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Annual Reviews of Heat Transfer

ISSN 1049-0787

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$175.00 (Must be sent to your home address)

You can order single issue or individual article. To purchase a single issue or an individual article as well as to view tables of contents and abstracts click on issue number.

Institutional price:

$349.00

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Year 1990

305 pages

Volume price - $141.00

MICROSCALES OF TURBULENCE AND HEAT TRANSFER CORRELATIONS

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

ABSTRACT

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

η_θ ∼ η_θ^C(1 + Pr^3/4) ; Pr << 1
η_θ ∼ (ν^5/3a^4/3/ε)^1/4 = η_θ^B Pr^−1/6 ; Pr ≥ 1
are proposed. Here, η_θ^C and η_θ^B denote the Oboukhov−Corrsin and Batchelor scales, respectively. Two heat transfer models,
Nu ∼ Pe^3/4/(1 + Pr^3/4) ; Pr<< 1
Nu ∼ Re^3/4Pr^1/3 ; 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,
Π_N ∼ (Pr/(1 + Pr))Ra
and two microscales,
η_θ* ∼ (1 + Pr)^1/4(a³/Ρ_β)^1/4 ; Pr ≤ 1
η_θ ∼ (1 + 1/Pr)^1/4 (νa²/Ρ_β)^1/4 ; Pr ≥ 1
is reviewed (here, Ρ_βdenotes the buoyant production of thermal energy). In terms of Π_N,
(η_θ/l, η_θ*/l) ∼ Π_N^−1/3
for any Pr (here, l denotes an integral scale). A two-layer turbulence model,
Nu ∼ sublayer/(1 − core) ∼ Π_N^1/3/(1 − Π_N^−1/9)
proposed for buoyancy-driven flow between two horizontal plates agrees very well with the experimental data.