Abstract

A universal dimensionless number,
ΠNNN1+Pr-1,
Pr being the usual Prandtl number and NN the limit of ΠN for Pr → ∞, is introduced for all natural convection processes. For
NN=Ra,
Ra being the usual Rayleigh number, ΠN describes buoyancy-driven natural convection. For
NN=Ma,
Ma being the usual Marangoni number, ΠN describes thermocapillary-driven natural convection. For
NN=TaPr,
Ta being the usual Taylor number, ΠN describes centrifugally-driven natural convection.
In terms of ΠN, a thermal Kolmogorov scale relative to an integral scale,
ηθΠN-1/3
is introduced for natural convection including buoyancy, thermocapillary and centrifugally-driven flows. Heat transfer associated with these flows is modeled by
NuΠN1/3,
Nu being the usual Nusselt number. A variety of turbulent natural convection phenomena are shown correlating the model.
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