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A thermocouple shielded by aluminum foil of emissivity $0.15$ is used to measure the temperature of hot gases flowing in a duct whose walls are maintained at $T_{w}=380 \mathrm{~K}$. The thermometer shows a temperature reading of $T_{\text {th }}=530 \mathrm{~K}$. Assuming the emissivity of the thermocouple junction to be $\varepsilon=0.7$ and the convection heat transfer coefficient to be $h=120 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}$, determine the actual temperature of the gas. What would the thermometer reading be if no radiation shield was used?

   A thermocouple shielded by aluminum foil of emissivity $0.15$ is used to measure the temperature of hot gases flowing in a duct whose walls are maintained at $T_{w}=380 \mathrm{~K}$. The thermometer shows a temperature reading of $T_{\text {th }}=530 \mathrm{~K}$. Assuming the emissivity of the thermocouple junction to be $\varepsilon=0.7$ and the convection heat transfer coefficient to be $h=120 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}$, determine the actual temperature of the gas. What would the thermometer reading be if no radiation shield was used?

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Heat and Mass Transfer: Fundamentals and Applications

Heat and Mass Transfer: Fundamentals and Applications

Yunus A. Cengel,… 5th Edition

Chapter 13, Problem 95

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Step 1

The heat transfer due to radiation can be calculated using the Stefan-Boltzmann law: $q_{rad} = \varepsilon \sigma (T_{gas}^4 - T_{th}^4)$ The heat transfer due to convection can be calculated using the convection heat transfer equation: $q_{conv} = h (T_{gas} Show more…

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