Multiple spatial and temporal scales method for numerical simulation of non-classical heat conduction problems: one dimensional case

2005 ◽  
Vol 42 (3-4) ◽  
pp. 877-899 ◽  
Author(s):  
Hongwu Zhang ◽  
Sheng Zhang ◽  
Xu Guo ◽  
Jinying Bi
Keyword(s):  
Numerical Simulation ◽  
Heat Conduction ◽  
Dimensional Case ◽  
Temporal Scales ◽  
One Dimensional ◽  
Spatial And Temporal Scales

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.

scholarly journals Thermoelasticity of Moore–Gibson–Thompson type with history dependence in the temperature

2020 ◽  
Vol 120 (1-2) ◽  
pp. 1-21 ◽  
Author(s):  
Monica Conti ◽  
Vittorino Pata ◽  
Ramon Quintanilla
Keyword(s):  
Heat Conduction ◽  
Differential System ◽  
Exponential Decay ◽  
Relaxation Parameter ◽  
Dimensional Case ◽  
Well Posedness ◽  
History Dependence ◽  
One Dimensional ◽  
Thermoelastic Model ◽  
The One

In this paper, we consider a thermoelastic model where heat conduction is described by the history dependent version of the Moore–Gibson–Thompson equation, arising via the introduction of a relaxation parameter in the Green-Naghdi type III theory. The well-posedness of the resulting integro-differential system is discussed. In the one-dimensional case, the exponential decay of the energy is proved.

scholarly journals Numerical Simulation of 1D Unsteady Heat Conduction-Convection in Spherical and Cylindrical Coordinates by Fourth-Order FDM

2018 ◽  
Vol 8 (1) ◽  
pp. 2389-2392
Author(s):  
E. C. Romao ◽  
L. H. P. De Assis
Keyword(s):  
Numerical Simulation ◽  
Heat Conduction ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Fourth Order ◽  
Spherical Coordinates ◽  
Cylindrical Coordinates ◽  
One Dimensional ◽  
Unsteady Heat Conduction ◽  
The One

This paper aims to apply the Fourth Order Finite Difference Method (FDM) to solve the one-dimensional unsteady conduction-convection equation with energy generation (or sink) in cylindrical and spherical coordinates. Two applications were compared through exact solutions to demonstrate the accuracy of the proposed formulation.

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