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antoniya [11.8K]
3 years ago
11

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?
Physics
1 answer:
Lisa [10]3 years ago
6 0

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

Lc = \frac{V}{A_s}

Lc = \frac{\frac{\pi D^2}{4} L}{\pi DL}

Lc = \frac{D}{4}

Lc = \frac{0.02}{6} = 0.005 m

Biot number is given as Bi = \frac{hLc}{k}

Bi = \frac{200*0.005}{401}

Bi = 0.0025

As Bi is greater than 0.1 therefore lumped system analysis is applicable

so we have

\frac{T(t) - T_∞}{Ti - T_∞} = e^{-bt} ............1

where b is given as

b = \frac{ hA}{\rho Cp V}

b = \frac{ h}{\rho Cp Lc}

b = \frac{200}{8933*385*0.005}

b = 0.01163 s^{-1}

putting value in equation 1

\frac{25-20}{100-20} = e^{-0.01163t}

solving for t we get

t = 4.0 min

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