Question

Question 3

A sheathed thermocouple is placed in a combustion chamber to measure the temperature of the gases at a certain point in the process. The thermocouple reading is 1110K and the inside wall temperature was measured at 1008K. The thermocouple has a surface area of 10 mm2 .

(a) A pitot probe is used to measure the velocity of the gas stream in the vicinity of the thermocouple tip. It measures a difference in static and dynamic pressure of 10 Pa. The convection heat coefficient (W/m2K) between the hot gases and the thermocouple is given by a correlation:

h = K.u^0.466

where: u is the velocity in m/s

K = empirical constant at high temperature = 50

What is the true gas temperature?

(b) A thermocouple is instead embedded inside the wall of a small conductive tube of inside diameter 20 mm, outside diameter 25 mm and length of 30 mm. The tube and embedded thermocouple are at a uniform temperature of 1110K. Suction is applied to the tube so that hot gas is drawn through the tube at 200 m/s. The heat transfer coefficient between gas and tube can be calculated by the correlation in part (a).

Assume the inside wall temperature of the combustion chamber is still 1008K. What is the true gas temperature? What is the temperature reduction of the gas in passing through the 30mm length of the tube?

Notes:

The Stefan Boltzmann constant is 5.669x10-8 W/m2 .K4 Assume gas density = 0.28 kg/m3 over the entire range of temperatures in this question. Assume gas Cp =1.19 kJ/kg.K over the entire range of temperatures in this question. The emissivity of the thermocouple and radiation shield and combustion chamber walls are all 0.75.

Answer 1