Analysis on Electrically Resistive Heat Transfer of Composites Reinforced by Nanopaper

The finite element software FLUENT was used to analyze how the heating power of the nanopaper affect the changes of the temperature with time and the heating rate during heating. Simulation results showed that the average temperature of the polymer composites reinforced by the bent nanopaper is increased with increasing heating power. The time reaching the stable state is longer with increasing heating power. For the composites with same heating power, the temperature difference between the maximum and minimum temperatures is increased with increasing heating time. For the composites under the same heating time, the temperature difference between the maximum and minimum temperatures is increased with increasing heating power.


Introduction
CNTs have been regarded as one of the most promising reinforcement materials or functional agents [1,2]. Carbon nanotube (CNT) nanopaper, which has large specific surface area and tunable network structures, shows great potential in the application of heat dissipation for high power electronic devices. Chen et al [3] investigated the effects of CNT diameter and length on the network formation of nanopapers by vacuum filtration and their thermal transport properties were thoroughly. The CNT architecture in nanopaper is found to be a key issue to affect the thermal conductivity of nanopapers. Gonnet et al [4] indicated that nanotube alignment has a measurable influence on the thermal conductivities of both nanopaper and nanocomposites, and the thermal conductivities were found to increase linearly with temperature for both nanopapers and composites. For the BP-reinforced composites, experimental results indicated an average 10 fold thermal conductivity improvement in comparison to the pure matrices. The temperature dependence of the thermal conductivity for both pristine BP and the laminates followed a quasi-linear relationship. Li et al [5] indicated that nanopaper/pCBT composites significantly improved thermal (70 W/mK) and electric conductivities (526 S/cm).
In this study, the thermal responses of the polymer composites reinforced by the flat and pulse bending nanopapers are systematically studied. The heating model of the polymer composite reinforced by flat and bent nanopaper is established to predict the thermal property of BP/composites. The finite element software FLUENT is used to analyze how the heating power affect the changes of the typical temperature with time and the heating rate of the composite materials during heating.

Numerical model
During the analysis, two different shapes of nanopaper were considered: flat and the bent; the heating powers were varied from 0.2, 0.3, 0.4, 0.6, 0.8, to 1W; the thermal conductivity of nanopaper and the polymer matrix was set to be 1.5 W/(m•K) and 0.20 W/(m•K). The natural convection heat transfer coefficient was set to be 10 W/(m 2 •K). The ambient temperature was set to be 300 K. The specific heat capacity of nanopaper and the polymer matrix was set to be 800 J/(kg•K) and 1000 J/(kg•K).

Results and discussion
As shown in Figure 2, the relationship of the average temperature with heating time for the polymer composites reinforced by the bent nanopaper was obtained as a function of heating power during heating until reaching the stable state. As shown in Figure 2, at the same heating power, the average temperature is increased with increasing the heating time, and for the same heating time, the average temperature is increased with increasing the heating power. Figure 2 also shows that the time reaching a stable state is much longer with increasing the heating power. Because the larger the unit volume of the nanopaper sheets is, the higher the temperature of the nanopaper sheets is when the heating power is increased. It means that the heat transfer rate is less than the increase rate of heat production, which results in the increase of  For the composites with same heating power, the temperature difference between the maximum and minimum temperatures is increased with increasing heating time. For the composites under the same heating time, the temperature difference between the maximum and minimum temperatures is increased with increasing heating power.

Conclusions
FLUENT was used to analyze how the bending shapes affect the changes of the temperature with time and the heating rate during heating. The average temperature of the polymer composites reinforced by the bent nanopaper is increased with increasing heating power. The time reaching the stable state is longer with increasing heating power. For the composites with same heating power, the temperature difference between the maximum and minimum temperatures is increased with increasing heating time. For the composites under the same heating time, the temperature difference between the maximum and minimum temperatures is increased with increasing heating power.