Abstract
This paper is concerned with an important class of heat transfer problems, which arises when the radiation heat transfer is the mechanism for energy transfer from/to a rigid and nonconvex black body. In such situations there will exist a direct energy interchange among points of the body boundary that do not belong to a given “small neighborhood”. Such phenomena are mathematically described by a partial differential equation subjected to nonlinear boundary conditions. It is demonstrated that the problem always admits a solution, which is unique. In addition, an algorithm for solving such problems is presented.
Résumé
Cet article aborde une classe importante de problèmes d'échange de chaleur qui a lieu lorsque la radiation thermique est le méchanisme qui assure le transfert d'énergie de ou vers un corps noir rigide et nonconvexe. Dans ce cas, il y aura un échange direct d'énergie entre les points de frontière du corps non nécessairement proches. Ces phénomènes sont décrits mathématiquement par une équation différentielle partielle où les conditions aux limites sont non-linéaires. On démontre que ce problème admet toujours une, et seulement une, solution. Un algorithme pour résoudre de tels problèmes est aussi présenté.
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Saldanha da Gama, R.M. Existence uniqueness and construction of the solution of the energy transfer problem in a rigid and nonconvex black body. Z. angew. Math. Phys. 42, 334–347 (1991). https://doi.org/10.1007/BF00945707
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DOI: https://doi.org/10.1007/BF00945707