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TECHNICAL BRIEF

# A Numerical Study of Transport in a Thermal Interface Material Enhanced With Carbon Nanotubes

[+] Author and Article Information
Anand Desai

Binghamton University, P.O. Box 6000, Vestal Pkwy East, Binghamton, NY 13790adesai0@binghamton.edu

Sanket Mahajan

School of Mechanical Engineering, 585 Purdue Mall, Purdue University, West Lafayette, IN 47907-2088

Ganesh Subbarayan

School of Mechanical Engineering, 585 Purdue Mall, Purdue University, West Lafayette, IN 47907-2088ganeshs@purdue.edu

Wayne Jones, James Geer, Bahgat Sammakia

Binghamton University, P.O. Box 6000, Vestal Pkwy East, Binghamton, NY 13790

J. Electron. Packag 128(1), 92-97 (May 10, 2005) (6 pages) doi:10.1115/1.2161231 History: Received July 23, 2004; Revised May 10, 2005

## Abstract

Power dissipation in electronic devices is projected to increase over the next $10years$ to the range of $150–250W$ per chip for high performance applications. One of the primary obstacles to the thermal management of devices operating at such high powers is the thermal resistance between the device and the heat spreader or heat sink that it is attached to. Typically the in situ thermal conductivity of interface materials is in the range of $1–4W∕mK$, even though the bulk thermal conductivity of the material may be significantly higher. In an attempt to improve the effective in situ thermal conductivity of interface materials nanoparticles and nanotubes are being considered as a possible addition to such interfaces. This paper presents the results of a numerical study of transport in a thermal interface material that is enhanced with carbon nanotubes. The results from the numerical solution are in excellent agreement with an analytical model (Desai, A., Geer, J., and Sammakia, B., “Models of Steady Heat Conduction in Multiple Cylindrical Domains  ,” J. Electron. Packaging (to be published)) of the same geometry. Wide ranges of parametric studies were conducted to examine the effects of the thermal conductivity of the different materials, the geometry, and the size of the nanotubes. An estimate of the effective thermal conductivity of the carbon nanotubes was used, obtained from a molecular dynamics analysis (Mahajan, S., Subbarayan, G., Sammakia, B. G., and Jones, W., 2003, Proceedings of the 2003 ASME International Mechanical Engineering Congress and Exposition, Washington, D.C., Nov. 15–21). The numerical analysis was used to estimate the impact of imperfections in the nanotubes upon the overall system performance. Overall the nanotubes are found to significantly improve the thermal performance of the thermal interface material. The results show that varying the diameter of the nanotube and the percentage of area occupied by the nanotubes does not have any significant effect on the total temperature drop.

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## Figures

Figure 1

Schematic diagram of the periodic element used in all models. This figure is not to scale.

Figure 2

Full-scale model in ANSYS 6.0

Figure 3

Temperature as a function of length for the multicylinder model. The temperature decreases sharply owing to the thermal conductivity of silicon, then between 600 and 610nm the slope is almost a straight line due to relatively high thermal conductivity of nanotubes and then decreases rapidly due to the thermal conductivity of aluminum.

Figure 4

Temperature as a function of length, for the interface model, in this thermal interface resistance is added to the model near the nanotube interfaces and as can be seen from the figure there is a temperature drop at those interfaces. The temperature drop across these interfaces is user specified.

Figure 5

Temperature as a function of length for the interface gap model, the gap for this model is 0.125μm. As can be seen from the figure there is a large temperature drop at the interface where the gap is present.

Figure 6

Plot of the maximum temperature as a function of the interface gap, the interface gap model was run for different gaps and the maximum temperature in each case was noted. Above is a plot of the maximum temperatures versus their corresponding interface gap.

Figure 7

Flux as a function of length for the conical model. The flux is uniform in the silicon cylinder, in the nanotube there is a sudden jump in the heat flux due to change in cross-sectional area, the steep rise continues as the cross-sectional area further decreases in a cone and then it gets back to the original value as it reaches the aluminum cylinder.

Figure 8

Plot of temperature as a function of length for different heat fluxes and varying diameters of the nanotube. Nonlinear length scale is used.

Figure 9

Plot of temperature as a function of length for different heat fluxes and varying conductivities of the nanotube and varying percentage of area occupied by the nanotube. Nonlinear length scale is used.

Figure 10

Plot of temperature as a function of length, for different heat fluxes and varying percentage of area occupied by the nanotube, K=1000W∕mK. From this plot it can be inferred that for the given power there is not much variation with percentage of area occupied by nanotubes. Nonlinear length scale is used.

Figure 11

Plot of temperature as a function of length, for different heat fluxes and varying the thermal conductivity of the nanotube, with 10% of the area occupied by the nanotubes and the diameter of the nanotube is 30nm. The result obtained here is from the numerical solution and the dotted points are the analytical solution results for the same case. Nonlinear length scale is used.

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