Spatial Nonlocality Effect Influence on the Plate Temperature State

Authors: Savelyeva I.Yu. Published: 21.02.2024
Published in issue: #1(112)/2024  
DOI: 10.18698/1812-3368-2024-1-28-40

Category: Mathematics and Mechanics | Chapter: Mathematical Simulation, Numerical Methods and Software Packages  
Keywords: mathematical model, nonlocality, heat transfer, multiscale approach, nonequilibrium molecular dynamics


Models used in the multiscale simulation are ranging from the quantum mechanics to the continuum mechanics models. At the microscale, the molecular dynamics models are computationally intensive. Thus, the macroscale models imply the modified continuum models, make it possible to take into account relationship between the material characteristics at the macro and micro levels, and are remaining relevant. One of the well-known approaches to constructing such models involves considering the influence of the continuum spatial and temporal nonlocality. All the nonlocality medium models include certain nonlocality parameters, which variation and selection make it possible to account for connection between medium characteristics at the macro and micro levels. Currently, establishing connections between these macroscale models parameters and parameters of the atomistic and molecular dynamics models becomes an urgent task. The paper uses the example of a problem in the stationary temperature state of a homogeneous plate taking into account the spatial nonlocality, and demonstrates a possibility to establish the indicated relationships between parameters of the different-scale models. An analytical solution was obtained for the one-dimensional problem when considering a simple influence function. Influence of the nonlocality coefficient on the degree of deviation of the temperature distribution over the plate thickness from the classical solution was analyzed. The plate temperature state obtained within the framework of the macroscale approach was compared with the mathematical simulation results at the temperature distribution nanolevel using the nonequilibrium molecular dynamics method

The work was supported by the Ministry of Science and Higher Education of the Russian Federation (project no. 0705-2023-0012)

Please cite this article in English as:

Savelyeva I.Yu. Spatial nonlocality effect influence on the plate temperature state. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2024, no. 1 (112), pp. 28--40 (in Russ.). EDN: EZWDQS


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