A stainless-steel component is exposed to laser heating at an initial temperature of \(300 \mathrm{~K}\). After a short transient the surface reaches its melting point, and the surface recedes at a rate of \(230 \mu \mathrm{m} / \mathrm{s}\) thereafter. The molten melt is assumed to be drained away and the solid surface is always exposed to the laser. The melting temperature is \(1670 \mathrm{~K}\). Estimate the heat flux at the surface delivered by the laser. Find the initial time needed to reach the melting point. Also find the temperature profile in the solid. The density of stainless steel is 7000 \(\mathrm{kg} / \mathrm{m}^{3}, c_{p}=600 \mathrm{~W} / \mathrm{kg} / \mathrm{K}\) and \(\alpha=4 \times 10^{-6} \mathrm{~m}^{2} / \mathrm{s}\).