A methodology is developed and used to evaluate the response sensitivity of the thermal systems to variations in their design parameters. Techniques for computing the sensitivity of temperature distributions to changes in processing parameters needed for deciding the more effective laser input parameters for laser surface hardening treatment are considered. In this study, a state equation governing the heat flow in laser surface treatment is analyzed using a three-dimensional finite element method and sensitivity data of the processing parameter obtained using a direct differentiation method applied for sensitivity analysis. The interesting processing parameter is taken as the characteristic beam radius (r_b) of the sensitivity of the temperature T versus r_b and is analyzed for variation in other conditions. And these sensitivity results obtained in other parameters are fixed conditions.
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