Thermodynamics HW Solutions 513

Thermodynamics HW Solutions 513 - 1 Steady operating...

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Chapter 6 Fundamentals of Convection 6-8 Heat transfer coefficients at different air velocities are given during air cooling of potatoes. The initial rate of heat transfer from a potato and the temperature gradient at the potato surface are to be determined. Assumptions 1 Steady operating conditions exist. 2 Potato is spherical in shape. 3 Convection heat transfer coefficient is constant over the entire surface. Properties The thermal conductivity of the potato is given to be k = 0.49 W/m. ° C. Analysis The initial rate of heat transfer from a potato is 2 2 2 m 03142 . 0 m) 10 . 0 ( = = = ππ D A s W 9.0 = ° ° = = C 5) )(20 m C)(0.03142 . W/m 1 . 19 ( ) ( 2 2 T T hA Q s s where the heat transfer coefficient is obtained from the table at 1 m/s velocity. The initial value of the temperature gradient at the potato surface is C/m 585 ° = ° ° ° = = = = = = = C) W/m. 49 . 0 ( C 5) C)(20 . W/m 1 . 19 ( ) ( ) ( 2 cond conv k T T h r T T T h r T k q q s R r s R r Air V = 1 m/s T = 5 ° C Potato T i = 20 ° C 6-9 The rate of heat loss from an average man walking in still air is to be determined at different walking velocities. Assumptions
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Unformatted text preview: 1 Steady operating conditions exist. 2 Convection heat transfer coefficient is constant over the entire surface. Analysis The convection heat transfer coefficients and the rate of heat losses at different walking velocities are ( a ) C . W/m 956 . 5 m/s) 5 . ( 6 . 8 6 . 8 2 0.53 53 . ° = = = V h Air V ∞ T ∞ = 10 ° C T s = 30 ° C W 214.4 = ° − ° = − = ∞ C ) 10 )(30 m C)(1.8 . W/m 956 . 5 ( ) ( 2 2 T T hA Q s s & ( b ) C . W/m 60 . 8 m/s) . 1 ( 6 . 8 6 . 8 2 0.53 53 . ° = = = V h W 309.6 = ° − ° = − = ∞ C ) 10 )(30 m C)(1.8 . W/m 60 . 8 ( ) ( 2 2 T T hA Q s s & ( c ) C . W/m 66 . 10 m/s) 5 . 1 ( 6 . 8 6 . 8 2 0.53 53 . ° = = = V h W 383.8 = ° − ° = − = ∞ C ) 10 )(30 m C)(1.8 . W/m 66 . 10 ( ) ( 2 2 T T hA Q s s & ( d ) C . W/m 42 . 12 m/s) . 2 ( 6 . 8 6 . 8 2 0.53 53 . ° = = = V h W 447.0 = ° − ° = − = ∞ C ) 10 )(30 m C)(1.8 . W/m 42 . 12 ( ) ( 2 2 T T hA Q s s & 6-2...
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This note was uploaded on 01/22/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.

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