Thermal conductivity of anharmonic crystals with self-consistent baths: Analytical computation with discrete time

2013 ◽  
Vol 87 (3) ◽  
Author(s):  
Emmanuel Pereira ◽  
Ricardo Falcao ◽  
Humberto C. F. Lemos
Keyword(s):  
Thermal Conductivity ◽  
Discrete Time ◽  
Analytical Computation ◽  
Self Consistent ◽  
Anharmonic Crystals

On the Dynamical Propeties of a Strongly Anharmonic Face-Centered Cubic Crystal

1998 ◽  
Vol 12 (27n28) ◽  
pp. 2869-2879 ◽  
Author(s):  
V. I. Zubov ◽  
C. G. Rodrigues ◽  
M. F. Pascual
Keyword(s):  
Crystallographic Direction ◽  
Face Centered Cubic ◽  
Mean Square ◽  
Cubic Crystal ◽  
Cubic Lattice ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Face Centered ◽  
Anharmonic Crystals

We study the interatomic correlations and mean square relative displacements (MSRD) in anharmonic crystals on the basis of the correlative method of unsymmetrized self-consistent field (CUSF). Here we present general formulae for crystals with the anharmonicity, including the strong one, up to the fourth anharmonic terms and perform calculations of the quadratic correlation moments (QCM) in a crystal with face centered cubic lattice, namely in solid Ar. The second order of CUSF allows one to investigate correlations in this lattice between the nearest, second, third and fourth neighbors. The anharmonicity was demonstrated to have strong effect on the interatomic correlations at temperatures above 0.4 of the melting temperature causing a drastic rise near the spinodal point. The dependence of QCM on the distance between atoms and on the crystallographic direction is discussed.

Self-Consistent Open-Celled Metal Foam Model for Thermal Applications

2006 ◽  
Vol 128 (11) ◽  
pp. 1194-1203 ◽  
Author(s):  
Eric N. Schmierer ◽  
Arsalan Razani
Keyword(s):  
Thermal Conductivity ◽  
Granular Material ◽  
Metal Foam ◽  
Foam Cell ◽  
Geometric Model ◽  
Active Material ◽  
Diameter Distribution ◽  
Thermal Conductivity Ratio ◽  
High Porosity ◽  
Self Consistent

Many engineering applications require thermal cycling of granular materials. Since these materials generally have poor effective thermal conductivity various techniques have been proposed to improve bed thermal transport. These include insertion of metal foam with the granular material residing in the interstitial space. The use of metal foam introduces a parasitic thermal capacitance, disrupts packing, and reduces the amount of active material. In order to optimize the combined high porosity metal foam-granular material matrix and study local thermal nonequilibrium, multiple energy equations are required. The interfacial conductance coefficients, specific interface area, and the effective thermal conductivities of the individual components, which are required for a multiple energy equation analysis, are functions of the foam geometry. An ideal three-dimensional geometric model of open-celled Duocell® foam is proposed. Computed tomography is used to acquire foam cell and ligament diameter distribution, ligament shape, and specific surface area for a range of foam parameters to address various shortcomings in the literature. These data are used to evaluate the geometric self-consistency of the proposed geometric model with respect to the intensive and extensive geometry parameters. Experimental thermal conductivity data for the same foam samples are acquired and are used to validate finite element analysis results of the proposed geometric model. A simple relation between density and thermal conductivity ratio is derived using the results. The foam samples tested exhibit a higher dependence on relative density and less dependence on interstitial fluid than data in the literature. The proposed metal foam geometric model is shown to be self-consistent with respect to both its geometric and thermal properties.

An Analytical Modeling for Effective Thermal Conductivity of Multi-Phase Transversely Isotropic Fiberous Composites Using Generalized Self-Consistent Method

2012 ◽  
Vol 249-250 ◽  
pp. 904-909 ◽  
Author(s):  
Syed Aadil Hassan ◽  
Hassaan Ahmed ◽  
Asif Israr
Keyword(s):  
Thermal Conductivity ◽  
Effective Thermal Conductivity ◽  
Composite System ◽  
Volume Fraction ◽  
Transversely Isotropic ◽  
Balance Principle ◽  
Isotropic Composite ◽  
Self Consistent ◽  
Consistent Method ◽  
Multi Phase

In this paper a theoretical relationship for the effective thermal conductivity of a multiphase transversely isotropic composite system is obtained. The Generalized Self-Consistent Method and simple energy balance principle is employed to derive a more appropriate model. In the derivation, it is assumed that the orientation of fiber within the transversely isotropic composite system is unidirectional and surrounded by two different phases of porous and matrix phase. A combined effect of these three different phases on the effective thermal conductivity of the composite system in transverse direction is studied. The effect of the interfacial contact conductance between the fibers and porous medium is also considered. Results of effective thermal conductivity are plotted against volume fraction and conductance which shows extremely good agreement.

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