Abstract
Laminar steady free surface flow having one permeable bounding wall is investigated in the presence of buoyancy force. The experimental results of Rajasekhara [1] were found to be in good agreement with our theoretical results based on a model which admits slip-velocity at the porous material. The effect of buoyancy force is to increase the velocity distribution in the case of greater heat addition (No>0) and to decrease it by a greater cooling (No<0). As a result, the mass flow rate increases and the friction factor decreases for No>0 and the opposite is true for No<0. We further find that the effect of buoyancy force on the temperature distribution is to increase its magnitude. In particular, we find that the rate of heat transfer at its nominal surface is increased in the case of heating (No>0) of flow.
Zusammenfassung
Die laminare Strömung entlang poröser Grenzflächen wird in Anwesenheit von Auftriebskräften theoretisch untersucht. Die Übereinstimmung zwischen Theorie und Experimenten von Rajasekhara [1] ist dann gut, wenn Strömungsgleitung an der porösen Oberfläche vorausgesetzt wird. Die Auftriebskräfte erhöhen die Geschwindigkeitsverteilung bei Wärmezufuhr (No>0) und verringern sie bei Kühlung (No<0). Im ersten Fall erhöht sich der Massenfluß bei abnehmenden Widerstandsbeiwert (No>0). Umgekehrte Verhältnisse liegen für No<0 vor. Insbesondere stellt sich heraus, daß der Wärmeübergang mit steigender Erwärmung der Strömung zunimmt.
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Abbreviations
- u:
-
the velocity
- T:
-
the entrance temperature
- T′:
-
the temperature of fluid
- Q:
-
the Darcy velocity
- ρ:
-
the density of fluid
- μ:
-
the viscosity of fluid
- No :
-
Buoyancy parameter
- k:
-
the permeability of porous media
- σ:
-
\(h/\sqrt k \)
- α:
-
the slip parameter
- η:
-
y/h
- x, y:
-
cartesian coordinates
- h:
-
the depth of flow above the bed
- Re:
-
2/-uh/v the Reynolds number
Literature
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Rudraiah, N., Veerabhadraiah, R. Effect of buoyancy on the free surface flow past a permeable bed. Warme- und Stoffubertragung 11, 265–275 (1978). https://doi.org/10.1007/BF02587790
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DOI: https://doi.org/10.1007/BF02587790