When a molten metal is cast in a mold that is a poor conductor, the dominant resistance to heat flow is within the mold wall. Consider conditions for which a liquid metal is solidifying in a thick-waned mold of thermal conductivity k... and thermal diffusivity a_n. The density and latent heat of fusion of the metal are designated as p and h_sf, respectively, and in both its molten and solid states the thermal conductivity of the metal is very much larger than that of the mold.

Just before the start of solidification (S = 0) the mold wan is everywhere at an initial uniform temperature T, and the molten metal is everywhere at its fusion (melting point) temperature of Tf' Following the start of solidification, there is conduction heat transfer into the mold wan and the thickness of the solidified metal, S. increases with time t.

(a) Sketch the one-dimensional temperature distribution, T(x), in the mold wall and the metal at t = 0 and at two subsequent times during the solidification. Clearly indicate any underlying assumptions.

(b) Obtain a relation for the variation of the solid layer thickness S with time t, expressing your result in terms of appropriate parameters of the system.

Transcribed Image Text:

Molten metal Solid metal p. hg Mold wall kw, aw