A vertical slab of Woods metal is joined to a substrate on one surface and is melted as it is uniformly irradiated by a laser source on the opposite surface. The metal is initially at its fusion temperature of Tf = 72°C and the melt runs off by gravity as soon as it is formed. The absorptivity of the metal to the laser radiation is al = 0.4, and its latent heat of fusion is hsf = 33 kJ/kg.

(a) Neglecting heat transfer from the irradiated surface by convection or radiation exchange with the surroundings determines the instantaneous rate of melting in kg/s∙m2 if the laser irradiation is 5kW/m2. How much material is removed if irradiation is maintained for a period of 2 s?

(b) Allowing for convection to ambient air, with T∞ = 20°C and h = 15 W/m2 ∙ K, and radiation exchange with large surroundings (ϵ = 0.4, Tsur = 20°C), determine the instantaneous rate of melting during irradiation.