Mathematical model of the heat transfer process taking into account the consequences of nonlocality in structurally sensitive materials

Original scientific paper https://doi.org/10.2298/TSCI19S4273KThe creation of new materials based on nanotechnology is an important direction of modern materials science development. Materials obtained by using nanotechnology can possess unique physicomechanical and thermophysical properties, allowing to use them effectively in structures exposed to high-intensity thermomechanical effects. An important step of the creation and usage of new materials is the construction of mathematical models to describe the behavior of these materials in a wide range of changes in external influences. One of the possible models for describing the process of thermal conductivity in structurally sensitive materials is proposed in this paper. The model is based on the laws of rational thermodynamics of irreversible processes and models of a continuous medium with internal state parameters. A qualitative study of the constructed model is carried out. A difference scheme is constructed in order to find the solution of the non-stationary heat conduction problem with allowance for the spatial nonlocality effect. The analysis of the solutions is carried out.

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“…Consider boundary and initial conditions for eq. (18) in the form (12)- (14). Then the solution can be obtained analogously to the case  = 0.…”

Section: Results For Curvilinear Shellmentioning

confidence: 99%

“…In [10][11][12][13][14], thermoelasticity models were introduced using effective variables of temperature and deformation. Based on these models, the temperature and stress fields in a flat layer were analyzed at high-intensity surface heating.…”

Section: Introductionmentioning

confidence: 99%

One mathematical model of thermal conductivity for materials with a granular structure

2019

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“…The effect of nonlocality of the environment is that the physical characteristics of the elements of the structure-sensitive material are influenced by other surrounding elements of the structure. In this regard, the expression for the heat flux can be written in the form [4]…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Nonlocal interpretation available suggested by Eringen. The development of this theory to describe the nonlocal behavior of materials under conditions of high-intensity surface illumination is considered in [4,5].…”

Section: Introductionmentioning

confidence: 99%

Temperature distribution in a composite rod, taking into account nonlocal spatial effects

2019

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One of the important directions in the field of creating new structural and functional materials is the study of materials with a complex structure and unique strength or temperature properties. Due to the heterogeneity of their structure, such materials are called “structurally sensitive”. The heterogeneity of the structure of such materials is justified by the technological features of their creation. Structurally sensitive materials can be obtained by compacting nanopowders, deposition on a substrate, etc. The paper considers a mathematical model of heat propagation in a composite rod. At one of the ends of the rod, a protective coating of structurally sensitive material is used. Using the finite element method, numerical solutions are found for a problem with conditions of ideal thermal contact of rod parts. The results of the numerical calculation for various materials are given. The influence of material parameters on the heat distribution in the rod is analysed.

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“…The classical theory of continuum is not suitable for the mechanical analysis of micro-and nanostructures, since it is scaleless and does not have parameters for the scale of structural elements. On the other hand, sizedependent theories of thermomechanics such as surface stress theory [1][2], gradient theory [3] and nonlocal theory [4][5][6][7] are widely used to study the mechanical behavior of materials at the micro and nanoscale due to their ability to take into account the effect of size. Among them, the nonlocal theory developed by Ehringen and his collaborators [7] is the well-known nonclassical theory of thermoelasticity, in which the behavior at a material point depends on the state of all points of the body.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal Thermodynamics: Mathematical Model of Two-Dimensional Thermal Conductivity

Кувыркин¹,

Savelyeva²,

Kuvshinnikova³

2021

E3S Web Conf.

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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.

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Mathematical model of the heat transfer process taking into account the consequences of nonlocality in structurally sensitive materials

Cited by 7 publications

References 5 publications

One mathematical model of thermal conductivity for materials with a granular structure

One mathematical model of thermal conductivity for materials with a granular structure

Temperature distribution in a composite rod, taking into account nonlocal spatial effects

Nonlocal Thermodynamics: Mathematical Model of Two-Dimensional Thermal Conductivity

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