Thermodynamics HW Solutions 971

# Thermodynamics HW Solutions 971 - determined from Air T f T...

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Chapter 12 Radiation Heat Transfer Review Problems 12-88 The temperature of air in a duct is measured by a thermocouple. The radiation effect on the temperature measurement is to be quantified, and the actual air temperature is to be determined. Assumptions The surfaces are opaque, diffuse, and gray. Properties The emissivity of thermocouple is given to be ε =0.6. Analysis The actual temperature of the air can be determined from K 1111 = ° × + = σ ε + = C W/m 60 ] ) K 500 ( ) K 850 )[( K W/m 10 67 . 5 )( 6 . 0 ( K 850 ) ( 2 4 4 4 2 8 4 4 h T T T T w th th th f Air, T f T w = 500 K Thermocouple T th = 850 K ε = 0.6 12-89 The temperature of hot gases in a duct is measured by a thermocouple. The actual temperature of the gas is to be determined, and compared with that without a radiation shield. Assumptions The surfaces are opaque, diffuse, and gray. Properties The emissivity of the thermocouple is given to be ε =0.7. Analysis Assuming the area of the shield to be very close to the sensor of the thermometer, the radiation heat transfer from the sensor is
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Unformatted text preview: determined from Air, T f T w = 380 K Thermocouple T th = 530 K ε 1 = 0.7 ε 2 = 0.15 2 4 4 4 2 8 2 1 4 2 4 1 sensor from rad, W/m 9 . 257 1 15 . 1 2 1 7 . 1 ] ) K 380 ( ) K 530 )[( K W/m 10 67 . 5 ( 1 1 2 1 1 ) ( = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − ⋅ × = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ε + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ε − σ = − T T Q & Then the actual temperature of the gas can be determined from a heat transfer balance to be K 532 = ⎯→ ⎯ = − ° ⋅ = − = f f th f T T T T h q q 2 2 2 sensor from conv, sensor to conv, W/m 9 . 257 ) 530 C( W/m 120 W/m 9 . 257 ) ( & & Without the shield the temperature of the gas would be K 549.2 = ° ⋅ − ⋅ × + = − σ ε + = − C W/m 120 ] ) K 380 ( ) K 530 )[( K W/m 10 67 . 5 )( 7 . ( K 530 ) ( 2 4 4 4 2 8 4 4 h T T T T w th th th f 12-68...
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