Answered

Consider a long, slender copper rod of diameter D = 1 cm and thermal conductivity k = 380 W/(m • °C), with one end thermally attached to a wall at 200°C. Heat is dissipated from the rod by convection with a heat transfer coefficient h^ = 15 W/(m2 • °C). Determine the heat transfer rate from the rod into the surrounding air at 7^ = 30°C.

Answer :

Answer:

Heat transfer rate = 20.08 W

Explanation:

Given that

D= 1 cm

K= 380 W/m.°C

Wall temperature = 200°C

Surrounding temperature = 30°C

[tex]h=15\ W/m^2C[/tex]

Rod is long so this is the case of long fin .

Heat transfer in long fin given as

[tex]Q=\sqrt{hPKA}\ \Delta T[/tex]

Here

P= π D

P = 3.14 x 0.01 m

P= 0.0314 m

[tex]A=\dfrac{\pi}{4}\times 0.01^2\ m^2[/tex]

[tex]A=7.8\times 10^{-5}\ m^2[/tex]

[tex]Q=\sqrt{hPKA}\ \Delta T[/tex]

[tex]Q=\sqrt{15\times 0.0314\times 380\times 7.8\times 10^{-5}}\ (200-30)[/tex]

Q=20.08 W

So heat transfer rate = 20.08 W

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