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The effect of radial thickness on the thermal conductivity of a free standing wire is investigated. The thermal conductivity is evaluated using the Boltzmann equation. A simple expression for the reduction in conductivity due to the increase of boundary scattering is presented. A comparison is made between the experimental results of indium wires and the theoretical calculations. It is shown that this decrease of conductivity in wires is smaller than that in film where heat flux is perpendicular to the surface.