Question

A vertical brick duct (tube) is filled with cast iron. The lower end of the duct is maintained at a temperature T₁ which is greater than the melting point Tm of cast iron and the upper end at a temperature T₂ which is less than the temperature of the melting point of cast iron. It is given that the conductivity of liquid cast iron is equal to k times the conductivity solid cast iron. Determine the fraction of the duct filled with molten metal.

Answer 1

 k_S → Conductivity of solid cast iron. At the point of junction of solid cast iron and liquid cast iron, temperature would be equal to melting point of iron.