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http://dx.doi.org/10.9713/kcer.2019.57.1.142

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

Kim, Min Chan (Department of Chemical Engineering, Jeju National University)
Publication Information
Korean Chemical Engineering Research / v.57, no.1, 2019 , pp. 142-147 More about this Journal
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 $Ra_c=669$ 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 ${\tau}_m$ 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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Times Cited By KSCI : 2  (Citation Analysis)
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