A close-form solution to predict the total melting time of an ablating slab in contact with a plasma

An exact melt-through time is derived for a one-dimensional heated slab in contact with a plasma when the melted material is immediately removed. The plasma is composed of a collisionless presheath and sheath on a slab, which partially reflects and secondarily emits ions and electrons. The energy transport from plasma to the surface accounting for the presheath and sheath is determined from the kinetic analysis. This work proposes a semi-analytical model to calculate the total melting time of a slab based on a direct integration of the unsteady heat conduction equation, and provides quantitative results applicable to control the total melting time of the slab. The total melting time as a function of plasma parameters and thermophysical properties of the slab are obtained. The predicted energy transmission factor as a function of dimensionless wall potential agrees well with the experimental data. The effects of reflectivities of the ions and electrons on the wall, electron-to-ion source temperature ratio at the presheath edge, charge number, ion-to-electron mass ratio, ionization energy, plasma flow work-to-heat conduction ratios, Stefan number, melting temperature, Biot number and bias voltage on the total melting time of the slab are quantitatively provided in this work.