BC 3 u rf = u ra at r = a , (11-124) 



BC4 T rr| = T rra "-^ at r = a, (II-12S) 



BC5 T a = at r=a. (H-126) 



Equations 11-122 through 11-126 have been labeled BC 1 through BC 5 for later convenience. Substitution of 

 equations 11-105, 11-109, 11-110, M-96, 11-112, 11-113, 11-114, and II-85 through II-88 into equations 11-122 

 through 11-126 yields: 



BC 1 ' ("P^) [ Ak 2 wJo'( k 2wb) + B w k 2w h '(k 2w b) ] 



= (~p^~)( 1 "p^c> )[ B - k ^'( k ^ b ) + E,k 2f n '(k 2( b) ; ( | M2 7) 



BC2, Aj (k 2w b) + B w h (k 2w b) = B f j (k 2f b) + E f n (k 2( b) 



+ (l^")( 1 " ^cV) [ B <W(k 2( b) + E 1 ^n "(k 2| b)] ; (11-128) 



BC3, (-^)( 1 " ^ ) [ B W( k 2,a) + E,k 2) n '(k 2f a) ] 



= (~^7 )[ D a k 1a j '(k la a) + B a k 2a j '(k 2a a) ] ; (11-129) 



BC4, B ( j (k 2f a) + E f n (k 2f a) + (Ji. ) ( 1 - ^i) [ B,k 2f V(k 2f a) + E f k 2( 2n "(k 2f a) ] 



= D a j (k 1a a) + B a j (k 2a a) + ( &jpfc ) [ D a k la j '(k 1a a) + B a k 2 J '(k 2a a) ] ; ( | M30 ) 



and BC 5, ( Ya - '^f ) D ^ k ^ + (Y * " 1) Bajo(k ^ a) = ° 



(11-131) 



18 



