A long copper rod of diameter 2.0 cm is initially at a uniform temperature of 100°C. It is now exposed to an air stream at 20°C
with a heat transfer coefficient of 200 W/m2·K. How long would it take for the copper road to cool to an average temperature of 25°C?
1 answer:
Answer:
t = 4.0 min
Explanation:
given data:
diameter of rod = 2 cm
T_1 = 100 degree celcius
Air stream temperature = 20 degree celcius
heat transfer coefficient = 200 W/m2. K
WE KNOW THAT
copper thermal conductivity = k = 401 W/m °C
copper specific heat Cp = 385 J/kg.°C
density of copper = 8933 kg/m3
charateristic length is given as Lc




Biot number is given as 

Bi = 0.0025
As Bi is greater than 0.1 therefore lumped system analysis is applicable
so we have
............1
where b is given as



b = 0.01163 s^{-1}
putting value in equation 1

solving for t we get
t = 4.0 min
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