Approximate Column Constants Expressed in Terms of Design Parameters for Hot-Wire Thermal Diffusion Column

Abstract

Although one-dimensional analysis developed by Jones & Furry is useful for predicting separative performances of hot-wire thermal diffusion column for isotope separation, it is not so simple and requires inevitably numerical calculations with computers, because it involves the column constants which cannot be evaluated analytically. Approximate formulae for the column constants were derived here by replacing the logarithmic function for the radial temperature distribution, which makes analytical integration impossible when exists at a denominator, with the radially constant and column-design-parameter dependent reference mean temperature. Laborious repeated integrals, with semi-explicit axial convection velocity profile being input, were performed manually through ignoring δ or ratio of radius between hot wire and cold wall, to the second and higher powers. The results were verified by the symbolic manipulating language REDUCE. Although the formulae obtained in terms of δ and ΔT/T c, or the ratio of temperature difference between hot and cold surfaces to cold wall temperature, were rather rough in approximation, calculations for dependence of column constants on (ΔT/T c) showed fairly good agreements with those by original expressions.