Heat Transfer Problem -
A thermocouple is to be utilized to measure the temperature of exhaust gases from an automobile engine and the effect of the cylindrical radiation shield installed as shown in the image, is to be investigated. The inner and outer shield diameters are 8mm and 12mm respectively. The emittance of the thermocouple bead and the shields can be taken to be 0.4. If the exhaust gases are at 1200K and the exhaust pipe walls are at 600K determine the temperature registered by the thermocouple for (a) no shield, (ii) one (inner) shield and (iii) two (inner and outer) shields.
Assumptions:
- pipe walls are black
- neglect the effect of the thermocouple leads
- neglect radiation loss through the ends of the shields
- neglect entrance flow effects in the shields
- assume laminar flow in the shields
- heat transfer coefficient on the thermocouple is 300 W/m2K
- thermal conductivity of exhaust gases 0.2 W/mK.