Abstract
The flow and heat transfer in partially heated and partially cooled cavities were numerically analyzed. Using the control volume approach, a computer program based on SIMPLE algorithm was developed. A square enclosure with variable size heater and cooler on the vertical walls was considered. Computations were carried out to investigate the effects of heater and cooler size on the heat transfer rate. It was observed that for a given cooler size, the mean Nusselt number decreases with increasing heater size. On the other hand, for a given heater size, the mean Nusselt number increases with increasing cooler size. For all Rayleigh numbers considered, the same behavior was observed.
Zusammenfassung
Es wurde ein numerisches Modell zur Analyse des Strömungs- und Wärmeübergangsverhaltens in teilweise beheizten und gekühlten Hohlräumen entwickelt und unter Verwendung des Kontrollvolumenprinzips und des Algorithmus „SIMPLE“ als Computer-Programm formuliert. Der Hohlraum ist rechteckig und die variablen Heiz- und Kühlflächen befinden sich auf gegenüberliegenden Vertikalseiten. Hauptziel der Berechnungen war es, den Einfluß der variablen Heiz- und Kühlflächen auf den Wärmeübergang zu ermitteln. Für eine bestimmte Kühlergröße zeigte sich eine Abnahme der gemittelten Nußelt-Zahl mit zunehmender Heizfläche. Andererseits — bei gegebener Heizfläche — stieg die Nußelt-Zahl mit der Kühlfläche an. Dieses Verhalten wurde bei allen untersuchten Rayleighzahlen gefunden.
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Abbreviations
- g :
-
gravitational acceleration
- H :
-
height of cavity
- k :
-
thermal conductivity of fluid
- l C :
-
cooler size
- l H :
-
heater size
- \(\overline {Nu}\) :
-
mean Nusselt number
- Nu y :
-
local Nusselt number
- P :
-
pressure
- Pr :
-
Prandtl number
- Ra :
-
Rayleigh number (Ra = gβH 3(T H −T C)/(αν))
- T :
-
temperature
- T C :
-
temperature of cold surface
- T H :
-
temperature of hot surface
- T R :
-
reference temperature (T R = (T C +T H)/2)
- u :
-
velocity component inx-direction
- x :
-
horizontal axis
- v :
-
velocity component iny-direction
- y :
-
vertical axis
- α :
-
thermal diffusivity
- β :
-
thermal expansion coefficient
- ρ :
-
density of fluid
- Ψ :
-
stream function
- ν :
-
kinematic viscosity
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Yücel, N. Natural convection in rectangular enclosures with partial heating and cooling. Warme - Und Stoffubertragung 29, 471–477 (1994). https://doi.org/10.1007/BF01539499
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DOI: https://doi.org/10.1007/BF01539499