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Journal Article

Momentum and heat transport scalings in laminar vertical convection.


Shiskina,  O.
Laboratory for Fluid Dynamics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Shiskina, O. (2016). Momentum and heat transport scalings in laminar vertical convection. Physical Review E, 93(5): 051102(R). doi:10.1103/PhysRevE.93.051102.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002A-C6FD-D
We derive the dependence of the Reynolds number Re and the Nusselt number Nu on the Rayleigh number Ra and the Prandtl number Pr in laminar vertical convection (VC), where a fluid is confined between two differently heated isothermal vertical walls. The boundary layer equations in laminar VC yield two limiting scaling regimes: Nu∼Pr1/4Ra1/4, Re∼Pr−1/2Ra1/2 for Pr≪1 and Nu∼Pr0Ra1/4, Re∼Pr−1Ra1/2 for Pr≫1. These theoretical results are in excellent agreement with direct numerical simulations for Ra from 105 to 1010 and Pr from 10−2 to 30. The transition between the regimes takes place for Pr around 10−1.