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 ofDi = 5 mm
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 Too. Assume that, for steel, k = 35 W/m · K, and, for air, p = 0.774 kg/m3, µ, = 251 X 10-7 N · s/m2, k = 0.0373 W/m · K, and Pr = 0.686.