The two-phase, three-zone melting problem—response to pulse heating

摘要

Under certain conditions, when a pure substance in solid form is partly melted by in-depth heating, three distincs zones appear: the solid, the liquid, and the intermediate zone containing both liquid and solid. Under these conditions, the equations for the free boundaries are uncoupled and may be solved independently until the boundaries coalence into a single (Stefan) interface between the liquid and solid phases. In this paper, the one dimensional equations for the three-zone problem resulting from instantaneous pulse in-depth heating are derived. These equations, together with the remaining describing equations, are solved by two different numerical techniques to illustrate the motion of the boundaries, both prior to coalescence (the uncoupled case), and following coalescence (the coupled, or Stefan, case).