GATE Papers >> Mechanical >> 2016 >> Question No 231

Question No. 231
Equal amounts of a liquid metal at the same temperature are poured into three moulds made of steel, copper and aluminum. The shape of the cavity is a cylinder with 15 mm diameter. The size of the moulds are such that the outside temperature of the moulds do not increase appreciably beyond the atmospheric temperature during solidification. The sequence of solidification in the mould from the fastest to slowest is

(Thermal conductivities of steel, copper and aluminum are 60.5, 401 and 237 W/m-K, respectively. Specific heats of steel, copper and aluminum are 434, 385 and 903 J/kg-K, respectively. Densities of steel, copper and aluminum are 7854, 8933 and 2700 kg/m3, respectively.)

Answer : (C) Copper - Aluminum - Steel

Solution of Question No 231 of GATE 2016 Mechanical Paper

Thermal diffusivity of any material represents heat storage ability compare to heat transfer.

$\mathrm\alpha=\frac{\mathrm k}{{\mathrm{ρc}}_\mathrm p}=\frac{\mathrm{Conductivity}}{\mathrm{Volumetric}\;\mathrm{heat}\;\mathrm{capacity}}$

Higher the value of thermal diffusivity less time heat is stored in the material

$\begin{array}{l}{\mathrm\alpha}_\mathrm{steel}=\frac{{\mathrm k}_\mathrm S}{{\mathrm\rho}_\mathrm S{\mathrm c}_{\mathrm P\;\mathrm S}}=\frac{60.5}{7854\times434}\\{\mathrm\alpha}_\mathrm{steel}=1.774\times10^{-5}\;\frac{\mathrm m^2}{\mathrm s}\\{\mathrm\alpha}_\mathrm{copper}=\frac{{\mathrm k}_\mathrm{Cu}}{{\mathrm\rho}_\mathrm{cu}{\mathrm C}_{\mathrm P\;\mathrm{cu}}}=\frac{701}{8933\times385}=1.165\times10^{-4}\;\frac{\mathrm m^2}{\mathrm s}\\{\mathrm\alpha}_\mathrm{Al}=\frac{{\mathrm k}_\mathrm{Al}}{{\mathrm\rho}_\mathrm{Al}{\mathrm C}_{\mathrm P\;\mathrm{Al}}}=\frac{237}{2700\times903}=9.72\times10^{-5}\;\frac{\displaystyle\mathrm m^2}{\displaystyle\mathrm s}\\{\mathrm\alpha}_\mathrm{cu}>{\mathrm\alpha}_\mathrm{Al}>{\mathrm\alpha}_\mathrm s\end{array}$

Hence,

Solidification sequence from fastest to slowest Copper $\rightarrow$ Aluminium $\rightarrow$ Steel

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