Thermodynamics HW Solutions 157

Thermodynamics HW Solutions 157 - 3 Thermal conductivity is...

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Chapter 2 Heat Conduction Equation r r r r r T ln 34 . 98 68 . 473 2 . 257 2 . 257 ln 34 . 98 ) 20 ( 4 894 , 37 ) ( 2 2 + = + + = The temperature at the center surface of the pipe is determined by setting radius r to be 17.5 cm, which is the average of the inner radius and outer radius. C 71.2 ° = + = ) 175 . 0 ln( 34 . 98 ) 175 . 0 ( 68 . 473 2 . 257 ) ( 2 r T 2-137 A spherical ball in which heat is generated uniformly is exposed to iced-water. The temperatures at the center and at the surface of the ball are to be determined. Assumptions 1 Heat transfer is steady since there is no indication of any change with time. 2 Heat transfer is one-dimensional., and there is thermal symmetry about the center point.
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Unformatted text preview: 3 Thermal conductivity is constant. 4 Heat generation is uniform. h T ∞ g D Properties The thermal conductivity is given to be k = 45 W/m ⋅ °C. Analysis The temperatures at the center and at the surface of the ball are determined directly from C 108.3 ° = ° × + ° = + = ∞ C) . W/m 1200 ( 3 m) 15 . )( W/m 10 6 . 2 ( C 3 2 3 6 h r g T T s & C 325 ° = ° × + ° = + = C) W/m. 45 ( 6 m) 15 . )( W/m 10 6 . 2 ( C 3 . 108 6 2 3 6 2 k r g T T s & 2-138 . ... 2-141 Design and Essay Problems 2-80...
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