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Abstract:
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.
