Abstract
The classical methods of boundary layer theory allow us to accurately model linear laminar horizontal buoyant plumes. Using the modern developments of the theory (matched asymptotic expansions) we could even produce still better solutions of the non-linear problems considered. However, for any reasonable design, the unit flux Fo is likely to be so large that the flow would be turbulent rather than laminar. The results of our forthcoming study of turbulent horizontal plumes are more qualitative, but the general approach to modeling closely resembles the one used here.
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Abbreviations
- u:
-
horizontal velocity component
- x:
-
horizontal distance
- y:
-
vertical distance
- Fo :
-
density difference flux per unit length of diffusor
- Gr:
-
GRASHOF-number
- Po :
-
mass flux of pollutant per unit length of diffusor
- Pr:
-
PRANDTL-number
- α:
-
thermal expansion coefficient
- ψ:
-
streamfunction
- Θ:
-
reduced density difference
- ρ:
-
specific mass
- Γ:
-
GAMMA-function
References
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Gebhart B., Pera L. and Schorr A.W., Steady laminar natural convection plumes above a horizontal line heat source, Int. J. Heat and Mass Transfer, 13, 161–171, 1970.
Spalding D.B. and Gruddace R.G., Theory of the steady laminar buoyant flow above a line heat source in a fluid of large Prandtl number and temperature-dependent viscosity, Int. J. Heat and Mass Transfer, 3, 55–59, 1961.
Tennekes H. and Lumley J.L., A First Course in Turbulence, M I T Press, Cambridge, U.S.A., 135–144, 1972.
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Koh, R.C.J. and Brooks N.H., Fluid Mechanics of Waste Water Disposal in the Ocean, in: Annual Reviews of Fluid Mechanics — Annual Reviews Inc. — Palo Alto, Cal., U.S.A., 7, 187, 1975.
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Rosenhead, L., ed., Laminar Boundary Layers, Oxford, Clarendon Press, 260, 1963.
Luenberger, D., Introduction to linear and nonlinear programming, Addison & Wesley, 1973.
Jacoby, S., Kowalik, J., Pizzo, J., Iterative methods for nonlinear optimization problems, Prentice-Hall, 1972.
Powell, M., On the calculation of orthogonal vectors, Computer Journal, 11, 302, 1968.
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© 1976 Springer-Verlag
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Spriet, J., Vansteenkiste, G.C., Baron, G., Wajc, S.J. (1976). Modeling dispersion in a submerged sewage field. In: Cea, J. (eds) Optimization Techniques Modeling and Optimization in the Service of Man Part 1. Optimization Techniques 1975. Lecture Notes in Computer Science, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07622-0_473
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DOI: https://doi.org/10.1007/3-540-07622-0_473
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