Exact solutions to gaseous flow time and temperature dependent parent and first-daughter fission-product plateout problems

Abstract

Exact solutions are obtained to the parent and first-daughter time and temperature dependent convective-diffusion equations with radioactive decay in an axisymmetric cylindrical conduit. Time invariant nominal gaseous flow conditions are assumed for which piecewise polynomial spatial representations of the axial temperature distribution are considered. The time dependence of the daughter-product inlet concentration due to parent decay is included. A mass transfer model incorporating these solutions is developed to predict the fission-product plateout on the conduit wall. The temperature dependence of both the diffusion and wall mass transfer coefficients is characterized using Arrhenius relationships. Comparison with experimental 134Cs, 137Cs, and 131I data demonstrates model viability in correctly predicting temperature dependent plateout under relevant flow conditions.