Journal
PHYSICAL REVIEW E
Volume 93, Issue 5, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.93.051102
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Funding
- Deutsche Forschungsgemeinschaft (DFG)-Heisenberg fellowship [Sh405/4]
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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 similar to Pr-1/4 Ra-1/4, Re similar to Pr-1/2 Ra-1/2 for Pr << 1 and Nu similar to Pr-0 Ra-1/4, Re similar to Pr-1 Ra-1/2 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).
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