Justification of Discrete and Asymptotic Approximations for the Complex Heat Transfer Problem

摘要

We justify discrete and asymptotic approximations for the radiative-conductive heat transfer problem in a system of heat-conductive rods with square cross-section separated by vacuum layers and placed in a square box. We obtain error estimates of order Oε/λdocumentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$ Oleft(sqrt{varepsilon }/lambda right) $$end{document} and Oε,documentclass12pt{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$ Oleft(sqrt{varepsilon}right), $$end{document} where ε is the length of the rod cross-section side, and λ is the heat conductivity.