An implicit method for reconstructing dynamic three-dimensional phase boundaries under low Peclet number conditions

Abstract

This article develops an implicit inverse method for reconstructing dynamic multidimensional phase boundaries. The technique is suitable for problems having small liquid phase Peclet numbers, Pe r = (V̂ rL̂/ α ̂ ), where V̂ r is the characteristic liquid phase velocity scale evaluated relative to the solid phase velocity scale, L̂ is a characteristic length scale, and α ̂ is a characteristic thermal diffusivity. Under these conditions, a multidimensional Stefan problem emerges. Explicit front-tracking procedures are eliminated by incorporating the latent heat effect in an effective, temperature dependent specific heat. Time-sequential reconstruction is then performed by solving a multidimensional nonlinear inverse heat conduction problem. As an illustration, evolving phase boundaries are reconstructed within moving and stationary plates subject to concentrated, high energy density heat sources. It is found that boundaries can be accurately reconstructed using either exact or noisy temperature measurements.