Question Solved1 Answer A spherical thermocouple bead is situated at the centerline of a cylindrical duct diameter D units in diameter by L units in length halfway between the ends to measure the temperature of the gas flowing through it. Since the surface area of the spherical thermocouple bead is very small in comparison with the surface area of the duct, the relationship below predicts the configuration factor Fb-d between the thermocouple bead and the surface of the duct. Fb-d = A thermocouple with a 3mm diameter bead located in a 0.92 m long duct indicates that the gas temperature is 179 C when the duct temperature is 65 C. Heat is transferred from the gas to the thermocouple bead by convection at the rate of 790 W/m2. Determine the error in the thermocouple reading if the emissivity of the thermocouple bead Eb=0.7 and the emissivity of the duct Ed=0.9.

MLALRX The Asker · Mechanical Engineering

A spherical thermocouple bead is situated at the centerline of a cylindrical duct diameter D units in diameter by L units in length halfway between the ends to measure the temperature of the gas flowing through it. Since the surface area of the spherical thermocouple bead is very small in comparison with the surface area of the duct, the relationship below predicts the configuration factor Fb-d between the thermocouple bead and the surface of the duct.

Fb-d =

A thermocouple with a 3mm diameter bead located in a 0.92 m long duct indicates that the gas temperature is 179 C when the duct temperature is 65 C. Heat is transferred from the gas to the thermocouple bead by convection at the rate of 790 W/m2. Determine the error in the thermocouple reading if the emissivity of the thermocouple bead Eb=0.7 and the emissivity of the duct Ed=0.9.

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Heat transfer between duct & thermocouple is given by{:[q_(12)=(sigmaA_(1)(T_(1)^(4)-T_(2)^(4)))/((1-epsi_(1))/(A_(1)epsi_(1))+(1)/(A_(1)F_(12))+(1-epsi_(2))/(A_(2)epsi_(2)))],[A_(2)=2pirL=piDL],[" given, "A_(1)=4pir^(2)","quadA_(2)=2pi rL=pi xx0.003 xx0.92],[=4pi xx((0.003)/(2))^(2)=2.8274 xx10^(-5)m^(2)],[T_(1)=179^(@)C=452K],[T_(2)=65^(@)C=338K],[F_(12)=(L)/(sqrt(D^(2)+L^(2)))],[epsi_(1)=0.7","epsi_(2)=0.9quad=(0.92)/(sqrt(0.003^(2)+0.92^(2)))],[q_(12)=(sigmaA_(1)(T_(1)^(4)-T_(2)^(4)))/((1)/(epsi_(1) ... See the full answer