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DOI: 10.1615/AnnualRevHeatTransfer.v3.90
pages 195-231

V. S. Arpaci
Department of Mechanical Engineering and Applied Mechanics, University of Michigan, Ann Arbor, Michigan


The classical microscales of turbulence for forced flows are reviewed. Two new scales for these flows,

ηθ ∼ ηθC(1 + Pr3/4) ; Pr << 1
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 ∼ Pe3/4/(1 + Pr3/4) ; Pr<< 1
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,
ΠN ∼ (Pr/(1 + Pr))Ra

and two microscales,
ηθ* ∼ (1 + Pr)1/4(a3/Ρβ)1/4 ; Pr ≤ 1
ηθ ∼ (1 + 1/Pr)1/4a2/Ρβ)1/4 ; Pr ≥ 1

is reviewed (here, Ρβdenotes the buoyant production of thermal energy). In terms of ΠN,
θ/l, ηθ*/l) ∼ ΠN−1/3

for any Pr (here, l denotes an integral scale). A two-layer turbulence model,
Nu ∼ sublayer/(1 − core) ∼ ΠN1/3/(1 − ΠN−1/9)

proposed for buoyancy-driven flow between two horizontal plates agrees very well with the experimental data.

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