Chapter 1, Problem 1.66P

A vertical slab of Wood’s metal is joined to a substrate onone surface and is incited as it is uniformly irradiated by alaser source on the opposite surface. The metal is initiallyat its fusion temperature of $T_f=72°\text{C}$ , and the melt runsoff by gravity as soon as it is formed. The absorptivity ofthe metal to the laser radiation is ${\alpha }_1=0.4$ , and its latentheat of fusion is $h_{sf}=33\text{kJ/kg}$ .
(a) Neglecting heat transfer from the irradiated surfaceby convection or radiation exchange with thesurroundings, determine the instantaneous rate ofmelting in $\text{Kg/s}\cdot {\text{m}}^{\text{2}}$ if the laser irradiation is $\text{5 kW}/{\text{m}}^{\text{2}}$ .How much material is removed if irradiation is maintained for a period of 2 s?
(b) Allowing for convection to ambient air, with $T_{\infty }=20°\text{C}$ and $h=15{\text{W/m}}^{\text{2}}\cdot \text{K}$ , and radiationexchange with large surroundings $\left(\in =0.4,T_{sur}=20°\text{C}\right)$ , determine the instantaneous rate of melting during irradiation.