Numerical Model for Thermal Transport in 3-D Nanotube Composites

2007 ◽  
Author(s):  
Satish Kumar ◽  
Jayathi Y. Murthy
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Finite Volume ◽  
Thermal Transport ◽  
Three Dimensional ◽  
Finite Volume Scheme ◽  
Interfacial Resistance ◽  
Volume Scheme ◽  
Numerical Predictions ◽  
Nanotube Composites

The effective thermal conductivity of three dimensional (3-D) nanocomposites composed of carbon nanotube (CNT) dispersions is computed using Fourier conduction theory. The random ensemble of nanotubes is generated numerically and each nanotube is discretized using a finite volume scheme. The background substrate mesh is also discretized using a finite volume scheme. We incorporate all parameters crucial for thermal transport studies, i.e. tube aspect ratio, tube density, composite sample size, substrate-CNT conductivity ratio and the interfacial resistance due to tube-tube and tube-substrate contact. Two-dimensional (thin film) nanocomposites are also simulated for comparison. Numerical predictions of effective thermal conductivity are in excellent agreement with the effective medium approximation (EMA) for both 2-D and 3-D nanocomposites at low tube densities, but depart significantly from EMA predictions when tube-tube interaction becomes significant. It is found that the effect of tube-tube contact on effective thermal conductivity is more significant for 2-D composites than 3-D composites. Hence percolation effects may play a more significant role in thermal transport in 2-D nano-composites.

Percolation Effects on the Thermal Conductivity of 3D Nanotube Composites

2008 ◽  
Author(s):  
Satish Kumar ◽  
Muhammad A. Alam ◽  
Jayathi Y. Murthy
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Thermal Transport ◽  
Three Dimensional ◽  
Linear Response Theory ◽  
Critical Parameters ◽  
Conductivity Ratio ◽  
Interfacial Resistance ◽  
Numerical Predictions ◽  
Nanotube Composites

We analyze thermal transport in three-dimensional (3D) nano-composites composed of carbon nanotube (CNT) dispersions to investigate percolation effects on the effective thermal conductivity of these composites. Thermal transport simulations for the randomly distributed nanotubes inside the host substrate are based on the diffusive Fourier conduction theory. The numerical model incorporates the effect of substrate-CNT conductivity ratio and the interfacial resistance due to tube-tube and tube-substrate contact, which are the most critical parameters governing thermal transport properties. Numerical predictions of effective thermal conductivity are in excellent agreement with the linear response theory and effective medium approximation (EMA) when assumptions of theory are incorporated in the model. The trends for the variation of effective thermal conductivity with increasing nanotube density are in broad agreement with previous experimental observations. Our numerical results also show that the onset of thermal percolation is gradual and largely dependent on the tube-to-substrate conductivity ratio and interfacial resistance at tube-tube and tube-substrate contact.

scholarly journals Computational Model for Transport in Nanotube-Based Composites With Applications to Flexible Electronics

2006 ◽  
Vol 129 (4) ◽  
pp. 500-508 ◽  
Author(s):  
Satish Kumar ◽  
Muhammad A. Alam ◽  
Jayathi Y. Murthy
Keyword(s):  
Thermal Conductivity ◽  
Electrical Conductivity ◽  
Effective Thermal Conductivity ◽  
Finite Volume ◽  
Flexible Electronics ◽  
Electrical Transport ◽  
Test Problems ◽  
Finite Volume Scheme ◽  
Electrical Measurements ◽  
Volume Scheme

Thermal and electrical transport in a new class of nanocomposites composed of random isotropic two-dimensional ensembles of nanotubes or nanowires in a substrate (host matrix) is considered for use in the channel region of thin-film transistors (TFTs). The random ensemble of nanotubes is generated numerically and each nanotube is discretized using a finite volume scheme. To simulate transport in composites, the network is embedded in a background substrate mesh, which is also discretized using a finite volume scheme. Energy and charge exchange between nanotubes at the points of contact and between the network and the substrate are accounted for. A variety of test problems are computed for both network transport in the absence of a substrate, as well as for determination of lateral thermal and electrical conductivity in composites. For nanotube networks in the absence of a substrate, the conductance exponent relating the network conductance to the channel length is computed and found to match experimental electrical measurements. The effective thermal conductivity of a nanotube network embedded in a thin substrate is computed for a range of substrate-to-tube conductivity ratios. It is observed that the effective thermal conductivity of the composite saturates to a size-independent value for large enough samples, establishing the limits beyond which bulk behavior obtains. The effective electrical conductivity of carbon nanotube-organic thin films used in organic TFTs is computed and is observed to be in good agreement with the experimental results.

A Numerical Model to Predict the Thermal and Psychrometric Response of Electronic Packages

1999 ◽  
Vol 123 (3) ◽  
pp. 200-210 ◽  
Author(s):  
J. V. C. Vargas ◽  
G. Stanescu ◽  
R. Florea ◽  
M. C. Campos
Keyword(s):  
Differential Equations ◽  
Physical Model ◽  
Finite Volume ◽  
Three Dimensional ◽  
Computational Time ◽  
Finite Volume Scheme ◽  
Electronic Packages ◽  
Simulation Design ◽  
Experimental Conditions ◽  
Volume Scheme

This paper introduces a general computational model for electronic packages, e.g., cabinets that contain electronic equipment. A simplified physical model, which combines principles of classical thermodynamics and heat transfer, is developed and the resulting three-dimensional differential equations are discretized in space using a three-dimensional cell centered finite volume scheme. Therefore, the combination of the proposed simplified physical model with the adopted finite volume scheme for the numerical discretization of the differential equations is called a volume element model (VEM). A typical cabinet was built in the laboratory, and two different experimental conditions were tested, measuring the temperatures at forty-six internal points. The proposed model was utilized to simulate numerically the behavior of the cabinet operating under the same experimental conditions. Mesh refinements were conducted to ensure the convergence of the numerical results. The converged mesh was relatively coarse (504 cells), therefore the solutions were obtained with low computational time. The model temperature results were directly compared to the steady-state experimental measurements of the forty-six internal points, with good quantitative and qualitative agreement. Since accuracy and low computational time are combined, the model is shown to be efficient and could be used as a tool for simulation, design, and optimization of electronic packages.

Thermal Transport in Nanotube Composites for Large-Area Macroelectronics

2005 ◽  
Author(s):  
Satish Kumar ◽  
Muhammad A. Alam ◽  
Jayathi Y. Murthy
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Thermal Transport ◽  
Channel Length ◽  
Tube Length ◽  
Finite Volume Scheme ◽  
Large Area ◽  
Contact Conductance ◽  
Channel Lengths ◽  
Contact Parameters

Thermal transport in a new class of nanocomposites composed of isotropic 2D ensembles of nanotubes or nanowires in a substrate is considered for use as the channel region of thin film transistors. The random ensemble is generated numerically and simulated using a finite volume scheme. The effective thermal conductivity of a nanotube network embedded in a thin substrate is computed. Percolating conduction in the composite is studied as a function of wire/tube densities and channel lengths. The conductance exponents are validated against available experimental data for long channels devices. The effect of tube-tube contact conductance, tube-substrate contact conductance and substrate-tube conductivity ratio is analyzed for various channel lengths. It is found that beyond a certain limiting value, contact parameters do not result in any significant change in the effective thermal conductivity of the composite. It is also observed that the effective thermal conductivity of the composite saturates beyond a limiting channel-length/tube length ratio for the range of contact parameters under consideration.

CONVERGENCE OF A FINITE VOLUME SCHEME FOR GAS–WATER FLOW IN A MULTI-DIMENSIONAL POROUS MEDIUM

2013 ◽  
Vol 24 (01) ◽  
pp. 145-185 ◽  
Author(s):  
MOSTAFA BENDAHMANE ◽  
ZIAD KHALIL ◽  
MAZEN SAAD
Keyword(s):  
Porous Medium ◽  
Finite Volume ◽  
Three Dimensional ◽  
Energy Estimates ◽  
Finite Volume Scheme ◽  
Convergence Properties ◽  
Finite Volume Schemes ◽  
Finite Element Scheme ◽  
Discrete Energy ◽  
Volume Scheme

This paper deals with construction and convergence analysis of a finite volume scheme for compressible/incompressible (gas–water) flows in porous media. The convergence properties of finite volume schemes or finite element scheme are only known for incompressible fluids. We present a new result of convergence in a two or three dimensional porous medium and under the only consideration that the density of gas depends on global pressure. In comparison with incompressible fluid, compressible fluids requires more powerful techniques; especially the discrete energy estimates are not standard.

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