Thermodynamics HW Solutions 736

Thermodynamics HW Solutions 736 - . 5 ( ) 7 . ( + C ) 30 (...

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Chapter 9 Natural Convection Insulation will lower the outer surface temperature, the Rayleigh and Nusselt numbers, and thus the convection heat transfer coefficient. For the evaluation of the heat transfer coefficient, we assume the surface temperature in this case to be 50 ° C. The properties of air at the film temperature of ( T s + T )/2 = (50+30)/2 = 40 ° C are (Table A-15) 1 - 2 5 K 003195 . 0 K ) 273 40 ( 1 1 7255 . 0 Pr /s m 10 702 . 1 C W/m. 02662 . 0 = + = = = × = ° = f T k β υ Then, 10 2 2 5 3 -1 2 2 3 10 256 . 1 ) 7255 . 0 ( ) /s m 10 702 . 1 ( ) m 2 )( K 30 50 )( K 003195 . 0 )( m/s 81 . 9 ( Pr ) ( × = × = = L T T g Ra s 0 . 272 7255 . 0 492 . 0 1 ) 10 256 . 1 ( 387 . 0 825 . 0 Pr 492 . 0 1 Ra 387 . 0 825 . 0 2 27 / 8 16 / 9 6 / 1 10 2 27 / 8 16 / 9 6 / 1 = + × + = + + = Nu C . W/m 620 . 3 ) 0 . 272 ( m 2 C W/m. 02662 . 0 2 ° = ° = = Nu L k h m ) 2 m)(2 2 ( 4 insul s t A + × = The total rate of heat loss from the outer surface of the insulated furnace by convection and radiation becomes ] ) K 273 30 ( ) K 273 )[( .K W/m 10 67
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Unformatted text preview: . 5 ( ) 7 . ( + C ) 30 ( C) . W/m 620 . 3 ( W 1512 ) ( ) ( 4 4 4 2 8 2 4 4 + + = + = + = s s surr s s s s rad conv T A T A T T A T T hA Q Q Q & & & I n steady operation, the heat lost by the side surfaces of the pipe must be equal to the heat lost from the exposed surface of the insulation by convection and radiation, which must be equal to the heat conducted through the insulation. Therefore, insul s s ins s s insulation t T A t T T kA Q Q C ) (110 C) W/m. 038 . ( W 1512 ) ( furnace = = = & & Solving the two equations above by trial-and error (or better yet, an equation solver) gives T s = 48.4 C and t insul = 0.0254 m = 2.54 cm 9-37...
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This note was uploaded on 01/24/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.

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