On the Temperature Distribution of a Body Heated by Radiation

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-05-14 DOI:10.1137/23m1580917

Jin Woo Jang, Juan J. L. Velázquez

引用次数: 0

Abstract

SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3478-3508, June 2024.
Abstract. In this paper, we study the temperature distribution of a body when the heat is transmitted only by radiation. The heat transmitted by convection and conduction is ignored. We consider the stationary radiative transfer equation in local thermodynamic equilibrium. We prove that the stationary radiative transfer equation coupled with the nonlocal temperature equation is well-posed in general geometries when emission-absorption or scattering of interacting radiation is considered. The emission-absorption and the scattering coefficients are assumed to be general, and they can depend on the frequency of radiation. We also establish an entropy production formula of the system which is used to prove the uniqueness of solutions for an incoming radiation with constant temperature.

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关于辐射加热体的温度分布

SIAM 数学分析期刊》，第 56 卷第 3 期，第 3478-3508 页，2024 年 6 月。摘要本文研究了仅通过辐射传热时的体温分布。对流和传导的热量被忽略。我们考虑局部热力学平衡下的静止辐射传递方程。我们证明，当考虑相互作用辐射的发射-吸收或散射时，与非局部温度方程耦合的静态辐射传递方程在一般几何条件下都能很好地求解。发射-吸收和散射系数被假定为一般系数，它们可以取决于辐射的频率。我们还建立了系统的熵产生公式，用来证明恒温入射辐射解的唯一性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.