Microscales of Natural Convection

Abstract

A universal dimensionless number, ΠN∼NN1+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, ηθℓ∼ΠN-1/3 is introduced for natural convection including buoyancy, thermocapillary and centrifugally-driven flows. Heat transfer associated with these flows is modeled byNu∼ΠN1/3 ,Nu being the usual Nusselt number. A variety of turbulent natural convection phenomena are shown correlating the model.