Abstract
An experimental and analytical investigation pertaining to the effect of density inversion on steady free convective heat transfer of water in a confined rectangular vessel in which different temperatures are imposed on the opposing vertical walls is carried out. Water, as a testing fluid, has its maximum density at 4‡C. Temperature of the cold wall is maintained at 0‡C, while that of the hot wall is varied from 1‡C to 12‡ C. Photographs and analytical descriptions of the flow patterns, temperature distributions and average Nusselt number are presented. Moreover, the effect of dimensions of a rectangular vessel on the average Nusselt number is investigated. From the present investigation, it can be demonstrated both experimentally and analytically that the density inversion of water have an influential effect on the free convection heat transfer in the prescribed water layer, moreover, the average Nusselt number is a peculiar function of temperature difference between the cold and the hot walls, unlike the previous results for common fluids without density inversion.
Zusammenfassung
Der Einflu\ der Dichteumkehr von Wasser auf die stationÄre freie Konvektion in einem geschlossenen rechtwinkligen BehÄlter, dessen gegenüberliegende senkrechte WÄnde auf verschiedenen Temperaturen gehalten werden, ist experimentell und analytisch untersucht. Wasser hat sein Dichtemaximum bei 4‡C. Die kalte Wand ist auf 0‡C gehalten, die Temperatur der warmen Wand liegt zwischen 1‡C und 12‡C. Die Strömungsform, die Temperaturverteilung und die mittlere Nu\elt-Zahl werden durch photographische Aufnahmen und analytische Rechnungen beschrieben. Auch der Einflu\ der BehÄlterdimensionen auf die mittlere Nu\eltZahl ist angegeben. Es zeigt sich, da\ die Dichteumkehr den WÄremübergang in der Wasserschicht grundsÄtzlich verÄndern kann und da\ die Nu\elt-Zahl in eigentümlicher Weise vom angelegten TemperaturgefÄlle abhÄngt, im Gegensatz zu Älteren Ergebnissen für übliche Flüssigkeiten ohne Dichteumkehr.
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Abbreviations
- Gr:
-
Grashof number, gW3/Ν 2c
- H:
-
height of rectangular vessel
- Nu:
-
average Nusselt number, defined as Eq. (11)
- Nu* :
-
average Nusselt number, qW/λδT
- Pr:
-
Prandtl number, Νc/α c
- q:
-
heat flux at wall
- Ra* :
-
Rayleigh number, g ¦Β¦δTW3/Να
- T:
-
temperature
- δT:
-
temperature difference, Th-Tc(=Th)
- u′, v′:
-
velocity components
- u,v:
-
non-dimensional velocity components, (u′,v′)W(√Gr Ν c )
- x′,y′:
-
coordinates
- x,y:
-
non-dimensional coordinates, (x′,y′)/W
- W:
-
width of rectangular vessel
- α :
-
thermal diffusivity
- Β:
-
coefficient of cubical expansion
- θ:
-
non-dimensional temperature,(T-Tc)/(Th-Tc)
- и:
-
thermal conductivity
- и* :
-
non-dimensional thermal conductivity, и/иc
- Μ:
-
viscosity
- Μ* :
-
non-dimensional viscosity, Μ/Μc
- Ν :
-
kinematic viscosity
- Ν* :
-
non-dimensional kinematic viscosity, Ν/Νc
- ρ:
-
density
- ρ* :
-
non-dimensional density, ρ/ρc
- ψ:
-
stream function, defined as Eq. (3)
- ψ:
-
non-dimensional stream function, ψ/(√Gr Νc)
- Ω:
-
vorticity, defined as Eq. (2)
- Ω:
-
non-dimensional vorticity, ΩW 2(√Gr Ν c )
- c:
-
refers to cold wall
- h:
-
refers to hot wall
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Seki, N., Fukusako, S. & Inaba, H. Free convective heat transfer with density inversion in a confined rectangular vessel. Wärme- und Stoffübertragung 11, 145–156 (1978). https://doi.org/10.1007/BF01805655
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DOI: https://doi.org/10.1007/BF01805655