Determination of thermal conductivity of gases at high temperatures: the column method

Abstract

The one-dimensional temperature distribution along an electrically heated isotropic metal wire stretched coaxially in a cylindrical container with its two ends maintained at the temperature of the latter is computed theoretically. The general heat transfer balance equation which considers the terms arising from energy conducted through the wire, gas radiation, Thomson heat and input electrical energy is solved numerically. The neglect of convection and nonradical heat flow at the ends renders the temperature profile calculations at the ends partially inaccurate. Experiments, however, indicate that such effects penetrate at the ends only and over a length equal to the diameter of the enclosing cylinder. The temperature profiles are computed for two different wire materials (platinum and tungsten) and three different diameters when the wires are heated to increasingly high temperatures up to 3000 K in vacuum and in the presence of gases of different thermal conductivities. It is found that if the wire is sufficiently long, the shape of the temperature profile near the ends is independent of the length. Under these conditions the radiation losses are conveniently isolated and very good estimates of the energy conducted through the gas are possible in the 'differential arrangement'. The numerical calculations reveal that the end segments of the wire at nonuniform temperature shrink as the thermal conductivity of the gas surrounding the hot wire is increased, the temperature of the hot wire is raised, and the wire diameter is reduced. For a precise determination of the shape of temperature profile it is necessary to consider the temperature variation of different material properties.