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A spherical thermocouple junction 1.0 mm in diameter is insertedin a combustion chamber to measure the temperature ?T? of theproducts of combustion. The hot gases have a velocity of V= 5 m/s.(a) If the thermocouple is at room temperature, Ti,when it isinserted in the chamber, estimate the time required for thetemperature difference, ?T?-T, to reach 2% of the initialtemperature difference, ?T?-Ti. Neglect radiation and conductionthrough the leads. Properties of the thermocouple junction areapproximated as k= 100 W/m·K, c=385 J/kg·K, and ?=8920kg/m³, while those of the combustion gases may beapproximated as k=0.05 W/m·K, ?=50 x 10^-6m²/s, and Pr=0.69.

(b) If the thermocouple junction has an emissivity of 0.1 and thecooled walls of the combustor are at Tc=400 K, what is thesteady-state temperature of the thermocouple junction if thecombustion gases are at 1000 K? Conduction through the lead wiresmay be neglected.

Assuming that the gas properties are constant, what is the valueof the Nusselt number?

What is the average convection heat transfer coefficient for thegas flowing over the thermocouple, in W/m²Â·K?

What is the Biot number for this problem?

How long does it take for the temperature difference (?T?-T) toget within 2% of the initial temperature difference (?T?-Ti), ins?

What is the final steady state temperature of the thermocouple,in K, if the combustion gases are at 1000 K?