Suppose that upon entering the Earth’s atmosphere, the surface of a meteorite has been heated to the melting point and the molten material is carried away by the flow. It is of interest to calculate the rate at which melting removes material from the meteorite. For this purpose, consider the following problem. The surface of a semi-infinite half-space moves downward into the half-space with constant velocity V, as indicated in Figure 4.39. The surface is always at the melting temperature Tm, and melted material above the instantaneous surface is removed from the problem. Assume that the surface of the half-space is melted by a constant heat flux into the half-space from above the surface. Assume also that far from the melting surface the temperature is T0; that is, T → T0 as ζ → ∞. Find the temperature distribution in the half-space as a function of time T(ζ,t), and determine V in terms of and the thermodynamic properties of the rock. Account for the latent heat L required to melt the material.
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