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Natural convection between two horizontal coaxial cylinders
Author(s) -
Passerini A.,
Růžička M.,
Thäter G.
Publication year - 2009
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200800222
Subject(s) - annulus (botany) , rayleigh number , prandtl number , natural convection , uniqueness , mechanics , rayleigh scattering , mathematics , convection , mathematical analysis , coaxial , physics , materials science , optics , engineering , composite material , electrical engineering
Abstract The objective of our paper is to start the theoretical investigation of the most commonly used mathematical model for natural convection in a horizontal annulus. First, one shows existence of solutions for the unsteady problem. Then, for any Prandtl number and inverse relative gap width, existence, and stability of a steady solution is proved, provided that the Rayleigh number is sufficiently small. The same is also proved for any Rayleigh number provided the inverse relative gap width is sufficiently small. Furthermore, exponential decay to the steady symmetric solution and uniqueness hold true under stronger restrictions to the Rayleigh number.