(Solution) - A thermocouple is inserted into a hot air duct to measure the -(2025 Original AI-Free Solution)

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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 Tx. Assume that, for steel, k = 35 W/m ? K, and, for air,


p = 0.774 kg/m3 ? ? = 251 X 10-7 N ? s/m2, k = 0.0373 W/m ? K, and Pr = 0.686.