A spherical thermocouple bead is situated at the centerline of a cylindrical duct diameter D units in diameter by L unit

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A spherical thermocouple bead is situated at the centerline of acylindrical duct diameter D units in diameter by L units inlength halfway between the ends to measure the temperature ofthe gas flowing through it. Since the surface area of thespherical thermocouple bead is very small in comparison with thesurface area of the duct, the relationship below predicts theconfiguration factor Fb-d between the thermocouple beadand the surface of the duct.
Fb-d =
A thermocouple with a 3mm diameter bead located in a 0.92 m longduct indicates that the gas temperature is 179 C when the ducttemperature is 65 C. Heat is transferred from the gas to thethermocouple bead by convection at the rate of 790 W/m2.Determine the error in the thermocouple reading if the emissivityof the thermocouple bead Eb=0.7 and the emissivity ofthe duct Ed=0.9.