A thermocouple, with a spherical junction diameter of 0.5 mm, is used for measuring the temperature of hot airflow in a circular
duct. The convection heat transfer coefficient of the airflow can be related with the diameter (D) of the sphere and the average airflow velocity (V) as h = 2.2(V /D)0.5, where D, h, and V are in m, W/m²•K, and m/s, respectively. The properties of the thermocouple junction are k = 35 W/m•K, rho = 8500 kg/m³, and cp = 320 J/kg•K.
If the maximum response time of the thermocouple to record 87 percent of the initially applied temperature difference is 5 s, determine the minimum airflow velocity that the thermocouple can be used.
If the maximum response time of the thermocouple to record 87 percent of the initially applied temperature difference is 5 s, determine the minimum airflow velocity that the thermocouple can be used.
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Answer:
Explanation:
Considering the one dimensional and steady state:
From Heat Conduction equation considering the above assumption:
Eq (1)
Where:
k is thermal Conductivity
is uniform thermal generation
Putt in Eq (1):
Energy balance is given by:
Eq (2)
Putting x=L
From Eq (2)