A laser-materials-processing apparatus encloses a sam-ple

Chapter 12, Problem 12.99

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A laser-materials-processing apparatus encloses a sam-ple in the form of a disk of diameter D?25 mm andthickness w?1 mm. The sample has a diffuse surfacefor which the spectral distribution of the emissivity,??(?), is prescribed. To reduce oxidation, an inert gasstream of temperature T??500 K and convectioncoefficient h?50 W/m2?K flows over the sampleupper and lower surfaces. The apparatus enclosure islarge, with isothermal walls at Tenc?300 K. To main-tain the sample at a suitable operating temperature ofTs?2000 K, a collimated laser beam with an operatingwavelength of ??0.5?m irradiates its upper surface.(a) Determine the total emissivity ?of the sample.(b) Determine the total absorptivity ? of the samplefor irradiation from the enclosure walls.(c) Perform an energy balance on the sample anddetermine the laser irradiation, Glaser, required tomaintain the sample at Ts?2000 K.(d) Consider a cool-downprocess, when the laser andthe inert gas flow are deactivated. Sketch the totalemissivity as a function of the sample temperature,Ts(t), during the process. Identify key features,including the emissivity for the final condition(tl?).(e) Estimate the time to cool a sample from its operat-ing condition at Ts(0)?2000 K to a safe-to-touchtemperature of Ts(t)?40C. Use the lumpedcapacitance method and include the effect of con-vection to the inert gas with h?50 W/m2?K andT??Tenc?300 K. The thermophysical propertiesof the sample material are ??3900 kg/m3,cp?760 J/kg?K, and k?45 W/m?K.