Phase changes following the initiation of a hot turbulent flow over a cold solid surface

Abstract

We analyse the melting and/or freezing that can occur when a very large layer of hot fluid begins to flow turbulently over a cold solid retaining boundary. This is a form of Stefan problem and the response is determined by the balance between the turbulent heat flux from the fluid, H, and the (initially infinite) conductive flux into the solid. We show that solidification of the flow at the boundary must always occur initially, unless the freezing temperature of the fluid, Tf, is less than the initially uniform temperature, T0, of the semi-infinite solid. We determine the evolution of the solidified region and show that with time it will be totally remelted. Melting and ablation of the solid retaining boundary will then generally follow, unless its melting temperature exceeds that of the turbulent flow. The maximum thickness of the solidified crust is shown to scale with k2(Tf − T0)2/ρkHL and its evolution takes place on a timescale of k2(Tf − T0)2/kH2, where k is the thermal conductivity, k the thermal diffusivity, ρ the density and L the latent heat, with all these material properties assumed to be equal for fluid and solid.