If V is volume of metal in casting and A is its surface area, then time of solidification of metal will be proportional to

Explanation:

Solidification time:

It is the time required for a casting to solidify after pouring. This time is dependent on the size and shape of the casting.

There is an empirical relationship known as Chvorinov’s rule –

\({{\rm{t}}_{\rm{s}}} = {\rm{K }}{\left( {\frac{{\rm{V}}}{{{{\rm{A}}_{\rm{s}}}}}} \right)^2}\)

where ts = solidification time of casting (min), V = volume of casting (mm3), As = surface area of casting (mm2) and K = solidification factor (min/mm2).

i.e it indicates that casting with a higher volume-to-surface area ratio will cool and solidify more slowly than one with a lower ratio.

The value of solidification time ts depends on the thermal properties of casting materials. Some relation is mentioned below:

\(t_s\propto\frac{1}{k}\)

\(t_s\propto\frac{1}{α}\)

\(t_s\propto{C}\)

where k = thermal conductivity, α = thermal diffusivity and C = specific heat of casting material.