Heat transfer due to natural convection in a periodically heated slot

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Original languageEnglish
Article number022503
Journal / PublicationJournal of Heat Transfer
Issue number2
Online published28 Dec 2012
Publication statusPublished - 1 Feb 2013
Externally publishedYes


Heat transfer resulting from the natural convection in a fluid layer contained in an infinite horizontal slot bounded by solid walls and subject to a spatially periodic heating at the lower wall has been investigated. The heating produces sinusoidal temperature variations along one horizontal direction characterized by the wave number with the amplitude expressed in terms of a suitably defined Rayleigh number Rap. The maximum heat transfer takes place for the heating with the wave numbers α=0(1) as this leads to the most intense convection. The intensity of convection decreases proportionally to when α→0, resulting in the temperature field being dominated by periodic conduction with the average Nusselt number decreasing proportionally to α2. When α→δ, the convection is confined to a thin layer adjacent to the lower wall with its intensity decreasing proportionally to α-3. The temperature field above the convection layer looses dependence on the horizontal direction. The bulk of the fluid sees the thin convective layer as a "hot wall". The heat transfer between the walls becomes dominated by conduction driven by a uniform vertical temperature gradient which decreases proportionally to the intensity of convection resulting in the average Nusselt number decreasing as α-3. It is shown that processes described above occur for Prandtl numbers 0.001 < Pr < 10 considered in this study.  

Research Area(s)

  • natural convection, periodic heating, spectral methods