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 D_i = 5 mm and D_o = 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 ∙ μ = 251 X 10^-7 N ∙ s/m², k = 0.0373 W/m ∙ K, and Pr = 0.686.

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-T2 Steel thermocouple well Air V. T D. D;