Along 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?

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

k2s for potassium sulphide