Nonlocal Thermodynamics: Mathematical Model of Two-Dimensional Thermal Conductivity

Nonlocal models of thermodynamics are becoming more and more popular in the modern world. Such models make it possible to describe materials with a complex structure and unique strength and temperature properties. Models of nonlocal thermodynamics of a continuous medium establish a relationship betw...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Kuvyrkin George, Savelyeva Inga, Kuvshinnikova Daria
Formato:	article
Lenguaje:	EN FR
Publicado:	EDP Sciences 2021
Materias:	Environmental sciences GE1-350
Acceso en línea:	https://doaj.org/article/f1e392f8e5d14c899e0883d85de0e5bb
Etiquetas:	Agregar Etiqueta Sin Etiquetas, Sea el primero en etiquetar este registro!

id	oai:doaj.org-article:f1e392f8e5d14c899e0883d85de0e5bb
record_format	dspace
spelling	oai:doaj.org-article:f1e392f8e5d14c899e0883d85de0e5bb2021-11-12T11:44:34ZNonlocal Thermodynamics: Mathematical Model of Two-Dimensional Thermal Conductivity2267-124210.1051/e3sconf/202132103005https://doaj.org/article/f1e392f8e5d14c899e0883d85de0e5bb2021-01-01T00:00:00Zhttps://www.e3s-conferences.org/articles/e3sconf/pdf/2021/97/e3sconf_icchmt2021_03005.pdfhttps://doaj.org/toc/2267-1242Nonlocal models of thermodynamics are becoming more and more popular in the modern world. Such models make it possible to describe materials with a complex structure and unique strength and temperature properties. Models of nonlocal thermodynamics of a continuous medium establish a relationship between micro and macro characteristics of materials. A mathematical model of thermal conductivity in nonlocal media is considered. The model is based on the theory of nonlocal continuum by A.K. Eringen. The interaction of material particles is described using local and nonlocal terms in the law of heat conduction. The nonlocal term describes the effect of decreasing the influence of the surrounding elements of the material structure with increasing distance. The effect of nonlocal influence is described using the standard non-locality function based on the Gaussian distribution. The nonlocality function depends on the distance between the elements of the material structure. The mathematical model of heat conduction in a nonlocal medium consists of an integro-differential heat conduction equation with initial and boundary conditions. A numerical solution to the problem of heat conduction in a nonlocal plate is obtained. The numerical solution of a two-dimensional problem based on the finite element method is described. The influence of nonlocal effects and material parameters on the thermal conductivity in a plate under highintensity surface heating is analyzed. The importance of nonlocal characteristics in modelling the thermodynamic behaviour of materials with a complex structure is demonstrated.Kuvyrkin GeorgeSavelyeva IngaKuvshinnikova DariaEDP SciencesarticleEnvironmental sciencesGE1-350ENFRE3S Web of Conferences, Vol 321, p 03005 (2021)
institution	DOAJ
collection	DOAJ
language	EN FR
topic	Environmental sciences GE1-350
spellingShingle	Environmental sciences GE1-350 Kuvyrkin George Savelyeva Inga Kuvshinnikova Daria Nonlocal Thermodynamics: Mathematical Model of Two-Dimensional Thermal Conductivity
description	Nonlocal models of thermodynamics are becoming more and more popular in the modern world. Such models make it possible to describe materials with a complex structure and unique strength and temperature properties. Models of nonlocal thermodynamics of a continuous medium establish a relationship between micro and macro characteristics of materials. A mathematical model of thermal conductivity in nonlocal media is considered. The model is based on the theory of nonlocal continuum by A.K. Eringen. The interaction of material particles is described using local and nonlocal terms in the law of heat conduction. The nonlocal term describes the effect of decreasing the influence of the surrounding elements of the material structure with increasing distance. The effect of nonlocal influence is described using the standard non-locality function based on the Gaussian distribution. The nonlocality function depends on the distance between the elements of the material structure. The mathematical model of heat conduction in a nonlocal medium consists of an integro-differential heat conduction equation with initial and boundary conditions. A numerical solution to the problem of heat conduction in a nonlocal plate is obtained. The numerical solution of a two-dimensional problem based on the finite element method is described. The influence of nonlocal effects and material parameters on the thermal conductivity in a plate under highintensity surface heating is analyzed. The importance of nonlocal characteristics in modelling the thermodynamic behaviour of materials with a complex structure is demonstrated.
format	article
author	Kuvyrkin George Savelyeva Inga Kuvshinnikova Daria
author_facet	Kuvyrkin George Savelyeva Inga Kuvshinnikova Daria
author_sort	Kuvyrkin George
title	Nonlocal Thermodynamics: Mathematical Model of Two-Dimensional Thermal Conductivity
title_short	Nonlocal Thermodynamics: Mathematical Model of Two-Dimensional Thermal Conductivity
title_full	Nonlocal Thermodynamics: Mathematical Model of Two-Dimensional Thermal Conductivity
title_fullStr	Nonlocal Thermodynamics: Mathematical Model of Two-Dimensional Thermal Conductivity
title_full_unstemmed	Nonlocal Thermodynamics: Mathematical Model of Two-Dimensional Thermal Conductivity
title_sort	nonlocal thermodynamics: mathematical model of two-dimensional thermal conductivity
publisher	EDP Sciences
publishDate	2021
url	https://doaj.org/article/f1e392f8e5d14c899e0883d85de0e5bb
work_keys_str_mv	AT kuvyrkingeorge nonlocalthermodynamicsmathematicalmodeloftwodimensionalthermalconductivity AT savelyevainga nonlocalthermodynamicsmathematicalmodeloftwodimensionalthermalconductivity AT kuvshinnikovadaria nonlocalthermodynamicsmathematicalmodeloftwodimensionalthermalconductivity
_version_	1718430592238878720

Nonlocal Thermodynamics: Mathematical Model of Two-Dimensional Thermal Conductivity

Ejemplares similares