hw09soln-typed

hw09soln-typed - 1. A long V groove 10 mm deep is machined...

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Unformatted text preview: 1. A long V groove 10 mm deep is machined on a block that is maintained at 1000 K. 10 mm 20° The groove surfaces are diffuse-gray with an emissivity of 0.6. (a) Determine the radiant flux leaving the groove to its surroundings. (b) The effective emissivity ε e of a cavity is defined as the ratio of the radiant power leaving the cavity to that from a blackbody having the area of the cavity opening and a temperature of the inner surfaces of the cavity. Determine the effective emissivity of the cavity. Opening, ε 2 = 1, T 2 = 0 K Groove, T 1 = 1000 K ε 1 = 0.6 This is a very practical problem for enhancing emissivity. Cutting grooves into a surface to enhance the surface can be very useful. The opening must absorb all the energy that it receives. There’s nothing to keep the energy from passing through. It accepts all the energy so it’s black! ∴ ε 2 = 1 Assuming ∃ no energy traveling back into the cavity from outside, T 2 = 0 K. This is reasonable if (1) is hot ∵ then any energy coming in is negligible. 1 1 1 1 A-ε ε q 1 q 2 E b1 E b2 J 1 J 2 2 21 1 A F 2 2 2 1 A-ε ε Radiant energy leaving the groove to the surroundings is 2 2 2 21 2 1 1 1 2 b 1 b 2 1 A ε ε 1 F A 1 A ε ε 1 E E q q- + +-- =- = → 1 A A ε ε 1 E E A q 1 2 1 1 2 b 1 b 2 2 +-- =- Note that A ε ε 1 1 ε 2 2 2 2 =- ⇒ = Radiant flux leaving is 2 . 46 1 20 sin 6 ....
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This note was uploaded on 08/01/2008 for the course MAE 310 taught by Professor Kuznetsov during the Fall '08 term at N.C. State.

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hw09soln-typed - 1. A long V groove 10 mm deep is machined...

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