Imaging the solidification of molten metal by eddy currents: I

This is the second part of two sister papers. The first paper developed an algorithm for imaging the solidification of molten metal inside a pipe where the conductivity of the metal inside the pipe was assumed to vary continuously (i.e., no clear boundary between the solid and the melt). Due to this nature, the algorithm shown in the first paper involves computationally expensive volume integrals. In this paper, the problem is slightly simplified where the molten metal and the solidification are assumed to have two distinct conductivities (i.e., there is a distinct boundary between the solid and the melt). This simplified problem allows us, in this paper, to develop a much faster imaging algorithm that involves a hybrid of volume and surface integrals. This hybrid technique provides great advantages over the surface or volume approaches alone.