Size effect on thermal conductivity of square wires

The size effect on thermal conductivity of free standing wires with square cross-section is investigated. The thermal conductivity is calculated using the Boltzmann transport equation (BTE). A simple expression for the reduction in conductivity due to the increase of boundary scattering is presented. The thermal conductivity of the wires is found to decrease rapidly below the bulk values. This decrease in square wires is smaller than that which occurs in a film with out-of-plane heat flux. The values of thermal conductivities deduced from our calculation agree well with the experimental data of sodium wires.