Morphology of a melt front under a condition of spatial varying latent heat

A melting model with spatially varying latent heat (applicable to the formation of sedimentary basins) is numerically investigated. The geometry is a rectangular channel with linearly increasing latent heat in the length direction and a step contrast in slope in the width direction. The melt front is driven by a heat flux. After introducing suitable scaling, it is shown that the significant evolution of the shape of the melt front occurs within 5 widths of the flux boundary and that the melt-thickness (the downstream length between the most and least advanced parts of the melt front) scales with the log of the ratio of latent heat slopes.