Inverse Method for Estimating Thermal Conductivity in One-Dimensional Heat Conduction Problems

2001 ◽  
Vol 15 (1) ◽  
pp. 34-41 ◽  
Author(s):  
Jiin-Hong Lin ◽  
Cha’o-Kuang Chen ◽  
Yue-Tzu Yang
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Inverse Method ◽  
One Dimensional

scholarly journals On the semi-inverse method and variational principle

2013 ◽  
Vol 17 (5) ◽  
pp. 1565-1568 ◽  
Author(s):  
Xue-Wei Li ◽  
Ya Li ◽  
Ji-Huan He
Keyword(s):  
Heat Conduction ◽  
Variational Principle ◽  
Inverse Method ◽  
Generalized Variational Principle ◽  
Open Forum ◽  
One Dimensional ◽  
History Of

In this Open Forum, Liu et al. proved the equivalence between He-Lee 2009 variational principle and that by Tao and Chen (Tao, Z. L., Chen, G. H., Thermal Science, 17(2013), pp. 951-952) for one dimensional heat conduction. We confirm the correction of Liu et al.?s proof, and give a short remark on the history of the semi-inverse method for establishment of a generalized variational principle.

Anharmonicity Dependent Heat Conduction in One-Dimensional Lattices

2013 ◽  
Vol 209 ◽  
pp. 129-132 ◽  
Author(s):  
Shreya Shah ◽  
Tejal N. Shah ◽  
P.N. Gajjar
Keyword(s):  
Thermal Conductivity ◽  
Numerical Simulation ◽  
Heat Flux ◽  
Heat Conduction ◽  
Temperature Gradient ◽  
Temperature Profile ◽  
Chain Length ◽  
Interparticle Interactions ◽  
One Dimensional ◽  
Harmonic Chain

The temperature profile, heat flux and thermal conductivity are investigated for the chain length of 67 one-dimensional (1-D) oscillators. FPU-β and FK models are used for interparticle interactions and substrate interactions, respectively. As harmonic chain does not produce temperature gradient along the chain, it is required to introduce anharmonicity in the numerical simulation. The anharmonicity dependent temperature profile, thermal conductivity and heat flux are simulated for different strength of anharmonicity β = 0, 0.1, 0.3, 0.5, 0.7, 0.9 and 1. It is concluded that heat flux obeys J = 0.3947 e0.553β with R2 = 0.9319 and thermal conductivity obeys κ = 0.0276 e0.5559β with R2 = 0.9319.

Molecular Dynamics Simulations of Relaxation and Heat Conduction in One-Dimensional FPU β Lattice

2009 ◽  
Author(s):  
Quan-Wen Hou ◽  
Bing-Yang Cao ◽  
Zeng-Yuan Guo
Keyword(s):  
Thermal Conductivity ◽  
Molecular Dynamics ◽  
Heat Flux ◽  
Heat Conduction ◽  
Relaxation Rate ◽  
Molecular Dynamics Simulations ◽  
One Dimensional ◽  
Non Equilibrium Molecular Dynamics ◽  
Dynamics Simulations ◽  
Non Equilibrium

The phonon relaxation and heat conduction of the Femi-Pasta-Ulam β lattice are studied via molecular dynamics simulations. The phonon relaxation rate is calculated from the energy autocorrelation function for different modes at various temperatures through equilibrium molecular dynamics simulations. The relaxation rate as a function of wave vector k is estimated to be proportional to k1.688, which leads to a N0.41 divergence of the thermal conductivity in the framework of Green-Kubo relation. This result is in agreement with that obtained by non-equilibrium molecular dynamics simulations which estimate the length dependence exponent of thermal conductivity as 0.415. Our results confirm the N2/5 divergence in one-dimensional FPU β lattice. The effect of the heat flux on the thermal conductivity is also studied by imposing large temperature differences on the two ends of the lattice in non-equilibrium molecular dynamics simulations. The results indicate that the thermal conductivity is insensitive to the heat flux under our simulation conditions, and the linear response theory is widely applicable.

scholarly journals The Transport Properties of Quasi–One-Dimensional Ba3Co2O6(CO3)0.7

2021 ◽  
Vol 9 ◽  
Author(s):  
Minnan Chen ◽  
Jiangtao Wu ◽  
Qing Huang ◽  
Jinlong Jiao ◽  
Zhiling Dun ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Heat Conduction ◽  
Specific Heat ◽  
Transport Properties ◽  
Thermoelectric Materials ◽  
Electrical Transport ◽  
Magnetic Entropy ◽  
Conductivity Measurements ◽  
Elastic Neutron ◽  
One Dimensional

We have performed combined elastic neutron diffuse, electrical transport, specific heat, and thermal conductivity measurements on the quasi–one-dimensional Ba3Co2O6(CO3)0.7 single crystal to characterize its transport properties. A modulated superstructure of polyatomic CO32− is formed, which not only interferes the electronic properties of this compound, but also reduces the thermal conductivity along the c-axis. Furthermore, a large magnetic entropy is observed to be contributed to the heat conduction. Our investigations reveal the influence of both structural and magnetic effects on its transport properties and suggest a theoretical improvement on the thermoelectric materials by building up superlattice with conducting ionic group.

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