hw08soln-typed

hw08soln-typed - 1. The "crossed-strings" method...

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1. The “crossed-strings” method of Hottel provides a simple means to calculate view factors between surfaces that are of infinite extent in one direction. For two such surfaces (a) with unobstructed views of one another, the view factor is of the form F 12 = 1 2 w 1 (a c + b d) - (a d + b c) Use this method to evaluate the view factors F 12 for sketches (b) and (c).   A 1 A 2 a b c d w 1   1 m 4 m A 1 A 2   1 m 4 m A 1 A 2 (a) (b) (c) (a) strings) Uncrossed strings Crossed ( 2 1 F A 12 1 - = 781 . 0 ) 1 2 17 2 ( ) 4 ( 2 1 F 12 = × - = (b) 110 . 0 ) 17 0 4 1 ( ) 4 ( 2 1 F 12 = - - + = 2. Determine the shape factor F 12 for the perpendicular rectangles shown.   0.2 m 0.4 m 0.3 m 0.5 m 1 2 Surface 3 is imaginary surface below surface 1, Z 2 =0.2 m is the height of this surface; Z 1 =0.4 m is the height of surface 1 Fig. 13.6, 4 . 0 50 20 X Z 2 = = , 6 . 0 50 30 X Y = = → F 23 = 0.19 21 23 ) 1 , 3 ( 2 F F F + = 8 . 0 50 40 X Z 1 = = , 6 . 0 50 30 X Y = = → F 2→(3,1) = 0.26 07 . 0 19 . 0 26 . 0 F F F 23 ) 1 , 3 ( 2 21 = - = - =
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105 . 0 F ) 50 )( 20 ( ) 50 )( 30 ( F A A F 21 21 1 2 12 = = = 3. Determine F 12 and F 21 for the following configurations using the reciprocity theorem and other basic shape factor relations. Do not use tables or charts. (a)   A 1 A 2 90° Long duct (b)   A 1 A 2 Small sphere of area A 1 under a concentric hemisphere of area A 2 =2A 1 (c)   A 2 A 1 Long duct. What is F 22 for this case? (d)   A 1 A 2 200 mm 100 mm B Long inclined plates (point B is directly above the center of A 1 ) (e)   A 1 A 2 Sphere lying on infinite plane (f)   A 2 A 3 hemisphere,  diameter D A disk,  diameter D/2 Hemisphere-disk arrangement (g)   A 2 A 1 2 m 1 m Long open channel (a) F 12 =1,
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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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hw08soln-typed - 1. The "crossed-strings" method...

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