Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Stability of time-periodic temperature fields

Authors: Chia-Shun Yih and Jinsong Shi
Journal: Quart. Appl. Math. 45 (1987), 39-50
MSC: Primary 76E15
DOI: https://doi.org/10.1090/qam/885166
MathSciNet review: 885166
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Abstract: The energy method developed by Joseph [4], Davis [2], and Homsy [3] is applied to the time-periodic temperature fields considered by Yih and Li [11] to obtain Rayleigh numbers below which the fluid is stable. This is done to see how far the Rayleigh numbers so determined fall below the critical Rayleigh numbers, above which the flow is unstable, as determined by the linear theory [11]. It is found that, unlike the case of classical Bénard cells, the gray area, or area of ignorance, is quite large, indicating the need for some improvement of the energy method to give sharper lower bounds on the Rayleigh number.

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DOI: https://doi.org/10.1090/qam/885166
Article copyright: © Copyright 1987 American Mathematical Society

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