LYAPOUNOV FUNCTIONS IN PARABOLIC ONE-DIMENSIONAL HEAT CONDUCTION WITH CONSTANT BOUNDARY TEMPERATURES AND WITH THERMAL CONDUCTIVITY AS A FUNCTION OF TEMPERATURE, OF THE COORDINATE IN THE HEAT FLUX DIRECTION AND OF TIME

1998 ◽  
Author(s):  
Giacomo Bisio ◽  
Claudio Pisoni
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Heat Conduction ◽  
One Dimensional

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.

Nonlinear Inverse Heat Conduction With a Moving Boundary: Heat Flux and Surface Recession Estimation

1999 ◽  
Vol 121 (3) ◽  
pp. 708-711 ◽  
Author(s):  
V. Petrushevsky ◽  
S. Cohen
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Fourier Series ◽  
Heat Conduction ◽  
Moving Boundary ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Variable Order ◽  
Inverse Heat Conduction ◽  
One Dimensional

A one-dimensional, nonlinear inverse heat conduction problem with surface ablation is considered. In-depth temperature measurements are used to restore the heat flux and the surface recession history. The presented method elaborates a whole domain, parameter estimation approach with the heat flux approximated by Fourier series. Two versions of the method are proposed: with a constant order and with a variable order of the Fourier series. The surface recession is found by a direct heat transfer solution under the estimated heat flux.

scholarly journals Nonlinear Heat Transport in Superlattices with Mobile Defects

Entropy ◽  
2019 ◽  
Vol 21 (12) ◽  
pp. 1200 ◽  
Author(s):  
David Jou ◽  
Liliana Restuccia
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Heat Conduction ◽  
Thermal Resistance ◽  
Heat Transport ◽  
Concentration Dependence ◽  
Transport Coefficients ◽  
Nonlinear Behavior ◽  
Strongly Nonlinear

We consider heat conduction in a superlattice with mobile defects, which reduce the thermal conductivity of the material. If the defects may be dragged by the heat flux, and if they are stopped at the interfaces of the superlattice, it is seen that the effective thermal resistance of the layers will depend on the heat flux. Thus, the concentration dependence of the transport coefficients plus the mobility of the defects lead to a strongly nonlinear behavior of heat transport, which may be used in some cases as a basis for thermal transistors.

scholarly journals Non-steady-state heat conduction in composite walls

2014 ◽  
Vol 470 (2165) ◽  
pp. 20130605 ◽  
Author(s):  
Bernard Deconinck ◽  
Beatrice Pelloni ◽  
Natalie E. Sheils
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Steady State ◽  
Composite Materials ◽  
Solution Method ◽  
One Dimensional ◽  
Infinite Domains ◽  
Steady State Heat ◽  
The One ◽  
Composite Walls

The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but neither temperature nor heat flux is prescribed there. Instead, the physical assumptions of their continuity at the interfaces are the only conditions imposed. The problem of two semi-infinite domains and that of two finite-sized domains are examined in detail. We indicate also how to extend the solution method to the setting of one finite-sized domain surrounded on both sides by semi-infinite domains, and on that of three finite-sized domains.

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