A thermocouple is inserted into a hot air duct to measure

Chapter , Problem 7.69

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A thermocouple is inserted into a hot air duct to measure the air temperature. The thermocouple (T1) is soldered to the tip of a steel thermocouple well of length L 0.15 m and inner and outer diameters of Di 5 mm and Do 10 mm. A second thermocouple (T2) is used to measure the duct wall temperature. Consider conditions for which the air velocity in the duct is V 3 m/s and the two thermocouples register temperatures of T1 450 K and T2 375 K. Neglecting radiation, determine the air temperature T. Assume that, for steel, k 35 W/m K, and, for air, 0.774 kg/m3 , 251 107 N s/m2 , k 0.0373 W/m K, and Pr 0.686.

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