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When is natural convection completely passive?
Author(s) -
Kay Anthony
Publication year - 2016
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201400177
Subject(s) - buoyancy , mechanics , boussinesq approximation (buoyancy) , natural convection , combined forced and natural convection , work (physics) , dissipation , momentum (technical analysis) , physics , convection , flow (mathematics) , forcing (mathematics) , classical mechanics , pressure gradient , plane (geometry) , thermodynamics , rayleigh number , mathematics , geometry , finance , atmospheric sciences , economics
Momentum and energy equations for vertical flow with viscous dissipation are derived and shown to require that the cross‐section mean density is taken as the reference density for calculation of buoyancy forces under the Boussinesq approximation. Solutions are obtained for flow between parallel plane walls, with and without the pressure work as an explicit term in the energy equation. Both walls are at the same temperature, so there is no thermal forcing, but solutions are obtained for all admissible values of dynamic pressure gradient. The passive convection condition, whereby the flow is driven entirely by buoyancy forces resulting from heat generated by the flow's own viscous dissipation, is found on one branch of the dual solutions. However, while theoretically possible, passive convection is not physically realisable with any real fluid.