A thermocouple junction, which may be approximated as a sphere, is to be used for temperature measurement in a gas stream. The convection coefficient between the junction surface and the gas is known to be h = 400 W/m2 ?K, and the junction thermophysical properties are k = 20 W/m?K, Cp = 400 J/kg?K, and ? = 8500 kg/m3 . Determine the junction diameter needed for the thermocouple to have a time constant of 1 s. If the junction is at 25 oC and is placed in a gas stream that is at 200 oC, how long will it take for the junction to reach 199 oC?

t=5.2seconds

Explanation:

First, we state our assumptions:

Given

and gas stream

We use the time constant to find the diameter of the junction:

Now, check the validity of the lumped system analysis. With

   #Lumped Analysis is OK

Bi<<0.1, therefore the lumped approximation is excellent. The time required for the junction to reach :

It takes 5.2seconds for the junction to reach 199 oC

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