A spectroscopic study of a laser-induced plume created during the welding of stainless steel and other materials (iron and chromium) has been carried out. A pulsed Nd:YAG laser of 1000 W average power is used. The evolutions of the electron temperature and electron density have been studied for several welding parameters. We use working powers from 300 to 900 W and pulse durations between 1.5 and 5 ms. The influence of shielding gases like nitrogen and argon has been taken into account. Temperature and density calculations are based on the observation of the relative intensities and shapes of the emission peaks. We assume that the plasma is in local thermal equilibrium. The temperature is calculated with the Boltzmann plot method and the density with the Stark broadening of an iron line. The electron temperatures vary in the range of 4500–7100 K, electron density between 3×1022 and 6.5×1022 m−3. The absorption of the laser beam in the plasma is calculated using the Inverse Bremsstrahlung theory.

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SUMMARYA ÿnite di erence solution for a system of non-linear integro-di erential equations modelling the steadystate combined radiative-conductive heat transfer is proposed. A new backward-forward ÿnite di erence scheme is formulated for the Radiative Transfer Equation. The non-linear heat conduction equation is solved using the Kirchho transformation associated with a centred ÿnite di erence scheme. The coupled system of equations is solved using a ÿxed-point method, which relates to the temperature ÿeld. An application on a real insulator composed of silica ÿbres is illustrated. The results show that the method is very e cient.

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