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

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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 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 + - - = -
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Note that  0 A ε ε 1 1 ε 2 2 2 2 = - = Radiant flux leaving is  2 . 46 1 20 sin 6 . 0
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