A laser-materials-processing apparatus encloses a sam- ple in the form of a disk of diameter D = 25 mm and thickness w^-1 mm. The sample has a diffuse surface for which the spectral distribution of the emissivity, 6(A), is prescribed. To reduce oxidation, an inert gas stream of temperature T[infinity]= 500K and convection coefficient h=50W/m^2.K flows over the sample upper and lower surfaces. The apparatus enclosure is large, with isothermal walls at Tenc= 300 K. To maintain the sample at a suitable operating temperature of Ts=2000 K, a collimated laser beam with an operating wavelength of λ = 0.5 μm irradiates its upper surface. a. Determine the total emissivity ε of the sample.
b. Determine the total absorptivity α of the sample for irradiation from the enclosure walls.
c. Perform an energy balance on the sample and determine the laser irradiation, Giaser, requi maintain the sample at Ts= 2000 K.
d. Consider a cool-down process, when the laser and the inert gas flow are deactivated. Sketch the total emissivity as a function of the sample temperature, Ts(t), during the process. Identify key features, including the emissivity for the final condition