Consider sand casting of a cube of edge length a. A cylindrical riser is placed at the top of the casting. Assume solidification time, t_s ∝ V/A, where V is the volume and A is the total surface area dissipating heat. If the top of the riser is insulated, which of the following radius/radii of riser is/are acceptable?

Which of these processes involve(s) melting in metallic workpieces?

The part of a gating system which regulates the rate of pouring of molten metal is

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 temper-ature 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 $$2700$$ $$kg/{m^3},$$ respectively.)