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.
1 answer:
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Answer:
β = = 0.7071 ≈ 1 ( damping condition )
closed-form expression for the response is attached below
Explanation:
Given : x + 2x + 2x = 0 for Xo = 0 mm and Vo = 1 mm/s
computing a solution :
M = 1,
c = 2,
k = 2,
Wn = =
next we determine the damping condition using the damping formula
β = = 0.7071 ≈ 1
from the condition above it can be said that the damping condition indicates underdamping
attached below is the closed form expression for the response
