Wärme - und Stoffübertragung

, Volume 26, Issue 3, pp 163–168 | Cite as

The mathematical modelling of thermal radiation in high temperature fluidized bed

  • M. Tunç
  • A. Karakaş


The aim of this study is composed of two parts. One of them is to calculate the radiation heat flux and the other is to determine the overall heat transfer coefficient for the gas-fluidized bed. The radiative heat transfer model is developed for predicting the total heat transfer coefficients between submerged surfaces and fluidized beds for several working temperatures. The role of radiation heat transfer in the overall heat transfer process at an immersed surface in a gas-fluidized bed at high temperatures is investigated. Analytical results are compared with the previously done experiments and a good agreement between the two, is obtained.


Heat Transfer Total Heat Heat Flux Heat Transfer Coefficient Radiation Heat 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


c (x)

specific heat capacity of packet [J/kg K]


specific heat capacity of particle [J/kg K]


specific heat capacity of gas [J/kg K]


average diameter of the bed particles [m]


the fraction of time that a unit surface exposed to the bubble phase


the fraction of time that a unit surface exposed to the packet phase


acceleration due to gravity [m/s2]


heat transfer coefficient for the surface in contact with bubble [W/m2 K]


conduction heat transfer coefficient for the surface/bubble [W/m2K]


radiation heat transfer coefficient for the surface/bubble [W/m2K]


heat transfer coefficient for the surface in contact with packet [W/m2K]


conduction heat transfer coefficient for the surface/packet [W/m2 K]


radiation heat transfer coefficient for the surface/packet [W/m2 K]


total heat transfer coefficient between bed and surface [W/m2 K]


thermal conductivity of the emulsion phase for fixed bed [W/m K]


thermal conductivity of packet [W/m K]


the logarithmic mean of conductivity for first layer in packet [W/m K]


the logarithmic mean of conductivity for the first layer in packet [W/m K]


extinction coefficient [1/m]


mass [kg]


number of layers


air pressure [pa]


mean local conduction heat transfer for packet [kW/m2]


mean local radiation heat transfer for packet [kW/m2]


average heat flux during packet contact with surface [kW/m2]


average heat flux during bubble contact with surface [kW/m2]


gas constant [287.04 J/kg K]


time [s]


residence time for gas bubble [s]


residence time for packet [s]


temperature [K]


bed temperature [K]


surface temperature [K]


minimum fluidization velocity [m/s]


terminal velocity [m/s]


distance [m]

Greek symbols


time increment


thickness of the layer




thermal diffusivity [m2/s]


voidage of fluidized bed


void ratio of the bed at minimum fluidization


voidage of fixed bed


dynamic viscosity of gas [kg/m s]


kinematic viscosity of gas [m2/s]


density of packet [kg/m3]


density of particles [kg/m3]


density of gas [kg/m3]


Stefan-Boltzmann constant [5.66·10−8 W/m2K4]


geometric shape factor for particles

Dimensionless numbers


Archimedes numberAr=g d p 3 (ϱ p −ϱ g )ϱ g /μ g 2


Nusselt numberNu=h·d/k


Reynolds numberRe=d p ·V mf /ν g


Prandtl numberPr=C pg μ g /k g

Bestimmung der Wärmeübertragungs-Koeffizienten in Gas-Wirbelschichten


Diese Untersuchung besteht aus folgenden zwei Teilen: 1. Kalkulation des Radiationswärmeübergangs in Gas-Wirbelschichten. 2. Bestimmung des Wärmeübergangs-Koeffizienten in Gas-Wirbelschichten. Dieses Radiationswärmeübergangsmodell wurde entwickelt, um die Wärmeübertragungs-Koeffizienten zwischen der eingetauchten Oberfläche und der Wirbelschicht bei verschiedener Wärme schätzungsweise zu bestimmen. Es wurde das Verhältnis der Radiationswärmeübertragung in Gas-Wirbelschichten zum totalen Wärmeübergang untersucht. Die Meßwerte wurden mit theoretischen Resultaten verglichen.


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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • M. Tunç
    • 1
  • A. Karakaş
    • 1
  1. 1.Thermodynamics Dep. Mechanical Eng. FacultyTechnical University of Istanbul ITUGümüssuyu, IstanbulTurkey

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