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Initiation of thermal convection in finite right circular cylinders
Author(s) -
Catton Ivan,
Edwards D. K.
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.690160415
Subject(s) - rayleigh number , cylinder , adiabatic process , convection , mechanics , perturbation (astronomy) , rayleigh scattering , thermal , natural convection , physics , combined forced and natural convection , materials science , geometry , mathematics , thermodynamics , optics , quantum mechanics
Linear perturbation analyses are extended to determine the lowest Rayleigh number at which convection initiates in a vertical cylinder heated on the bottom and cooled on the top. The critical Rayleigh number for the first mode of convection in a right circular cylinder with a perfectly conducting wall is shown to be three times larger than that in such a cell with a perfectly adiabatic side wall. An adjusted wave number is shown to make the results of Pellew and Southwell applicable to the adiabatic wall in a manner similar to that used by Pnueli and Ostrach for the perfectly conducting side wall. The results are compared with experiment and are in very good agreement.