Unique solvability of a stationary radiative‐conductive heat transfer problem in a system consisting of an absolutely black body and several semitransparent bodies

Abstract

We consider a stationary boundary value problem describing a radiative‐conductive heat transfer in a system consisting of one absolutely black body and several semitransparent bodies. To describe the radiative transfer, the integro‐differential radiative transfer equation is used. We do not take into account the dependence of the radiation intensity and the properties of semitransparent materials on the radiation frequency. We proved at the first time the unique solvability of this problem. Besides, we proved the comparison theorems and established the results on improving the properties of solutions with increasing exponents of data summability.

Nonstationary radiative–conductive heat transfer problem in an absolutely black body with semitransparent inclusions

“…We formulate some results on the properties of the problem (4.1), (4.2) which follow from literature. 1,10,12 Assume that ( F, J) ∈ L 1 (G 𝑗 , 𝜕G 𝑗 ). By a solution to the problem (4.1), (4.2), we mean a function I 𝑗 ∈ W 1 (D 𝑗 ) that satisfies the equation (4.1) almost everywhere in D 𝑗 and the condition (4.2) almost everywhere on Γ − 𝑗 .…”

“…A fairly complete overview of the relevant mathematical work from 1937 to 2020 can be found in Amosov. 1 At the same time, the problems of radiative-conductive heat transfer in systems consisting of both opaque and of semitransparent for radiation bodies remain as yet unexplored. In this direction, as far as the author knows, there are only articles.…”

“…In this direction, as far as the author knows, there are only articles. [1][2][3][4] The article 1 established the unique solvability of complex heat transfer problem in a convex absolutely black body containing semitransparent inclusions. This article establishes the unique solvability of a nonstationary variant of this problem.…”

“…To date, the solvability of various statements of stationary and non‐stationary boundary value problems of complex (radiative–conductive) heat transfer in systems consisting either only of opaque bodies or only of semitransparent for the radiation bodies has been studied in sufficient detail. A fairly complete overview of the relevant mathematical work from 1937 to 2020 can be found in Amosov 1 …”

“…At the same time, the problems of radiative–conductive heat transfer in systems consisting of both opaque and of semitransparent for radiation bodies remain as yet unexplored. In this direction, as far as the author knows, there are only articles 1–4 . The article 1 established the unique solvability of complex heat transfer problem in a convex absolutely black body containing semitransparent inclusions.…”