# Radiation shield | Mathematics homework help

Repeat Problem 9.40 with the addition of a radiation shield with emissivity e, = 0.1. From Problem 9.40: Calculate the equilibrium temperature of a thermocouple in a large air duct if the air temperature is 1367 K, the duct-wall temperature 533 K, the emittance of the couple 0.5, and the convective heat transfer coefficient, hc, is 114 W/(m2 K).
GIVEN
A thermocouple surrounded by a radiation shield in a large air duct
Air temperature (Ts) = 1367 K
Duct wall temperature (Td) = 533 K
The emissivity of the thermocouple (etc) = 0.5
The convective heat transfer coefficient (hc) = 114 W/(m2 K)
Shield emissivity (es) = 0.1
ASSUMPTIONS
Conduction along the thermocouple is negligible
The walls of the duct are black
The CO2 and H2O in the air are negligible
The heat transfer coefficient on the inside and outside of the shield is hc
The conductive thermal resistance of the shield is negligible
The view factor between the shield and the thermocouple ?^ 1
The surface area of the shield is large compared to that of the thermocouple
Shield and thermocouple are gray
The thermocouple and shield can be approximated by infinitely long concentric cylinders
Convective heat transfer between the shield and thermocouples isnegligible

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