In this study, a general methodology for estimating the temperature of the upper surface of the work piece and the melting depth during micro thermal machining using scanning thermal microscopy (SThM) has been proposed. First the probe in the processing system was considered as an inverse heat conduction problem with an unknown work piece temperature. Once the temperature of the upper surface of the work piece was estimated, then the work piece was also regarded as another inverse heat transfer problem due to an unknown melting depth in the boundary condition. The conjugate gradient method was used to solve the inverse problems. In addition, this methodology herein can also be applied to solve other transient heat conduction problems, which involve latent heat transfer and form a solid and liquid phase like laser processing, solidification in continuous casting process and transient recording system on phase-change material using AFM.
Journal of Applied Physics, v. 100, 2006, p. 064305