A thermocouple junction of 1.0-mm in diameter is inserted in alarge chamber to measure the temperature of hot gas flowing throughthe chamber. The hot gas has a velocity of 2 m/s and temperature(Tg) at 800 K. The chamber surface (Ts) is maintained at 500 K.

(a) If the thermocouple is at room temperature, Ti when it isinserted in the chamber, calculate the time required for thetemperature difference, (Tg–T) to reach 2% of the initialtemperature difference Tg-Ti . Neglect radiation and conductionthrough the leads. Properties of the thermocouple junction areapproximated as k = 100W/mK, c = 385 J/kgK and  = 8920 kg/m3 ,while those of the hot gases may be assumed to have the propertiesof air at atmospheric pressure.

(b) If the thermocouple junction has an emissivity of 0.5, whatis the steady state temperature of the thermocouple junction?

(c) The emissivity of the thermocouple junction can becontrolled through application of a thin coating. How would changesin the emissivity affect the temperature measurement error? Computethe steady state junction temperature for emissivities in the range0.1 ï‚£ É› ï‚£ 1. Results are to be presented in graphical and / ortabular forms and should be accompanied by substantial discussionsupported by heat transfer fundamentals.

(d) Suggest ways to eliminate the temperature measurementerror