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Phase changes following the initiation of a hot turbulent flow over a cold solid surface. (English) Zbl 0662.76072
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, ${T}_{f}$, is less than the initially uniform temperature, ${T}_{0}$, 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 ${k}^{2}{\left({T}_{f}-{T}_{0}\right)}^{2}/\rho \kappa HL$ and its evolution takes place on a timescale of ${k}^{2}{\left({T}_{f}-{T}_{0}\right)}^{2}/\kappa {H}^{2}$, where k is the thermal conductivity, $\kappa$ the thermal diffusivity, $\rho$ the density and L the latent heat, with all these material properties assumed to be equal for fluid and solid.

##### MSC:
 76F99 Turbulence 76T99 Two-phase and multiphase flows 80A20 Heat and mass transfer, heat flow 76M99 Basic methods in fluid mechanics
##### Keywords:
melting; Stefan problem; semi-infinite solid; solidified region