Heat Conduction of Air in Nano Spacing
© to the authors 2009
Received: 9 April 2009
Accepted: 24 April 2009
Published: 6 May 2009
The scale effect of heat conduction of air in nano spacing (NS) is very important for nanodevices to improve their life and efficiency. By constructing a special technique, the changes of heat conduction of air were studied by means of measuring the heat conduction with heat conduction instrument in NS between the hot plate and the cooling plate. Carbon nanotubes were used to produce the nano spacing. The results show that when the spacing is small down to nanometer scale, heat conduction plays a prominent role in NS. It was found that the thickness of air is a non-linear parameter for demarcating the heat conduction of air in NS and the rate of heat conduction in unit area could be regard as a typical parameter for the heat conduction characterization at nanometer scale.
KeywordsHeat conduction Air Nano spacing Thickness Rate
Heat transfer is the transition of thermal energy or simply heat from a hotter object to a cooler object. When an object is at a different temperature than its surroundings or another object, heat transfer occurs in such a way that the body and the surroundings reach thermal equilibrium. Heat transfer always occurs from a higher-temperature object to a cooler-temperature one, a result of the second law of thermodynamics. Where there is a temperature difference between objects in proximity, heat transfer between them can never be stopped.
Heat conduction is the transfer of heat by direct contact of particles of matter. The transfer of energy could be primarily by free electron diffusion as predominant in metals or phonon vibration as predominant in insulators. In other words, heat is transferred by conduction when adjacent atoms vibrate against one another, or as electrons move from atom to atom.
The mechanisms of heat conduction are different in solid , liquid , and gas  conditions. The mechanisms of heat conduction in gas can be divided into two parts, macro mechanisms and micro ones. In macro mechanisms, heat conduction is produced by the collision of a large number of molecules and randomly heat movement . In micro mechanisms, when the distance between gas molecules is less than that of mean free path of gas molecules, the way of heat conduction is changed .
Heat conduction is widely used in many industrial fields. On account of the development of the nanotechnology, nanodevices have attracted much attention in recent years . However, with the decreasing size of nanodevices , there are many problems about thermotics and electrics in nano spacing (NS), which cannot be solved by macro theories. So it is important to study and develop micro theories at nanometer scale.
Air is a common mixing gas in nature. However, it has a complicated composition and exists in everywhere. So many theories must be firstly taken into account in ambient air and then extended to other gaseous surroundings.
This present work will focus on heat conduction of air in NS. The change of heat conduction of air in NS will be measured with heat conduction instrument. It is very important for the nanodevices to improve their life and efficiency, which may lead to a new research direction.
The key point in the experiment was to obtain the different thickness of air in NS, so the suitable spacers needed to be found. Carbon nanotubes (CNTs) were put into the spacing between the hot plate and the cooling plate and utilized to produce 2 and 15 nm thicknesses of air in NS using the 2-nm-diameter single-walled carbon nanotubes and 15-nm-diameter multi-walled carbon nanotubes, respectively. In order to make parallel to two plates, CNTs were settled at three different points which size was less than 100 μm on the cooling plate. The papers were used to make the spacing at micron scale. The thickness of 100 pieces of papers was firstly measured to calculate the thickness of one piece of paper. According to the thickness of spacing, an appropriate numbers of papers were also set at three different points which size is less than 1 mm on the cooling plate.
Results and Discussion
Heat transfer has three kinds of forms, including conduction, convection, and radiation. In this experiment, convection can be ignored on the NS condition.
The equation of radiation is , whereM is the spectral radiance factor, ε is emissivity (for copper, ε = 0.03),σ is Stefan–Boltzmann constant (5.67 × 10−8 W K−4 m−2), andT is the absolute temperature. So the quantity of heat through radiation in NS is 0.5 W ~ 2 W. However, the quantity of heat through heat conduction in NS is 70 W ~ 500 W. So the quantity of heat through radiation in NS can be ignored.
Now the experiment only considers the heat conduction.
The diameter of the plate is 13 cm while the size of the CNTs and papers are less than 1 mm. The interface between plates and spacer is too much smaller relative to the area of plates so that the effect of materials properties of the samples on heat conduction of air can be ignored.
The plate is 0.8-cm-thick and enough hard to ensure that the two plates are parallel each other when the sample is settled between them.
Eq. 2 contains the temperature grads  and unit time (dt). Minus symbol represents the direction of heat conduction along the direction of the decreasing temperature.
In Eq. 4, is the quantity of heat conduction in unit time, which can be regarded as the heat conduction rate of air (v). These parameters, including ΔT,h, andA can be got by the experiment. The heat conduction coefficient can be calculated if only the heat conduction rate of air is known.
In this experiment, it can be supposed that temperature do not change with surroundings so that keeps stable . It is obvious that the rate of heat conduction is equal to the rate of heat diffusion.
According to Eq. 4, when heat is conducted from the cooling plate to air,v1is proportional toA1.
Eq. 11 shows the heat conduction coefficient. All the parameters can be measured from the experiment, so the heat conduction coefficient can be calculated.
In present work, the thickness of air ranging from 100 nm to 1000 nm is difficult to construct. Due to the systematic errors of the instrument by itself, the exactly demarcate point in 1.0 × 105 ~ 1.0 × 106 nm (thickness of air) has not been found. Further research is still required.
The changes of heat conduction of air in NS produced by CNTs were studied by means of measuring the heat conduction with heat conduction instrument. The results show when the thickness of air is small down to nanometer scale, the thickness of air present a complex non-linear relationship with heat conduction coefficient and is unsuitable for evaluating the change of heat conduction in NS. It was found that the rate of heat conduction in unit area could be more suitable as a typical parameter. The present study will draw lots of interests on heat conduction at nanometer scale.
This study is supported by National Natural Science Foundation of China No.50730008, Shanghai Science and Technology Grant No. 0752nm015, and National Basic Research Program of China No. 2006CB300406.
- Cahill DG, Ford WK, Goodson KE, Mahan GD, Majumdar A, Maris HJ, Merlin R, Phillpot SR: J. Appl. Phys.. 2003, 93: 793. ; COI number [1:CAS:528:DC%2BD38XpvVektbg%3D]; 10.1063/1.1524305View Article
- Healy JJ, de Groot JJ, Kestin J: Physica C. 1976, 82: 392. 10.1016/0378-4363(76)90203-5View Article
- Poling BE, Prausnitz JM: The Properties of Gases and Liquids. McGrawHill, New York; 2001.
- Peng YQ, Lu XC, Luo JB: Tribology. 2004, 24: 56.
- Flik MI, Choi OI, Goodson KE: J. Heat. Transf.. 1992, 114: 666. 10.1115/1.2911332View Article
- Thome JR: Heat Transf. Eng.. 2006, 27: 1. ; COI number [1:CAS:528:DC%2BD28XpsVOltL8%3D]; 10.1080/01457630600845283View Article
- Fu X, Yang HY: Chin. J. Chem. Eng.. 2001, 9: 123.
- Graebner JE, Mucha JA, Seibles L: J. Appl. Phys.. 1992, 71: 3143. ; COI number [1:CAS:528:DyaK38Xit1amu7c%3D]; 10.1063/1.350981View Article
- Tai YC, Mastrangelo CH, Muller RS: J. Appl. Phys.. 1988, 63: 1442. ; COI number [1:CAS:528:DyaL1cXhslClur8%3D]; 10.1063/1.339924View Article
- Sun P, Wang MF: Phys. Eng.. 2001, 11: 31.
- Feng Y, Liang MB: Guangzhou Chem. Ind.. 2006, 34: 31.
- Mountain RD, Macdonald RA: Phys. Rev. B. 1983, 28: 3022. Bibcode number [1983PhRvB..28.3022M] Bibcode number [1983PhRvB..28.3022M] 10.1103/PhysRevB.28.3022View Article
- Goodson KE, Flik MI: Appl. Mech. Rev.. 1994, 47: 101. 10.1115/1.3111073View Article
- Asael MJ, Nieto de Castrp CA, Roder HM: Transient Methods for Thermal Conductivity. Blackwell Scientific, London; 1991.