Abstract
The influence of free convection on forced convection heat transfer becomes important in laminar flows. Numerical methods have been applied for a study of mixed convection in vertical tubes for the following conditions: temperature-dependent fluid density, constant wall temperature and parabolic profile of axial velocity at the tube entrance. Both cases: heating and cooling have been considered.
Zusammenfassung
Der Einfluß der freien Konvektion auf den Wärmeübergang kann bei laminarer Strömung bedeutsam werden. Theoretisch-numerische Methoden wurden angewendet, um eine Untersuchung dieses Wärmeübergangproblems für folgende Bedingungen durchführen zu können: temperaturabhängige Dichte des Fluids bei konstanter Wandtemperatur und parabolischem Profil der Axialgeschwindigkeit am Einlauf des Rohres. Es wurden sowohl Beheizung als auch Abkühlung des Fluides behandelt.
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Abbreviations
- C p kJ/(kg K):
-
specific heat at constant pressure
- d m:
-
tube diameter
- g m/s2 :
-
gravitational acceleration
- m kg/(m2s):
-
mass flow rate
- p Pa:
-
pressure
- q kj/(m2s):
-
heat flow rate
- r m:
-
radial coordinate
- R m:
-
tube radius
- T K:
-
temperature
- To K:
-
fluid entrance temperature
- T w K:
-
fluid wall temperature
- w r m/s:
-
radial velocity
- wz m/s:
-
axial velocity
- w¯w m/s:
-
mean axial velocity
- z m:
-
axial coordinate
- β 1/K:
-
volumetric coefficient of expansion
- η kg/(m s):
-
dynamic viscosity
- λ kJ/(m s K):
-
thermal conductivity
- ν m2/s:
-
kinematic viscosity
- ϱ kg/m3 :
-
density
- dyn:
-
dynamic
- fo:
-
forced convection
- fr:
-
free convection
- o :
-
inlet
- r :
-
radial direction
- R :
-
centre-line
- w :
-
wall
- z:
-
axial direction
References
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Brauer, H., Dylag, M. & Kasz, J. Heat transfer by combined free and forced convection in vertical tubes. Wärme- und Stoffübertragung 23, 61–68 (1988). https://doi.org/10.1007/BF01637126
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DOI: https://doi.org/10.1007/BF01637126