Unique Solvability of Stationary Radiative-Conductive Heat Transfer Problem in a System of Semitransparent Bodies

Inhomogeneous boundary-value problem of radiation heat transfer for a multicomponent medium

“…Отметим статьи [2-18], посвященные краевым, экстремальным и обратным задачам для диффузионных уравнений радиационного теплообмена. Интересные краевые задачи, учитывающие радиационный теплообмен, рассмотрены в [19][20][21].…”

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

“…Proof We use some ideas of the method proposed in Krizek and Liu 107 for proving comparison theorems for quasilinear elliptic equations. Versions of this method were used in the literature 41,42,54‐57 for the radiative‐conductive heat transfer problems. Let 0 < δ < 1 be a parameter.…”

“…In the past 30 years, a large number of papers have been devoted to the solvability of complex heat transfer problems in radiation‐opaque or radiation‐semitransparent materials (cf. other works 16–47,48–64 ). Note that, in the literature, 46–51,53,59–64 the radiation transfer equation is changed by its diffusion P 1 approximation.…”

“…We do not take into account the dependence of the radiation intensity and the properties of semitransparent materials on the radiation frequency. To study the solvability of the problem under consideration, we use the technique developed in the articles 12,41,55,56 …”

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

“…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].…”