Thermodynamics HW Solutions 772

Thermodynamics HW Solutions 772 - Chapter 9 Natural...

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Chapter 9 Natural Convection ( T i + T o )/2 = (45+33.34)/2 = 39.17 ° C are (Table A-15) 1 - 2 5 K 003203 . 0 K ) 273 17 . 39 ( 1 1 7257 . 0 Pr /s m 10 694 . 1 C W/m. 02656 . 0 = + = = = × = ° = f T k β υ The characteristic length in this case is the distance between the two cylinders, cm 5 . 1 cm 2 / ) 4 7 ( 2 / ) ( = = = i o c D D L Then, 3125 ) 7257 . 0 ( ) /s m 10 694 . 1 ( ) m 015 . 0 )( K 34 . 33 45 )( K 003203 . 0 )( m/s 81 . 9 ( Pr ) ( 2 2 5 3 -1 2 2 3 2 1 = × = = c L T T g Ra The effective thermal conductivity is [] 1254 . 0 m) 07 . 0 ( m) 04 . 0 ( m) 015 . 0 ( m 04 . 0 m 07 . 0 ln ) ( ln 5 7/5 - 7/5 - 3 4 5 5 / 3 5 / 3 3 4 cyl = + = + = o i c i o D D L D D F C W/m. 03751 . 0 ) 3125 )( 1254 . 0 ( 7257 . 0 861 . 0 7257 . 0 ) C W/m. 02656 . 0 ( 386 . 0 ) Ra ( Pr 861 . 0 Pr 386 . 0 4 / 1 4 / 1 4 / 1 cyl 4 / 1 eff ° = + ° = + = F k k The heat transfer expression is C ) 34 . 33 ( m 04 . 0 m 07 . 0 ln ) C W/m. 03751 . 0 ( 2 ) ( ln 2 2 1 eff ° ° π = π = tube i o T T T D D k Q & The radiation heat loss is [ ] 4 4 4 2 8 2 4 4 ) K 273 34 . 33 ( ) K 273 ( ) .K W/m 10 67 . 5 )( m 1684 . 0 )( 1 ( ) ( + + × = = tııbe surr s s rad
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