A thermocouple (0.8-mm-OD wire) used to measure the temperature of quiescent gas in a furnace gives a reading of 165°C. It is known, however, that the rate of radiant heat flow per meter length from the hotter furnace walls to the thermocouple wire is 1.1 W/m and the convective heat transfer coefficient between the wire and the gas is 6.8 W/(m2K). With this information, estimate the true gas temperature. State your assumptions and indicate the equations used.

Question

GIVEN

• Thermocouple (0.8 mm OD wire) in a furnace

• Thermocouple reading (Tp) = 165°C

• Radiant heat transfer to the wire (qr/L) = 1.1 W/m

• Heat transfer coefficient ( ch ) = 6.8 W/(m2 K)

FIND

• Estimate the true gas temperature (TG)

ASSUMPTIONS

• The system is in equilibrium

• Conduction along the thermocouple is negligible

• Conduction between the thermocouple and the furnace wall is negligible

SKETCH

Answer 1

Equilibrium and the conservation of energy require that the heat gain of the probe by radiation if equal

to the heat lost by convection. The rate of heat transfer by convection is given



For steady state to exist the rate of heat transfer by convection must equal the rate of heat transfer by

radiation