A thermocouple, with a spherical junction diameter of 0.5 mm, is used for measuring the te...

A thermocouple, with a spherical junction diameter of 0.5 mm, is used for measuring the temperature of hot air flow in a circular duct. The convection heat transfer coefficient of the air flow can be related with the diameter (D) of the spherical junction and the average air flow velocity (V) as h = 2.2(V/D)^0.5, where D, h, and V are in m, W/m²·K and m/s, respectively. The properties of the thermocouple junction are k = 35 W/m·K, ρ = 8500 kg/m³, and c_p = 320 J/kg·K. Determine the minimum air flow velocity that the thermocouple can be used, if the maximum response time of the thermocouple to register 99 percent of the initial temperature difference is 5 s.