Air is flowing in a tube of diameter D = 100 mm with a Reynolds number based on tube diameter of Re = 1.5×10 5 . In order to measure the temperature of the air a thermometer well is installed in the...

Air is flowing in a tube of diameter D = 100 mm with a Reynolds number based on tube diameter of Re = 1.5×10⁵
. In order to measure the temperature of the air a thermometer well is installed in the pipe, normal to its axis. The thermometer well material has a thermal conductivity of 45 W/m◦ C, has an ID of 3 mm and an OD of 4.5 mm and has a depth of immersion of 50 mm. Determine the true air temperature if a thermocouple attached to the well bottom indicates a temperature of 77◦ C while a thermocouple attached to the pipe wall indicates a temperature of 56◦ C. Assume that the thermal conductivity of air is 0.03W/m◦ C and the Prandtl number of air is 0.7.