Temperature profile in thin wires during laser heating

The temperature distribution in a moving thin wire heated by a rectangular profile laser beam is studied. The output Gaussian profile beam of a laser system is transformed to a rectangular profile beam and the corresponding laser irradiance is integrated in the transverse direction to obtain the one-dimensional heat flux in the wire. The typical radius of the wire is in the range of hundreds of micrometers and the length of the wire can be infinitely long. The local temperature can vary from a few hundred to several thousand Kelvin depending on the laser intensity and, therefore, temperature-dependent thermophysical properties need to be considered. The resulting non-linear heat conduction equation is solved analytically to express the temperature distribution as an integral equation. The integral was determined numerically and the solution adopted is computationally robust. The results are presented in terms of two dimensionless numbers Bi and Pe so that a graphical representation of the solution can be easily applied to determine the laser processing parameters for other wires.