Abstract
In all studies concerning mixed convection in plane laminar plumes a linear relationship between fluid density and temperature has been used. However, it is known that the water density-temperature relationship is non-linear at low temperatures with a density maximum at 3.98°C for pure water. In this note the problem of plane laminar water plume in a coflowing vertical free stream has been investigated taking into account the non-linearity between density and temperature. This is the first work in the literature which treats plane mixed convection plumes with nonlinear relation between density and temperature. Both rising and descending plumes have been investigated. It was found that the ambient water temperature plays an important role on the results. When the ambient temperature is greater than maximum density temperature (T a > T m), the water plume behavior is similar to that of the classical plume with linear density-temperature relationship. However, when the ambient temperature is equal or lower than the maximum density temperature the water plume behavior is completely different from the classical plume with linear density-temperature relationship. The centerline velocity shows a series of maxima and minima which are produced by the combination of the nonlinear density-temperature relation and the free stream.
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Abbreviations
- c p :
-
specific heat under constant pressure
- d:
-
slot width at the plume exit
- g:
-
gravitational acceleration
- Gr:
-
Grashof number
- K:
-
mean bulk modulus of water
- p:
-
pressure
- Pr:
-
Prandtl number
- Q:
-
heat release at the plume origin
- Re:
-
Reynolds number
- s:
-
salinity
- T:
-
temperature
- u:
-
vertical velocity
- v:
-
horizontal velocity
- V:
-
specific volume of water
- x:
-
vertical coordinate
- y:
-
horizontal coordinate
- β:
-
thermal expansion coefficient
- α:
-
thermal diffusivity
- ν:
-
kinematic viscosity
- ξ:
-
buoyancy parameter
- ρ:
-
density
- a:
-
ambient
- c:
-
centerline
- m:
-
maximum
- o:
-
origin
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Pantokratoras, A. A note on mixed convection of laminar plane water plumes at temperatures around the density extremum. Arch Appl Mech 78, 11–20 (2008). https://doi.org/10.1007/s00419-007-0139-8
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DOI: https://doi.org/10.1007/s00419-007-0139-8