Question

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 1

Heat transfer rate = 20.08 W

Step-by-step explanation:

Given that

D= 1 cm

K= 380 W/m.°C

Wall temperature = 200°C

Surrounding temperature = 30°C

`h=15\ W/m^2C`

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

Heat transfer in long fin given as

`Q=√(hPKA)\ \Delta T`

Here

P= π D

P = 3.14 x 0.01 m

P= 0.0314 m

`A=(\pi)/(4)* 0.01^2\ m^2`

`A=7.8* 10^(-5)\ m^2`

`Q=√(hPKA)\ \Delta T`

`Q=\sqrt{15* 0.0314* 380* 7.8* 10^(-5)}\ (200-30)`

Q=20.08 W

So heat transfer rate = 20.08 W