Solution

The temperature measured by the thermocouple is lower than that of gas because thermocouple radiates to the wall. Energy balance at steady state is

Radiant heat flow from the thermocouple to the wall = Convective heat flow form gas to thermocouple

                      
 
 surface area of thermocouple

  emissivity,  Stefan’s Boltzmann constant. 

 Temperature of thermocouple, and  Temperature of duct wall 
 temperature of fluid.

 

Substituting the values

 
                                                                                                     

 


One notes that there is an appreciable error and this must be taken into account. It should be recognized that in an oven or furnace gas temperature may not be equal to the temperature of the major source of radiation. This may lead to overheating of materials. Proper shielding of thermocouple would be necessary. 

References:
Y.V. Deshmukh: industrial heating. 2004.