The temporal evolution of thermal instability in fluid layers isothermally heated from below |
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Authors: | Tae?Joon?Chung Min?Chan?Kim Email author" target="_blank">Chang?Kyun?ChoiEmail author |
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Affiliation: | (1) School of Chemical Engineering, Seoul National University, 151-744 Seoul, Korea;(2) Department of Chemical Engineering, Cheju National University, 690-756 Cheju, Korea |
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Abstract: | The temporal development of thermal disturbances in the fluid layer heated isothermally from below is investigated, based
on propagation theory. This theory is examined by using scaling. To examine the behavior of thermal instability the mean-field
approximation is employed and resulting equations are solved by Galerkin method. The stability criteria to mark the onset
of convective instability are newly suggested as the intersection point of the growth rate of averaged temperature with that
of its fluctuation. The resulting critical time is close to that derived from propagation theory. By considering the nonlinear
effects, the characteristic times to represent the detection time of manifest convection and also to exhibit the minimum Nusselt
number are discussed. |
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Keywords: | Mean-field Approximation Natural Convection Propagation Theory |
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