.25bN-1/k*, where γ is ratio of length, b = 0.3 to approximately 0.4 on the single-walled CNTs, b = 0.6 to approximately 0.8 on the multiwalled CNTs, k* = 2 and N is the bifurcation number (N = 2, 3, 4 ...). The findings of this research provide a blueprint in designing miniaturized electronic devices with outstanding heat dissipation.PACS numbers: 44.10.+i, 44.05.+e, 66.70.-f, 61.48.De.

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Schematic diagram of a generalized branched structure. (a) is a schematic diagram of a generalized branched structure of single-walled carbon nanotube with bifurcate number N = 2, and total level m = 2, which can be considered as an equivalent thermal resistance network to that in (b), TH and TL representing areas of high and low temperatures, respectively.
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Figure 3: Schematic diagram of a generalized branched structure. (a) is a schematic diagram of a generalized branched structure of single-walled carbon nanotube with bifurcate number N = 2, and total level m = 2, which can be considered as an equivalent thermal resistance network to that in (b), TH and TL representing areas of high and low temperatures, respectively.

Mentions: Figure 3(a) and 3(b) illustrate a generalized branched structure of single-walled carbon nanotube with bifurcate number N = 2 and total level m = 2 and the equivalent thermal-electrical analogy network, respectively. According to Fourier's law, the thermal resistance of a single-walled CNT of the kth level channel can be expressed as: Rk = lk/(λAk) [28], where the [29-31] (The constant a is a function of heat capacity, the averaged velocity, mean free path of the energy carriers, temperature, etc. The power exponent b = 0.3 to approximately 0.4 [29,30] on the single-walled CNTs, while multiwalled CNTs of b = 0.6 to approximately 0.8 [31]). The total thermal resistance, Rt, of the entire branched structure of single-walled carbon nanotubes is given as follows:(11)


Optimizing the design of nanostructures for improved thermal conduction within confined spaces.

Kou J, Qian H, Lu H, Liu Y, Xu Y, Wu F, Fan J - Nanoscale Res Lett (2011)

Schematic diagram of a generalized branched structure. (a) is a schematic diagram of a generalized branched structure of single-walled carbon nanotube with bifurcate number N = 2, and total level m = 2, which can be considered as an equivalent thermal resistance network to that in (b), TH and TL representing areas of high and low temperatures, respectively.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3211839&req=5

Figure 3: Schematic diagram of a generalized branched structure. (a) is a schematic diagram of a generalized branched structure of single-walled carbon nanotube with bifurcate number N = 2, and total level m = 2, which can be considered as an equivalent thermal resistance network to that in (b), TH and TL representing areas of high and low temperatures, respectively.
Mentions: Figure 3(a) and 3(b) illustrate a generalized branched structure of single-walled carbon nanotube with bifurcate number N = 2 and total level m = 2 and the equivalent thermal-electrical analogy network, respectively. According to Fourier's law, the thermal resistance of a single-walled CNT of the kth level channel can be expressed as: Rk = lk/(λAk) [28], where the [29-31] (The constant a is a function of heat capacity, the averaged velocity, mean free path of the energy carriers, temperature, etc. The power exponent b = 0.3 to approximately 0.4 [29,30] on the single-walled CNTs, while multiwalled CNTs of b = 0.6 to approximately 0.8 [31]). The total thermal resistance, Rt, of the entire branched structure of single-walled carbon nanotubes is given as follows:(11)

Bottom Line: Maintaining constant temperature is of particular importance to the normal operation of electronic devices.Branched structure made of single-walled carbon nanotubes (CNTs) are shown to be particularly suitable for the purpose.It was found that the total thermal resistance of a branched structure reaches a minimum when the diameter ratio, β* satisfies the relationship: β* = γ-0.25bN-1/k*, where γ is ratio of length, b = 0.3 to approximately 0.4 on the single-walled CNTs, b = 0.6 to approximately 0.8 on the multiwalled CNTs, k* = 2 and N is the bifurcation number (N = 2, 3, 4 ...).

View Article: PubMed Central - HTML - PubMed

Affiliation: College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, PR China. wfm@zjnu.cn.

ABSTRACT
Maintaining constant temperature is of particular importance to the normal operation of electronic devices. Aiming at the question, this paper proposes an optimum design of nanostructures made of high thermal conductive nanomaterials to provide outstanding heat dissipation from the confined interior (possibly nanosized) to the micro-spaces of electronic devices. The design incorporates a carbon nanocone for conducting heat from the interior to the exterior of a miniature electronic device, with the optimum diameter, D0, of the nanocone satisfying the relationship: D02(x) ∝ x1/2 where x is the position along the length direction of the carbon nanocone. Branched structure made of single-walled carbon nanotubes (CNTs) are shown to be particularly suitable for the purpose. It was found that the total thermal resistance of a branched structure reaches a minimum when the diameter ratio, β* satisfies the relationship: β* = γ-0.25bN-1/k*, where γ is ratio of length, b = 0.3 to approximately 0.4 on the single-walled CNTs, b = 0.6 to approximately 0.8 on the multiwalled CNTs, k* = 2 and N is the bifurcation number (N = 2, 3, 4 ...). The findings of this research provide a blueprint in designing miniaturized electronic devices with outstanding heat dissipation.PACS numbers: 44.10.+i, 44.05.+e, 66.70.-f, 61.48.De.

No MeSH data available.


Related in: MedlinePlus