12.76 A laser-materials-processing apparatus encloses a sample 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, ɛ(1), is prescribed. To reduce oxidation, an inert gas stream of temperature T = 500 K and convection coefficient h = 50 W/m² · K flows over the sample upper and lower surfaces. The apparatus enclosure is large,with iso thermal walls at Tene = 300 K. To maintain the sample at a suitable operating temperature of T, = 2000K, a collimated laser beam with an operating wavelength of = 0.5 um irradiates its upper surface. (a) Determine the total emissivity e of the sample. (b) Determine the total absorptivity a of the sample for irradiation from the enclosure walls. (c) Perform an energy balance on the sample and determine the laser irradiation, Gjaser, required to maintain the sample at T = 2000 K.