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Conflict of Interest: In relation to this article, we declare that there is no conflict of interest.

Publication history: Received September 1, 2018
Accepted November 20, 2018

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/bync/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Energy Stability Analysis on the Onset of Buoyancy-Driven Convection in a Horizontal Fluid Layer Subject to Evaporative Cooling

Min Chan Kim^†

Department of Chemical Engineering, Jeju National University, 102, Jejudaehak-ro, Jeju-si, Jeju-do, 63243, Korea

mckim@cheju.ac.kr

Korean Chemical Engineering Research, February 2019, 57(1), 142-147(6), 10.9713/kcer.2019.57.1.142 Epub 31 January 2019

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Abstract

The onset of buoyancy-driven convection in an initially isothermal and quiescent horizontal fluid layer was analyzed theoretically. It is well-known that at the critical Rayleigh number Rac = 669 convective motion sets in with a constant-heat-flux cooling through the upper boundary. Here, based on the momentary instability concept, the dimensionless critical time τm to mark the onset of convective motion for Ra > 669 was analyzed theoretically. The energy method under the momentary stability concept was used to find the critical conditions as a function of the Rayleigh number Ra and the Prandtl number Pr. The predicted critical conditions were compared with the previous theoretical and experimental results. The momentary stability criterion gives more reasonable wavenumber than the conventional energy method.

Keywords

Buoyancy-driven convection Energy stability Relative energy Momentary stability

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