Unique solvability of a nonstationary problem of radiative-conductive heat exchange in a system of semitransparent bodies

Амосов, А. А.

doi:10.1134/s106192081603002x

Cited by 28 publications

(13 citation statements)

References 37 publications

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“…Отметим работы , в которых представлен анализ краевых, экстремальных и обратных задач для диффузионных уравнений радиационного теплообмена. Краевые задачи, учитывающие радиационный теплообмен, рассмотрены в [22][23][24][25][26][27]. Отметим также, что разрешимость краевых задач для уравнений сложного теплообмена с условиями (4) для температуры доказана в [20,21].…”

Section: задача оптимального управленияunclassified

An algorithm for solving the boundary value problem of radiation heat transfer without boundary conditions for radiation intensity

Chebotarëv¹,

Mesenev²

2020

FEMJ

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An optimization algorithm for solving the boundary value problem for the stationary equations of radiation-conductive heat transfer in the three-dimensional region is presented in the framework of the $ P_1 $ - approximation of the radiation transfer equation. The analysis of the optimal control problem that approximates the boundary value problem where they are not defined boundary conditions for radiation intensity. Theoretical analysis is illustrated by numerical examples.

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Section: задача оптимального управленияunclassified

An algorithm for solving the boundary value problem of radiation heat transfer without boundary conditions for radiation intensity

Chebotarëv¹,

Mesenev²

2020

FEMJ

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“…We can also find in the literature some results in multidimensional case, see [2,3,11,4,5,10,12]. For example in [4,5] the authors considered three-dimensional stationary case.…”

Section: Introductionmentioning

confidence: 96%

“…For example in [4,5] the authors considered three-dimensional stationary case. Recently, A.A. Amosov [12] proves a result on the unique solvability of a nonstationary problem of radiative-conductive heat transfer in a system of semitransparent bodies (3D case) for the homogeneous conductive boundary conditions. The radiation transfer equation is associated with boundary conditions of mirror reflection and refraction according to the Fresnel laws is used to describe the propagation of radiation.…”

Section: Introductionmentioning

confidence: 99%

Existence and uniqueness of a transient state for the coupled radiative–conductive heat transfer problem

Gabsi

Roche

Schmitt

2018

Computers & Mathematics with Applications

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This paper deals with existence and uniqueness results for a transient nonlinear radiative-conductive system in threedimensional case. This system describes the heat transfer for a grey, semi-transparent and non-scattering medium with general boundary conditions. We reformulate the full transient state system as a fixed-point problem. The existence and uniqueness proof is based on Banach fixed point theorem.

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“…Reviews of the results on the solvability of problems of complex heat transfer can be found, e.g., in [5,6].…”

Section: Introductionmentioning

confidence: 99%

“…A similar nonstationary problem with conditions of mirror reflection and refraction by the Fresnel laws was studied in [8,6]. Earlier, in [9] (see also [10]), the existence of the solution to the stationary problem of radiative-conductive heat transfer in a system of semitransparent bodies in a simplified formulation without regard for reflection and refraction at the boundaries of bodies was proven.…”

Section: Introductionmentioning

confidence: 99%

Stationary problem of complex heat transfer in a system of semitransparent bodies with boundary conditions of diffuse reflection and refraction of radiation

Амосов

2017

Comput. Math. and Math. Phys.

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A boundary value problem describing complex (radiation-conductive) heat transfer in a system of semitransparent bodies is considered. Complex heat transfer is described by a system consisting of a stationary heat equation and an equation of radiative transfer with the boundary conditions of diffuse reflection and diffuse refraction of radiation. The dependence of the radiation intensity and optical properties of bodies on the frequency of radiation is taken into account. The unique existence of the weak solution to this problem is established. The comparison theorem is proven. Estimates of the weak solution are derived, and its regularity is established.

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Unique solvability of a nonstationary problem of radiative-conductive heat exchange in a system of semitransparent bodies

Cited by 28 publications

References 37 publications

An algorithm for solving the boundary value problem of radiation heat transfer without boundary conditions for radiation intensity

An algorithm for solving the boundary value problem of radiation heat transfer without boundary conditions for radiation intensity

Existence and uniqueness of a transient state for the coupled radiative–conductive heat transfer problem

Stationary problem of complex heat transfer in a system of semitransparent bodies with boundary conditions of diffuse reflection and refraction of radiation

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