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Free convective heat transfer and criterion of onset of free convection in a horizontal melt layer of ice heated by upper rigid surface

Wärmeübergang bei freier Konvektion und Kriterien für den Konvektionseinsatz in einer waagerechten Schicht aus geschmolzenem Eis bei Heizung von oben durch eine starre Fläche

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Abstract

An experimental and analytical investigation pertaining to the effect of density inversion of water on the free convective heat transfer and the onset of free convection in a horizontal melt layer of ice heated by upper rigid surface is carried out. Temperatures of the upper surface are varied from 1°C to 15°C, with Rayleigh number ranging from 2 × 102 to 1 × 105. From the present study, it can be demonstrated both experimentally and analytically that the density inversion of water plays an influential role in such a melt layer and the onset of free convection and the free convective heat transfer are considerably affected by the temperature of upper rigid surface T2, in the case of T2 ≤ 8° C, unlike the results obtained for common fluids without density inversion.

Zusammenfassung

Es handelt sich um eine experimentelle und analytische Untersuchung über den Einfluß der Dichteinversion von Wasser auf den Wärmeübergang bei freier Konvektion und den Konvektionseinsatz in einer waagerechten Schicht aus geschmolzenem Eis bei Heizung von oben durch eine starre Fläche. Die Temperaturen dieser Fläche variierten von 1°C bis 15°C bei Rayleigh-Zahlen von 2 × 102 bis 1 × 105. Das Ergebnis zeigt den grundsätzlichen Einfluß der Dichteinversion in der geschmolzenen Schicht; Konvektionseinsatz und Wärme-übergang hängen stark von der Temperatur der oberen Begrenzung ab, sofern diese kleiner oder gleich 8° C ist, im deutlichen Gegensatz zu normalen Fluiden.

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Abbreviations

a:

wave number

C:

constant

D:

operator

g:

acceleration of gravity

Gr:

Grashof number, defined in Eq.(12)

h:

depth of potentially unstable layer

H:

depth of melted water layer

Nu:

average Nusselt number, defined in Eqs.(23) and (24)

Pr:

Prandtl number, v/χ

q:

average heat flux at wall surface

Ra:

Rayleigh number, Pr · Gr

Rac :

critical Rayleigh number

¯Ra:

modified Rayleigh number, defined in Eqs.(19) and (20)

¯Rac :

modified critical Rayleigh number

To :

rest-state temperature

T1 :

temperature of lower surface

T2 :

temperature of upper surface

Tm :

temperature at maximum density, 4°C

u′,v′,w′:

velocity components

u, v, w:

non-dimensional velocity components, (u′, v′, w′)H/(√Grv)

x′, y′, z′:

coordinates

x, y, z:

non-dimensional coordinates, (x′, y′, z′)/H

α :

average heat transfer coefficient

β:

coefficient of thermal expansion

θ:

non-dimensional temperature, (T −T1)/(T2 −T1)

χ:

thermal diffusivity

λ:

thermal conductivity

v :

kinematic viscosity

ρ:

density

ψ:

stream function, defined in Eq.(2)

Ψ:

non-dimensional stream function ψ/(√Grv)

ω:

vorticity, defined in Eq. (1)

Ω:

non-dimensional vorticity, ωH2/(√Grv)

*:

perturbation quantity

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Authors and Affiliations

  1. Department of Mechanical Engineering, Hokkaido University, 060, Sapporo, Japan

    N. Seki (Professor), S. Fukusako (Assistant Professor) & M. Sugawara (Assistant)

Authors
  1. N. Seki
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  2. S. Fukusako
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  3. M. Sugawara
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Seki, N., Fukusako, S. & Sugawara, M. Free convective heat transfer and criterion of onset of free convection in a horizontal melt layer of ice heated by upper rigid surface. Wärme- und Stoffübertragung 10, 269–279 (1977). https://doi.org/10.1007/BF00998728

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