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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 ...).

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

The effect of structural parameters on effective thermal resistance (R+). (a) for different total levels (m), with N = 2, γ = 0.6, and b = 0.35, (b) for different ratios of length (γ), with N = 2, m = 3, and b = 0.35, (c) for different bifurcate numbers (N), with m = 3, γ = 0.6, and b = 0.35 (d) for different power exponents (b) with γ = 0.6, N = 3, and m = 3. The optimum design of branched single-wall carbon nanotubes with m = 2, N = 2 and two different length ratio γ are inserted as background in (a) and (b), respectively.
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Figure 4: The effect of structural parameters on effective thermal resistance (R+). (a) for different total levels (m), with N = 2, γ = 0.6, and b = 0.35, (b) for different ratios of length (γ), with N = 2, m = 3, and b = 0.35, (c) for different bifurcate numbers (N), with m = 3, γ = 0.6, and b = 0.35 (d) for different power exponents (b) with γ = 0.6, N = 3, and m = 3. The optimum design of branched single-wall carbon nanotubes with m = 2, N = 2 and two different length ratio γ are inserted as background in (a) and (b), respectively.

Mentions: To characterize the influence of the structural parameters of branched structures of single-walled carbon nanotubes on the overall thermal resistance, under the volume constraint, the effective thermal resistance of the entire structure (shown in Figure 1(II)) is first analyzed. Based on Eq. 17, the results of the detailed analysis are plotted in Figure 4. Figures 4 shows the effective thermal resistance, R+, plotted against the diameter ratio β, for different values of m, γ, N, and b, respectively. From these plots, it is apparent that, for a fixed volume, the total branched structure has a higher thermal resistance than the single-walled carbon nanotube. It is therefore strategically important to establish the optimum structure. It can be seen that the effective thermal resistance R+, first decreases then increases with increasing diameter ratio β. There is an optimum diameter ratio β*, at which the total thermal resistance of the branched structure is at its minimum and equal to the thermal resistance of the single-walled carbon nanotube. This represents an optimum condition in designing the branched structure. Furthermore, as can be seen from Figure 4a, the optimum diameter ratio β*, is independent of the number of branching levels m. On the other hand, as can be seen from Figure 4b, c, d, length ratio γ, the bifurcation number N, and power exponents b affect the optimum diameter ratio β*. In other words, the value of the optimum diameter ratio β*, depends on the length ratio γ, bifurcation number N and power exponents b. For example, when b = 0.3, β* = 0.735 at N = 2, and γ = 0.6; β* = 0.726 at N = 2 and γ = 0.7; β* = 0.60 at N = 3 and γ = 0.6; and β* = 0.593 at N = 3 and γ = 0.7. In addition, from Figure 4a, it can be seen that the effective thermal resistance R+ increases with increase of the number of the branching levels m. This is because when the branching levels m increases, the network becomes densely filled with much slenderer branches. Figure 4b also denotes that the effective thermal resistance R+ increases with the increase of the length ratio γ. This is because a higher length ratio γ implies longer branches. From Figure 4c, it also can be seen that when the diameter ratio is smaller than optimum diameter ratio (viz., β <β*), the effective thermal resistance R+ decreases with increase of bifurcation number N, while the diameter ratio is bigger than optimum diameter ratio (viz., β >β*), the trends is just opposite. The reason is that when β <β*, the increase of the parallel channels in every level leads to lower total thermal resistance; but when β >β*, the increase of the parallel channels in every level will increase effective volume of total branched structure, leading to an opposite trend. By plotting the logarithm of the optimum diameter ratio β*, against the logarithm of the bifurcation number N (see Figure 5), it is apparent that or β* = γ-0.25b N-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, N is the bifurcation number, N = 2, 3, 4,......, k* is the power exponent and k = -1/k* = -0.5 as shown in Figure 5. From Figures 4c and 5a, it can be observed that there is a smaller optimum diameter ratio with the increase of bifurcation number N.


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)

The effect of structural parameters on effective thermal resistance (R+). (a) for different total levels (m), with N = 2, γ = 0.6, and b = 0.35, (b) for different ratios of length (γ), with N = 2, m = 3, and b = 0.35, (c) for different bifurcate numbers (N), with m = 3, γ = 0.6, and b = 0.35 (d) for different power exponents (b) with γ = 0.6, N = 3, and m = 3. The optimum design of branched single-wall carbon nanotubes with m = 2, N = 2 and two different length ratio γ are inserted as background in (a) and (b), respectively.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 4: The effect of structural parameters on effective thermal resistance (R+). (a) for different total levels (m), with N = 2, γ = 0.6, and b = 0.35, (b) for different ratios of length (γ), with N = 2, m = 3, and b = 0.35, (c) for different bifurcate numbers (N), with m = 3, γ = 0.6, and b = 0.35 (d) for different power exponents (b) with γ = 0.6, N = 3, and m = 3. The optimum design of branched single-wall carbon nanotubes with m = 2, N = 2 and two different length ratio γ are inserted as background in (a) and (b), respectively.
Mentions: To characterize the influence of the structural parameters of branched structures of single-walled carbon nanotubes on the overall thermal resistance, under the volume constraint, the effective thermal resistance of the entire structure (shown in Figure 1(II)) is first analyzed. Based on Eq. 17, the results of the detailed analysis are plotted in Figure 4. Figures 4 shows the effective thermal resistance, R+, plotted against the diameter ratio β, for different values of m, γ, N, and b, respectively. From these plots, it is apparent that, for a fixed volume, the total branched structure has a higher thermal resistance than the single-walled carbon nanotube. It is therefore strategically important to establish the optimum structure. It can be seen that the effective thermal resistance R+, first decreases then increases with increasing diameter ratio β. There is an optimum diameter ratio β*, at which the total thermal resistance of the branched structure is at its minimum and equal to the thermal resistance of the single-walled carbon nanotube. This represents an optimum condition in designing the branched structure. Furthermore, as can be seen from Figure 4a, the optimum diameter ratio β*, is independent of the number of branching levels m. On the other hand, as can be seen from Figure 4b, c, d, length ratio γ, the bifurcation number N, and power exponents b affect the optimum diameter ratio β*. In other words, the value of the optimum diameter ratio β*, depends on the length ratio γ, bifurcation number N and power exponents b. For example, when b = 0.3, β* = 0.735 at N = 2, and γ = 0.6; β* = 0.726 at N = 2 and γ = 0.7; β* = 0.60 at N = 3 and γ = 0.6; and β* = 0.593 at N = 3 and γ = 0.7. In addition, from Figure 4a, it can be seen that the effective thermal resistance R+ increases with increase of the number of the branching levels m. This is because when the branching levels m increases, the network becomes densely filled with much slenderer branches. Figure 4b also denotes that the effective thermal resistance R+ increases with the increase of the length ratio γ. This is because a higher length ratio γ implies longer branches. From Figure 4c, it also can be seen that when the diameter ratio is smaller than optimum diameter ratio (viz., β <β*), the effective thermal resistance R+ decreases with increase of bifurcation number N, while the diameter ratio is bigger than optimum diameter ratio (viz., β >β*), the trends is just opposite. The reason is that when β <β*, the increase of the parallel channels in every level leads to lower total thermal resistance; but when β >β*, the increase of the parallel channels in every level will increase effective volume of total branched structure, leading to an opposite trend. By plotting the logarithm of the optimum diameter ratio β*, against the logarithm of the bifurcation number N (see Figure 5), it is apparent that or β* = γ-0.25b N-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, N is the bifurcation number, N = 2, 3, 4,......, k* is the power exponent and k = -1/k* = -0.5 as shown in Figure 5. From Figures 4c and 5a, it can be observed that there is a smaller optimum diameter ratio with the increase of bifurcation number N.

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