Thermodynamics HW Solutions 54

Thermodynamics HW Solutions 54 - Chapter 1 Basics of Heat...

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Chapter 1 Basics of Heat Transfer 1-105 A 1000-W iron is left on the iron board with its base exposed to the air at 20°C. The temperature of the base of the iron is to be determined in steady operation. Assumptions 1 Steady operating conditions exist. 2 The thermal properties of the iron base and the convection heat transfer coefficient are constant and uniform. 3 The temperature of the surrounding surfaces is the same as the temperature of the surrounding air. Properties The emissivity of the base surface is given to be ε = 0.6. Analysis At steady conditions, the 1000 W energy supplied to the iron will be dissipated to the surroundings by convection and radiation heat transfer. Therefore, &&& QQQ total conv rad 1000 W =+ = where W K) 293 ( 0.7 K) 293 ( ) m K)(0.02 W/m (35 2 2 conv = = Δ = s s s T T T hA Q & and W ] K) (293 [ 10 0.06804 ] K) (293 )[T K W/m 10 )(5.67 m 0.6(0.02 ) ( 4 4 8 4 4 s 4 2 8 2 4 4 rad × = × = = s o s s T T T A Q εσ & Iron 1000 W Substituting, ] K) (293 [ 10 06804 . 0 ) K 293 ( 7 . 0 W 1000 4 4 8 × + = s s T T Solving by trial and error gives C 674 K 947
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