International Journal of Scientific Research and Engineering Development

International Journal of Scientific Research and Engineering Development


( International Peer Reviewed Open Access Journal ) ISSN [ Online ] : 2581 - 7175

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Rayleigh Model of Radiation Heat Transfer in Spherical Medium



     International Journal of Scientific Research and Engineering Development (IJSRED)

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 Published Issue : Volume-3 Issue-5
 Year of Publication : 2020
 Unique Identification Number : IJSRED-V3I5P55
 Authors : Hamza Mohamed
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Abstract :

In certain extremely low probability, severe accident scenarios which have been postulated for liquid metal cooled fast reactors, large bubble cavities containing fuel vapor and fission products transit a layer of coolant and release this material to the cover gas thereby presenting a contribution to an accident-specific source term [5]. Rayleigh model in radiation heat transfer has been investigated to analysis and interpret the experiments that conducted during 1980’s for oxide UO2 fueled reactors in Fuel Aerosol Simulant Test (FAST) facility at Oak Ridge National Laboratory (ORNL).These analyses are applied to estimate the bubble collapse of Liquid Metal reactors (LMR’s) during a hypothetical core disruptive accident (HCDA). In Rayleigh non-scattering model the particle size was 0.01 µm [6],and according to Mie theory principle, the absorption coefficient for small particle –size distribution was estimated (k = 10 m-1 was used) from reference [7] at complex refractive index of UO2 at λ = 600 µm and x = 0.0785.A MATLAB code was used to solvethe radiative heat equation (RTE) in spherical coordinates. The mixture is in local thermodynamic equilibrium inside the bubble which has a black body surface boundary.The mixture in the cavity contains three components: the non-condensable gas Xenon, Uranium dioxide vapor, and fog.To simulate fuel bubble’s geometry as realistically as possible, according to experimental observation, the energy equation in a spherical coordinate system has been solved with the radiative flux heat transfer equation (RTE) to obtain the effect of fuel bubble’s geometry on the transient radiative heat flux and to predict the transient temperature distribution in the participating medium during a hypothetical core disruptive accident (HCDA) for liquid metal fast breeding reactor (LMFBR) for FAST. The transient temperature distribution in fog region was utilized to predict the amount of condensable UO2 vapor m_fog= (4π C_0 M_(〖UO〗_2 ))/k^3 ∫_(τ_f)^(τ_o)▒〖[x_sat-g_0 (T) ] τ^2 dτ〗 . The conclusion that can be drawn from the present study, is that the Fuel Aerosol Simulant Test (FAST) facility at Oak Ridge National Laboratory has a larger margin of safety since the bubble rising time is greater than the bubble collapse time.