Consider a 5-mm-square, diffuse surface Aohavinga total

Chapter 12, Problem 12.17

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Consider a 5-mm-square, diffuse surface Aohavinga total emissive power of Eo?4000 W/m2. Theradiation field due to emission into the hemispheri-cal space above the surface is diffuse, therebyproviding a uniform intensity I(,). Moreover,if the space is a nonparticipating medium (nonab- sorbing, nonscattering, and nonemitting), the inten-sity is independent of radius for any (, ) direction.Hence intensities at any points P1and P2wouldbe equal.(a) What is the rate at which radiant energy is emittedby Ao, qemit?(b) What is the intensity Io,eof the radiation field emit-ted from the surface Ao?(c) Beginning with Equation 12.13 and presumingknowledge of the intensity Io,e, obtain an expres-sion for qemit.(d) Consider the hemispherical surface located atr?R1?0.5 m. Using the conservation of energyrequirement, determine the rate at which radiantenergy is incident on this surface due to emissionfrom Ao.(e) Using Equation 12.10, determine the rate at whichradiant energy leaving Aois intercepted by thesmall area A2located in the direction (45, ) onthe hemispherical surface. What is the irradiationon A2?(f) Repeat part (e) for the location (0, ). Are theirradiations at the two locations equal?(g) Using Equation 12.18, determine the irradiationG1on the hemispherical surface at r? 1