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numerical investigation of free convection between two vertical coaxial cylinders
Author(s) -
Schwab Thomas H.,
De Witt Kenneth J.
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.690160624
Subject(s) - prandtl number , streamlines, streaklines, and pathlines , grashof number , rayleigh number , nusselt number , annulus (botany) , mechanics , natural convection , mathematics , geometry , steady state (chemistry) , finite difference , convection , mathematical analysis , physics , materials science , reynolds number , chemistry , turbulence , composite material
Free convection between two vertical coaxial cylinders was studied by solving the governing transport equations as an initial‐value problem. The coupled, nonlinear, partial differential equations were converted into a set of difference equations by use of an alternating‐direction implicit finite‐difference numerical scheme. Twenty‐four different combinations of Prandtl and Grashof numbers, and height to annular spacing ratios were used to characterize the problem. The results are presented primarily in the form of contour maps for the steady‐state isotherms and streamlines. For Rayleigh numbers greater than 5 × 10 3 , a fully developed boundary‐layer flow was found to exist in the cavity. The interior region of the annulus was found to be thermally stratified and to possess a nearly uniform vertical temperature gradient, with a unicellular flow pattern being generated. With Rayleigh numbers of 5 × 10 4 and greater, it was found that the flow patterns could not be properly described with a grid spacing of 1/10. The variation of the steady‐state mean Nusselt number with Prandtl and Rayleigh numbers and with geometric ratios was also investigated.