MICROSCALES OF TURBULENCE AND HEAT TRANSFER CORRELATIONS
V. S. Arpaci
The classical microscales of turbulence for forced flows are reviewed. Two new scales for these flows,
ηθ ∼ (ν5/3a4/3/ε)1/4 = ηθB Pr−1/6 ; Pr ≥ 1
are proposed. Here, ηθC and ηθB denote the Oboukhov−Corrsin and Batchelor scales, respectively. Two heat transfer models,
Nu ∼ Re3/4Pr1/3 ; Pr ≥ 1
are developed based on these scales. The agreement with the experimental data is fair for the first model and excellent for the second model.
For buoyancy-driven flows, a fundamental dimensionless number involving a combination of Prandtl and Rayleigh numbers,
and two microscales,
ηθ ∼ (1 + 1/Pr)1/4 (νa2/Ρβ)1/4 ; Pr ≥ 1
is reviewed (here, Ρβdenotes the buoyant production of thermal energy). In terms of ΠN,
for any Pr (here, l denotes an integral scale). A two-layer turbulence model,
proposed for buoyancy-driven flow between two horizontal plates agrees very well with the experimental data.
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