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Unformatted text preview: ε , ρ ” ,T 1 ε , ρ ” ,T 2 Absorbing, Emitting, Isotropically Scattering Extinction Coefficient K e ε , ρ ” ,T 1 ε , ρ ” ,T 2 2.58J MIDTERM EXAM No.2 Due May 18, 2006, 11:00 am Instruction: This is a take home exam. You should complete the problems independently. The only person you may consult is the TA. The last question is a bonus. Question 1 . Consider radiative heat transfer between two parallel plates (infinite wide and deep) maintained at two temperatures T 1 and T 2 , as shown in the following figure. The medium in between the plates is gray, isotropically scattering, absorbing, and emitting with an extinction coefficient K e . The emission of both plates is diffuse-gray with an emissivity ε . The reflection of both surfaces is gray but specular with a bidirectional reflectivity ρ ” that is independent of angle. The medium is in radiative equilibrium, i.e., neglect molecular heat conduction. (a) Derive a relation between ρ ” and ε . (b) Derive an integral equation that determines the temperature distribution in the medium. You do not need to solve this equation, but the integral equation should be expressed in terms of the local blackbody emissivity power (and hence the local medium temperature)...
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This note was uploaded on 11/27/2011 for the course CHEMICAL E 20.410j taught by Professor Rogerd.kamm during the Spring '03 term at MIT.
- Spring '03