The temperature of a gas stream is measured by a thermocouple whose junction can be approximated as a 1-mm-diameter sphere. Take the junction’s properties as: k of 32 W/m K, density of 8.2 kg/m^3, c of 300 J/Kg K. On its surface, the overall heat transfer coefficient is 200 W/m^2 K. Neglect any conduction loss from the sphere to other parts of the thermocouple. Create a plot of measurement error as a function of time for the thermocouple, expressed as a fraction of the initial temperature difference.
The temperature of a gas stream is measured by a thermocouple whose junction can be approximated as a 1-mm-diameter sphere. Take the junction’s properties as: k of 32 W/m K, density of 8.2 kg/m^3, c of 300 J/Kg K. On its surface, the overall heat transfer coefficient is 200 W/m^2 K. Neglect any conduction loss from the sphere to other parts of the thermocouple. Create a plot of measurement error as a function of time for the thermocouple, expressed as a fraction of the initial temperature difference.
To create a plot of the measurement error as a function of time for the thermocouple, we need to first determine the rate of heat transfer from the gas stream to the thermocouple.
This can be calculated using the equation:
q = h A (Tgas - Tjunction)
where q is the rate of heat transfer (W), h is the overall heat transfer coefficient (W/m2 K), A is the surface area of the junction (m2), T_gas is the temperature of the gas stream (K), and Tjunction is the temperature of the junction (K).
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