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On the temperature field of a square column embedding a heating cylinder
Author(s) -
Shih F. S.
Publication year - 1970
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690160125
Subject(s) - cylinder , parametrization (atmospheric modeling) , series (stratigraphy) , square (algebra) , embedding , mathematics , boundary value problem , field (mathematics) , column (typography) , mathematical analysis , mechanics , geometry , physics , computer science , optics , pure mathematics , geology , paleontology , connection (principal bundle) , artificial intelligence , radiative transfer
An analysis of the two‐dimensional temperature field of a square column embedding a heating cylinder is presented. The analysis leads to a solution in finite series which gives rise to rapidly converging numerical results. The series coefficients computed for the extreme case of the cylinder being a line find a way of parametrization, which then furnishes the solutions for finite cylinders up to the case of the cylinder diameter being half of the column thickness. Results in five‐digit accuracy are presented. The method is simple and direct. In addition, it retains the same concise formal solution for a variety of boundary conditions.