GATE MT 2015 Q57. At the mould exit of a continuous caster, the metal consisting of a solidified shell with a m=liquid metal core exists at the range of 35 kg s-1. Given that the latent heat of fusion is 3 ×105 J Kg-2 and the total rate of heat removal by the mould is 4.2 × 106 W, the mass fraction of solid at the mould exit is _____. Assume both the solid and liquid remain at the melting point while they are in the mould.

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Correct answer is in the range of 0.39-0.41 Let us assume fraction of solid as x. Given, liquid metal exiting rate= 35 kg s-1 latent heat of fusion = 3 ×105 J Kg-2 total rate of heat removal by the mould = 4.2 × 10 6 W Total heat in the liquid metal= 35 kg s-1× 3 ×105 J Kg-2 = 105×105 Js-1, which isRead more

Correct answer is in the range of 0.39-0.41

Let us assume fraction of solid as x.

Given, liquid metal exiting rate= 35 kg s

^{-1}latent heat of fusion = 3 ×105 J Kg

^{-2}total rate of heat removal by the mould = 4.2 × 10

^{6 }WTotal heat in the liquid metal= 35 kg s

^{-1}× 3 ×105 J Kg^{-2 }= 105×10^{5 }Js^{-1}, which is also equal to heat to be removed to completely solidify the liquid metal.Fraction of solid formed(x) = (Total rate of heat removal by the mould)/(Total heat in the liquid metal) = (4.2 × 10

^{6 })/( 105×10^{5 })= 0.4