Radiation errors in temperature measurements 

The temperature of an air stream in a duct is being measured by means of a thermocouple. The thermocouple wires and junction are cylindrical, 0.05 in. in diameter, and extend across the duct perpendicular to the flow with the junction in the center of the duct. Assuming a junction emissivity e = 0.8, estimate the temperature of the gas stream from the following data obtained under steady conditions: 

Thermocouple junction temperature                                        = 5000F 

Duct wall temperature                                                                 = 3000F 

Convection heat transfer coefficient from wire to air             = 50 Btu/hr ∙ ft² ∙ F 

The wall temperature is constant at the value given for 20 duct diameters upstream and downstream of the thermocouple installation. The thermocouple leads are positioned so that the effect of heat conduction along them on the junction temperature may be neglected.