GATE 2024 ME – Question 61

Casting, Forming and Joining Processes · Casting: patterns, moulds, cores, solidification, riser and gating design, defects · 2 marks · Numerical answer

Aluminium is casted in a cube-shaped mold having dimensions as 20 mm × 20 mm × 20 mm. Another mold of the same mold material is used to cast a sphere of aluminium having a diameter of 20 mm. The pouring temperature for both cases is the same. The ratio of the solidification times of the cube-shaped mold to the spherical mold is ________ (*answer in integer*).

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Correct answer: 1

Explanation

By Chvorinov's rule the solidification time is $t = B\left(\frac{V}{A}\right)^2$. For the cube, $\frac{V}{A} = \frac{a^3}{6a^2} = \frac{a}{6} = 3.33$ mm. For the sphere, $\frac{V}{A} = \frac{\pi d^3/6}{\pi d^2} = \frac{d}{6} = 3.33$ mm. The two are equal, so the ratio of the solidification times is 1.